title,authors,year,citations,abstract,result_id,publication_info,pdf_links,url,total_results,search_time,cluster,arxiv_id,all_pdfs,ntitle,clusters,n_hits,journal_ref,pub_year
Mutual information functions of natural language texts,W Li,1989.0,39,"The mutual information function M(d), which is a quantity used to detect correlations in symbolic sequences, is applied to natural language texts. For some English and German texts being analyzed, M(d)’s for both the letter sequences and letter-type sequences exhibit approximate inverse power law function at shorter distance with exponents close to 3. This decay of M(d) is too fast to lead a 1/f power spectrum. Due to finite size effects, it is not conclusive as to whether the same inverse power law function extends beyond short distances. Also included are discussions on various topics concerning other scaling phenomena in formal and natural languages.",MIrmxTgMOv0J,W Li - 1989 - researchgate.net,['https://www.researchgate.net/profile/Wentian-Li/publication/253562758_Mutual_Information_Functions_of_Natural_Language_Texts/links/560029ee08ae07629e5286ac/Mutual-Information-Functions-of-Natural-Language-Texts.pdf'],https://www.researchgate.net/profile/Wentian-Li/publication/253562758_Mutual_Information_Functions_of_Natural_Language_Texts/links/560029ee08ae07629e5286ac/Mutual-Information-Functions-of-Natural-Language-Texts.pdf,unknown,unknown,互信息/标度,,['https://www.researchgate.net/profile/Wentian-Li/publication/253562758_Mutual_Information_Functions_of_Natural_Language_Texts/links/560029ee08ae07629e5286ac/Mutual-Information-Functions-of-Natural-Language-Texts.pdf'],mutual information functions of natural language texts,互信息/标度,1,,
"Entanglement, quantum phase transitions, and density matrix renormalization","TJ Osborne, MA Nielsen",2002.0,141,… show that the success of the density matrix renormalization group (DMRG) in … entanglement under renormalization. We provide a reinterpretation of the DMRG in terms of the language …,03PnntS3ffoJ,"TJ Osborne, MA Nielsen - Quantum Information Processing, 2002 - Springer",['https://arxiv.org/pdf/quant-ph/0109024'],https://link.springer.com/article/10.1023/A:1019601218492,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/quant-ph/0109024'],entanglement quantum phase transitions and density matrix renormalization,互信息/标度,1,Quantum Information Processing,
Entanglement entropy and quantum field theory,"P Calabrese, J Cardy",2004.0,4838,"… In the language of string theory, the objects we consider are correlators of orbifold points in … under conformal transformations, we conclude that the renormalized Zn(A)/Zn ∝ Tr ρn …",qlHQ11suiMEJ,"P Calabrese, J Cardy - Journal of statistical mechanics: theory …, 2004 - iopscience.iop.org",['https://arxiv.org/pdf/hep-th/0405152'],https://iopscience.iop.org/article/10.1088/1742-5468/2004/06/P06002/meta,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/hep-th/0405152'],entanglement entropy and quantum field theory,互信息/标度,1,,
Entanglement renormalization,G Vidal,2007.0,1667,"We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.",0OHtsWK8jpMJ,"G Vidal - Physical review letters, 2007 - APS",['https://arxiv.org/pdf/cond-mat/0512165'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.99.220405,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/cond-mat/0512165'],entanglement renormalization,互信息/标度,1,Physical Review Letters,
Area laws for the entanglement entropy-a review,"J Eisert, M Cramer, MB Plenio",2008.0,562,"Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: The entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ""area laws"" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium we review the current status of area laws in these fields. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation, and disordered systems, non-equilibrium situations, classical correlation concepts, and topological entanglement entropies are discussed. A significant proportion of the article is devoted to the quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. We discuss matrix-product states, higher-dimensional analogues, and states from entanglement renormalization and conclude by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations.",NAABP-wTNTMJ,"J Eisert, M Cramer, MB Plenio - arXiv preprint arXiv:0808.3773, 2008 - arxiv.org",['https://arxiv.org/pdf/0808.3773'],https://arxiv.org/abs/0808.3773,unknown,unknown,互信息/标度,0808.3773,['https://arxiv.org/pdf/0808.3773'],area laws for the entanglement entropy a review,互信息/标度,1,"Rev. Mod. Phys. 82, 277 (2010)",
Entanglement renormalization and topological order,"M Aguado, G Vidal",2008.0,242,… entanglement entropy [10] (the subleading term in a large-perimeter expansion of the entanglement entropy … The stabilizer formalism [14] also furnishes a useful language to analyze …,JmqaOt0GfOoJ,"M Aguado, G Vidal - Physical review letters, 2008 - APS",['https://arxiv.org/pdf/0712.0348'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.070404,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/0712.0348'],entanglement renormalization and topological order,互信息/标度,1,,
Visualization of tree-structured data through generative topographic mapping,"N Gianniotis, P Tino",2008.0,37,"… The class of local generative models used in this paper, the hidden Markov tree model (… VII, we present another local generative model, the Markov tree model, that is used to derive an …",-MxNcEfMBwIJ,"N Gianniotis, P Tino - IEEE Transactions on Neural Networks, 2008 - ieeexplore.ieee.org",['https://www.researchgate.net/profile/Peter-Tino/publication/3304190_Visualization_of_Tree-Structured_Data_Through_Generative_Topographic_Mapping/links/09e4150be38b1a9851000000/Visualization-of-Tree-Structured-Data-Through-Generative-Topographic-Mapping.pdf'],https://ieeexplore.ieee.org/abstract/document/4588975/,unknown,unknown,TTN/MERA/PEPS,,['https://www.researchgate.net/profile/Peter-Tino/publication/3304190_Visualization_of_Tree-Structured_Data_Through_Generative_Topographic_Mapping/links/09e4150be38b1a9851000000/Visualization-of-Tree-Structured-Data-Through-Generative-Topographic-Mapping.pdf'],visualization of tree structured data through generative topographic mapping,TTN/MERA/PEPS,1,,
Variational matrix-product-state approach to quantum impurity models,"A Weichselbaum, F Verstraete, U Schollwöck…",2009.0,186,"… ’s density-matrix renormalization group DMRG9 for treating quantum chain models is in its … to have the same formal basis of matrixproduct-states, resolving a long-standing question …",-CHuQbrRX7YJ,"A Weichselbaum, F Verstraete, U Schollwöck… - Physical Review B …, 2009 - APS",['https://arxiv.org/pdf/cond-mat/0504305'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165117,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/cond-mat/0504305'],variational matrix product state approach to quantum impurity models,MPS 语言模型,1,,
Concatenated tensor network states,"R Hübener, V Nebendahl, W Dür",2009.0,0,"We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes -- already for tensor dimension two -- all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional- and tree tensor networks.",,"R Hübener, V Nebendahl, W Dür - New J. Phys. 12, 025004 (2010)",[],https://arxiv.org/abs/0904.1925,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,0904.1925,['https://arxiv.org/pdf/0904.1925'],concatenated tensor network states,TTN/MERA/PEPS,1,"New J. Phys. 12, 025004 (2010)",
Colloquium: Area laws for the entanglement entropy,"J Eisert, M Cramer, MB Plenio",2010.0,3839,"Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ``area laws'' for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.",6PQHLtFQzWoJ,"J Eisert, M Cramer, MB Plenio - Reviews of modern physics, 2010 - APS",['https://webhome.phy.duke.edu/~kotwal/tensorNetworks/eisert_RevModPhys.82.277.pdf'],https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.277,unknown,unknown,互信息/标度,,['https://webhome.phy.duke.edu/~kotwal/tensorNetworks/eisert_RevModPhys.82.277.pdf'],colloquium area laws for the entanglement entropy,互信息/标度,1,Reviews of Modern Physics,
Entanglement renormalization in noninteracting fermionic systems,"G Evenbly, G Vidal",2010.0,67,"We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show the validity of the multiscale entanglement renormalization ansatz to describe certain ground states in two dimensions, including quantum critical states. They also unveil a connection between the performance of ER and the logarithmic violations of the boundary law for entanglement in systems with a one-dimensional Fermi surface. ER is recast in the language of creation/annihilation operators and correlation matrices.",qqFj3q_q5NMJ,"G Evenbly, G Vidal - Physical Review B—Condensed Matter and Materials …, 2010 - APS",['https://arxiv.org/pdf/0710.0692'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.81.235102,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/0710.0692'],entanglement renormalization in noninteracting fermionic systems,互信息/标度,1,Physical Review B,
Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms,"G Evenbly, G Vidal",2010.0,57,"The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D =1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.",OnkqxVh-wXYJ,"G Evenbly, G Vidal - New Journal of Physics, 2010 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/1367-2630/12/2/025007/pdf'],https://iopscience.iop.org/article/10.1088/1367-2630/12/2/025007/meta,unknown,unknown,互信息/标度,,['https://iopscience.iop.org/article/10.1088/1367-2630/12/2/025007/pdf'],entanglement renormalization in free bosonic systems real space versus momentum space renormalization group transforms,互信息/标度,1,New Journal of Physics,
Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks,"V Murg, Ö Legeza, R M Noack, F Verstraete",2010.0,1,"We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following Shi. et. al. [Phys. Rev. A, 74, 022320 (2006)], we treat a tree-like network ansatz with arbitrary coordination number z, where the z=2 case corresponds to the one-dimensional scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1-d interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach.",,"V Murg, Ö Legeza, R M Noack, F Verstraete - Phys. Rev. B 82, 205105 (2010)",[],https://arxiv.org/abs/1006.3095,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1006.3095,['https://arxiv.org/pdf/1006.3095'],simulating strongly correlated quantum systems with tree tensor networks,TTN/MERA/PEPS,1,"Phys. Rev. B 82, 205105 (2010)",
Entanglement renormalization and gauge symmetry,"L Tagliacozzo, G Vidal",2011.0,148,"… bound to the entanglement entropy of the deformed toric code model without Wexact. For comparison, the green (middle) curve corresponds to the entanglement entropy of the ground …",pTvo9O9Qmw0J,"L Tagliacozzo, G Vidal - Physical Review B—Condensed Matter and Materials …, 2011 - APS",['https://arxiv.org/pdf/1007.4145'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.83.115127,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/1007.4145'],entanglement renormalization and gauge symmetry,互信息/标度,1,,
Entanglement entropy of Fermi liquids via multidimensional bosonization,"W Ding, A Seidel, K Yang",2012.0,96,"… in the language of high-dimensional bosonization, and lead to a correction to the … in renormalization-group analysis [40]. As the leading-order contribution of the entanglement entropy is …",uyKYFKFPuxkJ,"W Ding, A Seidel, K Yang - Physical Review X, 2012 - APS",['https://link.aps.org/pdf/10.1103/PhysRevX.2.011012'],https://journals.aps.org/prx/abstract/10.1103/PhysRevX.2.011012,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PhysRevX.2.011012'],entanglement entropy of fermi liquids via multidimensional bosonization,互信息/标度,1,,
Perfect Sampling with Unitary Tensor Networks,"A J Ferris, G Vidal",2012.0,0,"Tensor network states are powerful variational ansätze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions, potentially leading to a substantial increase in computational efficiency. Previous proposals are based on a Markov chain Monte Carlo scheme generated by locally updating configurations and, as such, must deal with equilibration and autocorrelation times, which result in a reduction of efficiency. Here we propose a perfect sampling scheme, with vanishing equilibration and autocorrelation times, for unitary tensor networks -- namely tensor networks based on efficiently contractible, unitary quantum circuits, such as unitary versions of the matrix product state (MPS) and tree tensor network (TTN), and the multi-scale entanglement renormalization ansatz (MERA). Configurations are directly sampled according to their probabilities in the wavefunction, without resorting to a Markov chain process. We also describe a partial sampling scheme that can result in a dramatic (basis-dependent) reduction of sampling error.",,"A J Ferris, G Vidal - Phys. Rev. B 85, 165146 (2012)",[],https://arxiv.org/abs/1201.3974,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1201.3974,['https://arxiv.org/pdf/1201.3974'],perfect sampling with unitary tensor networks,TTN/MERA/PEPS,1,"Phys. Rev. B 85, 165146 (2012)",
Multiscale entanglement renormalisation ansatz,"M Hauru, E Keski-Vakkuri, K Rummukainen",2013.0,12,"This thesis reviews the multiscale entanglement renormalisation ansatz or MERA, a numerical tool for the study of quantum many-body systems and a discrete realisation of the AdS/CFT duality. The thesis covers an introduction to the necessary background concepts of entanglement, entanglement entropy and tensor network states, the structure and main features of MERA and its applications in condensed matter theory and holography. Also covered are details on the algorithmic implementation of MERA and some of its generalisations and extensions. MERA belongs to a class of variational ansatze for quantum many-body states known as tensor network states. It is especially well-suited for the study of scale invariant critical points. MERA is based on a real-space renormalisation group procedure called entanglement renormalisation, designed to systematically handle entanglement at different length scales along the coarse-graining flow. Entanglement renormalisation has be used for example to efficiently describe Kitaev states of the toric code, the prime example of topological order, and numerically study the ground state of the highly frustrated spin-1/2 Heisenberg model on a kagome lattice and various other one- and two-dimensional lattice models. The geometric and causal structure of MERA, which underlies its effectiveness as a numerical tool, also makes it a discrete version of the AdS/CFT duality. This duality describes a conformal field theory by a gravity theory in a higher dimensional space, and vice versa. The duality is manifest in the scaling of entanglement entropy in MERA, which is governed by a law highly analogous to the Ryu-Takayanagi formula for holographic entanglement entropy, in the connection between thermal states and a black-hole-like MERA and in the connection between correlation functions and holographic geodesics in a scale invariant MERA. The aim of this thesis is to lead the reader to an understanding of what MERA is, how it works and how it can be used. MERA's core features and uses are presented in a comprehensive and explicit way, and a broad view of possible applications and further directions is given. Plenty of references are also offered to direct the reader to further research on how MERA may relate to his/her interests.",RnsFkN0GXjYJ,"M Hauru, E Keski-Vakkuri, K Rummukainen - 2013 - helda.helsinki.fi",['https://helda.helsinki.fi/bitstreams/0d28abbd-44a5-47bb-8851-5a058a14d9dc/download'],https://helda.helsinki.fi/bitstreams/0d28abbd-44a5-47bb-8851-5a058a14d9dc/download,unknown,unknown,互信息/标度,,['https://helda.helsinki.fi/bitstreams/0d28abbd-44a5-47bb-8851-5a058a14d9dc/download'],multiscale entanglement renormalisation ansatz,互信息/标度,1,Työväentutkimus Vuosikirja,
Faster identification of optimal contraction sequences for tensor networks,"R N C Pfeifer, J Haegeman, F Verstraete",2013.0,2,"The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly upon the order in which the index sums are evaluated, and determination of the operation-minimising contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoisation, but these approaches are impractical for many of the larger tensor network Ansaetze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimising contraction sequence for a single tensor network. A reference implementation for MATLAB, compatible with the ncon() and multienv() network contractors of arXiv:1402.0939 and arXiv:1310.8023 respectively, is supplied.",,"R N C Pfeifer, J Haegeman, F Verstraete - Phys. Rev. E 90, 033315 (2014)",[],https://arxiv.org/abs/1304.6112,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1304.6112,['https://arxiv.org/pdf/1304.6112'],faster identification of optimal contraction sequences for tensor networks,MPO/TT 压缩 / MPS/序列建模,1,"Phys. Rev. E 90, 033315 (2014)",
Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm,"N Nakatani, G K Chan",2013.0,0,"We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an ilustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.",,"N Nakatani, G K Chan - J. Chem. Phys. 138, 134113 (2013)",[],https://arxiv.org/abs/1302.2298,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1302.2298,['https://arxiv.org/pdf/1302.2298'],efficient tree tensor network states ttns for quantum chemistry generalizations of the density matrix renormalization group algorithm,TTN/MERA/PEPS,1,"J. Chem. Phys. 138, 134113 (2013)",
Fourier transform of fermionic systems and the spectral tensor network,A J Ferris,2013.0,0,"Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with Evenbly & Vidal's branching MERA, but with some important differences and greatly reduced computational demands.",,"A J Ferris - Phys. Rev. Lett. 113, 010401 (2014)",[],https://arxiv.org/abs/1310.7605,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1310.7605,['https://arxiv.org/pdf/1310.7605'],fourier transform of fermionic systems and the spectral tensor network,TTN/MERA/PEPS / 互信息/标度,1,"Phys. Rev. Lett. 113, 010401 (2014)",
Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension,"S Singh, G Vidal",2013.0,0,"Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension χof the bond indices that connect its tensors controls the number of variational parameters and associated computational costs. In the absence of any symmetry, the minimal bond dimension χ^{min} required to represent a given many-body wave-function |Ψ> leads to the most compact, computationally efficient tensor network description of |Ψ>. In the presence of a global, on-site symmetry, one can use a tensor network N_{sym} made of symmetric tensors. Symmetric tensors allow to exactly preserve the symmetry and to target specific quantum numbers, while their sparse structure leads to a compact description and lowers computational costs. In this paper we explore the trade-off between using a tensor network N with minimal bond dimension χ^{min} and a tensor network N_{sym} made of symmetric tensors, where the minimal bond dimension χ^{min}_{sym} might be larger than χ^{min}. We present two technical results. First, we show that in a tree tensor network, which is the most general tensor network without loops, the minimal bond dimension can always be achieved with symmetric tensors, so that χ^{min}_{sym} = χ^{min}. Second, we provide explicit examples of tensor networks with loops where replacing tensors with symmetric ones necessarily increases the bond dimension, so that χ_{sym}^{min} > χ^{min}. We further argue, however, that in some situations there are important conceptual reasons to prefer a tensor network representation with symmetric tensors (and possibly larger bond dimension) over one with minimal bond dimension.",,"S Singh, G Vidal - Phys. Rev. B 88, 115147 (2013)",[],https://arxiv.org/abs/1307.1522,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1307.1522,['https://arxiv.org/pdf/1307.1522'],global symmetries in tensor network states symmetric tensors versus minimal bond dimension,TTN/MERA/PEPS,1,"Phys. Rev. B 88, 115147 (2013)",
Matrix product state applications for the ALPS project,"M Dolfi, B Bauer, S Keller, A Kosenkov, T Ewart…",2014.0,130,… Solution method: The matrix product states ansatz provides a controllable truncation of the Hilbert space which makes it currently the method of choice to investigate low-dimensional …,E13zNbrDWXcJ,"M Dolfi, B Bauer, S Keller, A Kosenkov, T Ewart… - Computer Physics …, 2014 - Elsevier",['https://arxiv.org/pdf/1407.0872'],https://www.sciencedirect.com/science/article/pii/S0010465514003002,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/1407.0872'],matrix product state applications for the alps project,MPS 语言模型,1,,
Matrix-product operators and states: NP-hardness and undecidability,"M Kliesch, D Gross, J Eisert",2014.0,128,"… values with respect to matrix-product states (MPS) of small bond dimension, see Fig. 2. … [29] local purifications of positive MPOs in terms of matrix-product states are investigated and it is …",5Tuu6VaK9Q4J,"M Kliesch, D Gross, J Eisert - Physical review letters, 2014 - APS",['https://arxiv.org/pdf/1404.4466'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160503,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/1404.4466'],matrix product operators and states np hardness and undecidability,MPS 语言模型,1,,
Renormalization of entanglement entropy and the gravitational effective action,"JH Cooperman, MA Luty",2014.0,98,"… to the renormalized entanglement entropy depend nontrivially … to the renormalized entanglement entropy, finding agreement … 1In the language of effective field theory, the …",QsSqjsGDWngJ,"JH Cooperman, MA Luty - Journal of High Energy Physics, 2014 - Springer",['https://link.springer.com/content/pdf/10.1007/JHEP12(2014)045.pdf'],https://link.springer.com/article/10.1007/JHEP12(2014)045,unknown,unknown,互信息/标度,1302.1878,['https://link.springer.com/content/pdf/10.1007/JHEP12(2014)045.pdf'],renormalization of entanglement entropy and the gravitational effective action,互信息/标度,1,Journal of High Energy Physics 12 (2014) 045,
Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance,"M Gerster, P Silvi, M Rizzi, R Fazio, T Calarco, S Montangero",2014.0,0,"We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional numerical freedom, combined with the loop-free topology of the tree network, allows one to maximally exploit the internal gauge invariance of tensor networks, ultimately leading to a computationally flexible and efficient algorithm able to treat open and periodic boundary conditions on the same footing. We benchmark the novel approach against the 1D Ising model in transverse field with periodic boundary conditions and discuss the strategy to cope with the broken translational invariance generated by the network structure. We then perform investigations on a state-of-the-art problem, namely the bilinear-biquadratic model in the transition between dimer and ferromagnetic phases. Our results clearly display an exponentially diverging correlation length and thus support the most recent guesses on the peculiarity of the transition.",,"M Gerster, P Silvi, M Rizzi, R Fazio, T Calarco, S Montangero - Phys. Rev. B 90, 125154 (2014)",[],https://arxiv.org/abs/1406.2666,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1406.2666,['https://arxiv.org/pdf/1406.2666'],unconstrained tree tensor network an adaptive gauge picture for enhanced performance,TTN/MERA/PEPS,1,"Phys. Rev. B 90, 125154 (2014)",
Tensorizing neural networks,"A Novikov, D Podoprikhin, A Osokin…",2015.0,1360,… the fully-connected layers to the Tensor Train [17] format such that … Deep VGG networks [21] we report the compression factor of … and review the Tensor Train (TT) format in Sec. 3. In Sec. …,8v8dX0Foet0J,"A Novikov, D Podoprikhin, A Osokin… - Advances in neural …, 2015 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2015/file/6855456e2fe46a9d49d3d3af4f57443d-Paper.pdf'],https://proceedings.neurips.cc/paper_files/paper/5787-tensorizing-neural-networks,unknown,unknown,MPO/TT 压缩,1509.06569,['https://proceedings.neurips.cc/paper_files/paper/2015/file/6855456e2fe46a9d49d3d3af4f57443d-Paper.pdf'],tensorizing neural networks,MPO/TT 压缩,1,,
Entanglement-based machine learning on a quantum computer,"XD Cai, D Wu, ZE Su, MC Chen, XL Wang, L Li, NL Liu…",2015.0,277,"Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing ""big data"" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning.",YUXHIpuQ_2oJ,"XD Cai, D Wu, ZE Su, MC Chen, XL Wang, L Li, NL Liu… - Physical review …, 2015 - APS",['https://arxiv.org/pdf/1409.7770'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.110504,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1409.7770'],entanglement based machine learning on a quantum computer,TTN/MERA/PEPS,1,Physical Review Letters,
Mutual information area laws for thermal free fermions,"H Bernigau, MJ Kastoryano…",2015.0,31,"We provide a rigorous and asymptotically exact expression of the mutual information of translationally invariant free fermionic lattice systems in a Gibbs state. In order to arrive at this result, we introduce a novel framework for computing determinants of Töplitz operators with smooth symbols, and for treating Töplitz matrices with system size dependent entries. The asymptotically exact mutual information for a partition of the 1D lattice satisfies an area law, with a prefactor which we compute explicitly. As examples, we discuss the fermionic XX model in one dimension and free fermionic models on the torus in higher dimensions in detail. Special emphasis is put on the discussion of the temperature dependence of the mutual information, scaling like the logarithm of the inverse temperature, hence confirming an expression suggested by conformal field theory. We also comment on the applicability of the formalism to treat open systems driven by quantum noise. In the appendix, we derive useful bounds to the mutual information in terms of purities. Finally, we provide a detailed error analysis for finite system sizes. This analysis is valuable in its own right for the abstract theory of Töplitz determinants.",BDlt0FcBW10J,"H Bernigau, MJ Kastoryano… - Journal of Statistical …, 2015 - iopscience.iop.org",['https://arxiv.org/pdf/1301.5646'],https://iopscience.iop.org/article/10.1088/1742-5468/2015/02/P02008/meta,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/1301.5646'],mutual information area laws for thermal free fermions,互信息/标度,1,Journal of Statistical Mechanics Theory and Experiment,
Local scale transformations on the lattice with tensor network renormalization,"G Evenbly, G Vidal",2015.0,0,"Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization (TNR) algorithm [\emph{G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405}] can be used to implement local scale transformations on these objects, namely a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.",,"G Evenbly, G Vidal - Phys. Rev. Lett. 116, 040401 (2016)",[],https://arxiv.org/abs/1510.00689,arxiv-completion,2026-09-26 (citations:OpenAlex),,1510.00689,['https://arxiv.org/pdf/1510.00689'],local scale transformations on the lattice with tensor network renormalization,,1,"Phys. Rev. Lett. 116, 040401 (2016)",
On the Expressive Power of Deep Learning: A Tensor Analysis,"N Cohen, O Sharir, A Shashua",2015.0,,"It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast empirical evidence supporting this belief, theoretical justifications to date are limited. In particular, they do not account for the locality, sharing and pooling constructs of convolutional networks, the most successful deep learning architecture to date. In this work we derive a deep network architecture based on arithmetic circuits that inherently employs locality, sharing and pooling. An equivalence between the networks and hierarchical tensor factorizations is established. We show that a shallow network corresponds to CP (rank-1) decomposition, whereas a deep network corresponds to Hierarchical Tucker decomposition. Using tools from measure theory and matrix algebra, we prove that besides a negligible set, all functions that can be implemented by a deep network of polynomial size, require exponential size in order to be realized (or even approximated) by a shallow network. Since log-space computation transforms our networks into SimNets, the result applies directly to a deep learning architecture demonstrating promising empirical performance. The construction and theory developed in this paper shed new light on various practices and ideas employed by the deep learning community.",,"N Cohen, O Sharir, A Shashua - 29th Annual Conference on Learning Theory, pp. 698-728, 2016",[],https://arxiv.org/abs/1509.05009,arxiv-completion,2026-09-26 (citations:OpenAlex),,1509.05009,['https://arxiv.org/pdf/1509.05009'],on the expressive power of deep learning a tensor analysis,,1,"29th Annual Conference on Learning Theory, pp. 698-728, 2016",
Geometric Structures in Tensor Representations (Final Release),"A Falco, W Hackbusch, A Nouy",2015.0,,"The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the dimensions of the associated minimal subspaces, we introduce, in the underlying algebraic tensor space, the set of tensors in a tree-based format with either bounded or fixed tree-based rank. This class contains the Tucker format and the Hierarchical Tucker format (including the Tensor Train format). In particular, we show that the set of tensors in the tree-based format with bounded (respectively, fixed) tree-based rank of an algebraic tensor product of normed vector spaces is an analytic Banach manifold. Indeed, the manifold geometry for the set of tensors with fixed tree-based rank is induced by a fibre bundle structure and the manifold geometry for the set of tensors with bounded tree-based rank is given by a finite union of connected components. In order to describe the relationship between these manifolds and the natural ambient space, we introduce the definition of topological tensor spaces in the tree-based format. We prove under natural conditions that any tensor of the topological tensor space under consideration admits best approximations in the manifold of tensors in the tree-based format with bounded tree-based rank. In this framework, we also show that the tangent (Banach) space at a given tensor is a complemented subspace in the natural ambient tensor Banach space and hence the set of tensors in the tree-based format with bounded (respectively, fixed) tree-based rank is an immersed submanifold. This fact allows us to extend the Dirac-Frenkel variational principle in the framework of topological tensor spaces.",,"A Falco, W Hackbusch, A Nouy - arXiv preprint arXiv:1505.03027, 2015 - arxiv.org",[],https://arxiv.org/abs/1505.03027,arxiv-completion,2026-09-26 (citations:OpenAlex),,1505.03027,['https://arxiv.org/pdf/1505.03027'],geometric structures in tensor representations final release,,1,,
Holographic duality from random tensor networks,"P Hayden, S Nezami, XL Qi, N Thomas…",2016.0,857,"… random tensor networks there are two kinds of scaling … In the holographic context, it was in fact previously shown … approaches the von Neumann mutual information for large D. …",W5dfRCuECN8J,"P Hayden, S Nezami, XL Qi, N Thomas… - Journal of High Energy …, 2016 - Springer",['https://link.springer.com/content/pdf/10.1007/JHEP11%282016%29009.pdf'],https://link.springer.com/article/10.1007/JHEP11(2016)009,unknown,unknown,互信息/标度,1601.01694,['https://link.springer.com/content/pdf/10.1007/JHEP11%282016%29009.pdf'],holographic duality from random tensor networks,互信息/标度,1,JHEP 11 (2016) 009,
Renormalized entanglement entropy,"M Taylor, W Woodhead",2016.0,122,"… the renormalization of entanglement entropy by differentiation. In section 3 we setup area renormalization for entangling … , and show that the renormalized entanglement entropy for disk …",yLHfyQwdhgwJ,"M Taylor, W Woodhead - Journal of High Energy Physics, 2016 - Springer",['https://link.springer.com/content/pdf/10.1007/JHEP08(2016)165.pdf'],https://link.springer.com/article/10.1007/JHEP08(2016)165,unknown,unknown,互信息/标度,1604.06808,['https://link.springer.com/content/pdf/10.1007/JHEP08(2016)165.pdf'],renormalized entanglement entropy,互信息/标度,1,,
Supervised Learning with Quantum-Inspired Tensor Networks,"E M Stoudenmire, D J Schwab",2016.0,102,Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize models for classifying images. For the MNIST data set we obtain less than 1% test set classification error. We discuss how the tensor network form imparts additional structure to the learned model and suggest a possible generative interpretation.,,"E M Stoudenmire, D J Schwab - Advances in Neural Information Processing Systems 29, 4799 (2016)",[],https://arxiv.org/abs/1605.05775,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,1605.05775,['https://arxiv.org/pdf/1605.05775'],supervised learning with quantum inspired tensor networks,MPS 生成/Born机,1,"Advances in Neural Information Processing Systems 29, 4799 (2016)",
"Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles",J P Garrahan,2016.0,0,"Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach ""biased"" or ""conditioned"" ensembles where the probability of trajectories is biased from that of the natural dynamics by some condition on trajectory observables. In particular, we show that the generalised Doob transform which maps a conditioned process to an equivalent ""auxiliary"" or ""driven"" process (one where the same conditioned set of trajectories is generated by a proper stochastic dynamics) is just a gauge transformation of the corresponding cMPS. We also discuss how within this framework one can easily prove properties of the dynamics such as trajectory ensemble equivalence and fluctuation theorems.",,J P Garrahan - J. Stat. Mech. 073208 (2016),[],https://arxiv.org/abs/1602.07966,arxiv-completion,2026-09-26 (citations:OpenAlex),,1602.07966,['https://arxiv.org/pdf/1602.07966'],classical stochastic dynamics and continuous matrix product states gauge transformations conditioned and driven processes and equivalence of trajectory ensembles,,1,J. Stat. Mech. 073208 (2016),
Multimodal Compact Bilinear Pooling for Visual Question Answering and Visual Grounding,"A Fukui, D H Park, D Yang, A Rohrbach, T Darrell, M Rohrbach",2016.0,,"Modeling textual or visual information with vector representations trained from large language or visual datasets has been successfully explored in recent years. However, tasks such as visual question answering require combining these vector representations with each other. Approaches to multimodal pooling include element-wise product or sum, as well as concatenation of the visual and textual representations. We hypothesize that these methods are not as expressive as an outer product of the visual and textual vectors. As the outer product is typically infeasible due to its high dimensionality, we instead propose utilizing Multimodal Compact Bilinear pooling (MCB) to efficiently and expressively combine multimodal features. We extensively evaluate MCB on the visual question answering and grounding tasks. We consistently show the benefit of MCB over ablations without MCB. For visual question answering, we present an architecture which uses MCB twice, once for predicting attention over spatial features and again to combine the attended representation with the question representation. This model outperforms the state-of-the-art on the Visual7W dataset and the VQA challenge.",,"A Fukui, D H Park, D Yang, A Rohrbach, T Darrell, M Rohrbach - arXiv preprint arXiv:1606.01847, 2016 - arxiv.org",[],https://arxiv.org/abs/1606.01847,arxiv-completion,2026-09-26 (citations:OpenAlex),,1606.01847,['https://arxiv.org/pdf/1606.01847'],multimodal compact bilinear pooling for visual question answering and visual grounding,,1,,
Deep Multi-task Representation Learning: A Tensor Factorisation Approach,"Y Yang, T Hospedales",2016.0,,"Most contemporary multi-task learning methods assume linear models. This setting is considered shallow in the era of deep learning. In this paper, we present a new deep multi-task representation learning framework that learns cross-task sharing structure at every layer in a deep network. Our approach is based on generalising the matrix factorisation techniques explicitly or implicitly used by many conventional MTL algorithms to tensor factorisation, to realise automatic learning of end-to-end knowledge sharing in deep networks. This is in contrast to existing deep learning approaches that need a user-defined multi-task sharing strategy. Our approach applies to both homogeneous and heterogeneous MTL. Experiments demonstrate the efficacy of our deep multi-task representation learning in terms of both higher accuracy and fewer design choices.",,"Y Yang, T Hospedales - arXiv preprint arXiv:1605.06391, 2016 - arxiv.org",[],https://arxiv.org/abs/1605.06391,arxiv-completion,2026-09-26 (citations:OpenAlex),,1605.06391,['https://arxiv.org/pdf/1605.06391'],deep multi task representation learning a tensor factorisation approach,,1,,
Convolutional Rectifier Networks as Generalized Tensor Decompositions,"N Cohen, A Shashua",2016.0,,"Convolutional rectifier networks, i.e. convolutional neural networks with rectified linear activation and max or average pooling, are the cornerstone of modern deep learning. However, despite their wide use and success, our theoretical understanding of the expressive properties that drive these networks is partial at best. On the other hand, we have a much firmer grasp of these issues in the world of arithmetic circuits. Specifically, it is known that convolutional arithmetic circuits possess the property of ""complete depth efficiency"", meaning that besides a negligible set, all functions that can be implemented by a deep network of polynomial size, require exponential size in order to be implemented (or even approximated) by a shallow network. In this paper we describe a construction based on generalized tensor decompositions, that transforms convolutional arithmetic circuits into convolutional rectifier networks. We then use mathematical tools available from the world of arithmetic circuits to prove new results. First, we show that convolutional rectifier networks are universal with max pooling but not with average pooling. Second, and more importantly, we show that depth efficiency is weaker with convolutional rectifier networks than it is with convolutional arithmetic circuits. This leads us to believe that developing effective methods for training convolutional arithmetic circuits, thereby fulfilling their expressive potential, may give rise to a deep learning architecture that is provably superior to convolutional rectifier networks but has so far been overlooked by practitioners.",,"N Cohen, A Shashua - Proceedings of The 33rd International Conference on Machine Learning, pp. 955-963, 2016",[],https://arxiv.org/abs/1603.00162,arxiv-completion,2026-09-26 (citations:OpenAlex),,1603.00162,['https://arxiv.org/pdf/1603.00162'],convolutional rectifier networks as generalized tensor decompositions,,1,"Proceedings of The 33rd International Conference on Machine Learning, pp. 955-963, 2016",
Quantum entanglement growth under random unitary dynamics,"A Nahum, J Ruhman, S Vijay, J Haah",2017.0,1172,"… In 1D, we show that noise causes the entanglement entropy … The language of quantum entanglement ties together … product states or the density matrix renormalization group [31]. The …",5lwwEgsmlecJ,"A Nahum, J Ruhman, S Vijay, J Haah - Physical Review X, 2017 - APS",['https://link.aps.org/pdf/10.1103/PhysRevX.7.031016'],https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.031016,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PhysRevX.7.031016'],quantum entanglement growth under random unitary dynamics,互信息/标度,1,,
Quantum entanglement in neural network states,"DL Deng, X Li, S Das Sarma",2017.0,683,"… Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with a longrange interaction. In …",-avXqa7s9AwJ,"DL Deng, X Li, S Das Sarma - Physical Review X, 2017 - APS",['https://link.aps.org/pdf/10.1103/PhysRevX.7.021021'],https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.021021,unknown,unknown,TTN/MERA/PEPS,,['https://link.aps.org/pdf/10.1103/PhysRevX.7.021021'],quantum entanglement in neural network states,TTN/MERA/PEPS,1,,
Machine learning topological states,"DL Deng, X Li, S Das Sarma",2017.0,414,… neural networks can describe the excited states with Abelian anyons and their … reinforcement learning we show that neural networks are capable of finding the topological ground states …,zXcreOv3aY8J,"DL Deng, X Li, S Das Sarma - Physical Review B, 2017 - APS",['https://arxiv.org/pdf/1609.09060'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.195145,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1609.09060'],machine learning topological states,TTN/MERA/PEPS,1,,
Tensor networks for dimensionality reduction and large-scale optimizations part 2 applications and future perspectives,"A Cichocki, AH Phan, Q Zhao, N Lee…",2017.0,398,"Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.",yOswxTx3nSAJ,"A Cichocki, AH Phan, Q Zhao, N Lee… - … and Trends® in …, 2017 - emerald.com",['https://arxiv.org/pdf/1708.09165'],https://www.emerald.com/ftmal/article/9/6/431/1332832,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/1708.09165'],tensor networks for dimensionality reduction and large scale optimizations part 2 applications and future perspectives,互信息/标度,1,Foundations and Trends® in Machine Learning,
Tensor-train recurrent neural networks for video classification,"Y Yang, D Krompass, V Tresp",2017.0,367,… tensor and then factorize this tensor using Tensor-Train. This was applied to compress very large weight matrices in deep Neural Networks where the entire model was trained end…,YFe90ixiVmkJ,"Y Yang, D Krompass, V Tresp - International conference on …, 2017 - proceedings.mlr.press",['http://proceedings.mlr.press/v70/yang17e/yang17e.pdf'],http://proceedings.mlr.press/v70/yang17e,unknown,unknown,MPO/TT 压缩,,['http://proceedings.mlr.press/v70/yang17e/yang17e.pdf'],tensor train recurrent neural networks for video classification,MPO/TT 压缩,1,,
Compressing recurrent neural network with tensor train,"A Tjandra, S Sakti, S Nakamura",2017.0,166,… Proposed Tensor Train based RNN … our proposed approach to compress RNN using Tensor Train (TT) format representation. We start with the description of Tensor Train [14] and then …,B9xInX8YIGwJ,"A Tjandra, S Sakti, S Nakamura - … on Neural Networks (IJCNN), 2017 - ieeexplore.ieee.org",['https://arxiv.org/pdf/1705.08052'],https://ieeexplore.ieee.org/abstract/document/7966420/,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/1705.08052'],compressing recurrent neural network with tensor train,MPO/TT 压缩,1,,
Neural networks compression for language modeling,"AM Grachev, DI Ignatov, AV Savchenko",2017.0,43,"… compression techniques for the language modeling problem based on recurrent neural networks … It is known that conventional RNNs, eg, LSTM-based networks in language modeling, …",P3oBCFYr9igJ,"AM Grachev, DI Ignatov, AV Savchenko - International Conference on …, 2017 - Springer",['https://arxiv.org/pdf/1708.05963'],https://link.springer.com/chapter/10.1007/978-3-319-69900-4_44,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/1708.05963'],neural networks compression for language modeling,MPO/TT 压缩,1,,
Tensor network language model,"V Pestun, Y Vlassopoulos",2017.0,40,"We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and vector spaces in the edges, called tensor network. Such tensor networks have been previously employed for effective numerical computation of the renormalization group flow on the space of effective quantum field theories and lattice models of statistical mechanics. We provide explicit algebro-geometric analysis of the parameter moduli space for tree graphs, discuss model properties and applications such as statistical translation.",h4971agd31AJ,"V Pestun, Y Vlassopoulos - arXiv preprint arXiv:1710.10248, 2017 - arxiv.org",['https://arxiv.org/pdf/1710.10248'],https://arxiv.org/abs/1710.10248,unknown,unknown,MPS/序列建模,1710.10248,['https://arxiv.org/pdf/1710.10248'],tensor network language model,MPS/序列建模 / TTN/MERA/PEPS,2,,
Scalable Gaussian Processes with Billions of Inducing Inputs via Tensor Train Decomposition,"P Izmailov, A Novikov, D Kropotov",2017.0,28,"We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure exploiting algebra. The key idea of our method is to use Tensor Train decomposition for variational parameters, which allows us to train GPs with billions of inducing inputs and achieve state-of-the-art results on several benchmarks. Further, our approach allows for training kernels based on deep neural networks without any modifications to the underlying GP model. A neural network learns a multidimensional embedding for the data, which is used by the GP to make the final prediction. We train GP and neural network parameters end-to-end without pretraining, through maximization of GP marginal likelihood. We show the efficiency of the proposed approach on several regression and classification benchmark datasets including MNIST, CIFAR-10, and Airline.",,"P Izmailov, A Novikov, D Kropotov - arXiv preprint arXiv:1710.07324, 2017 - arxiv.org",[],https://arxiv.org/abs/1710.07324,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,1710.07324,['https://arxiv.org/pdf/1710.07324'],scalable gaussian processes with billions of inducing inputs via tensor train decomposition,MPS 生成/Born机,1,,
Language as a matrix product state,"V Pestun, J Terilla, Y Vlassopoulos",2017.0,20,"We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability measure. We interpret the probability measure as arising via the Born rule from a translation invariant matrix product state.",DHZi-NemHwcJ,"V Pestun, J Terilla, Y Vlassopoulos - arXiv preprint arXiv:1711.01416, 2017 - arxiv.org",['https://arxiv.org/pdf/1711.01416'],https://arxiv.org/abs/1711.01416,unknown,unknown,MPS 语言模型,1711.01416,['https://arxiv.org/pdf/1711.01416'],language as a matrix product state,MPS 语言模型,1,arXiv (Cornell University),
Learning Compact Recurrent Neural Networks with Block-Term Tensor Decomposition,"J Ye, L Wang, G Li, D Chen, S Zhe, X Chu, Z Xu",2017.0,17,"Recurrent Neural Networks (RNNs) are powerful sequence modeling tools. However, when dealing with high dimensional inputs, the training of RNNs becomes computational expensive due to the large number of model parameters. This hinders RNNs from solving many important computer vision tasks, such as Action Recognition in Videos and Image Captioning. To overcome this problem, we propose a compact and flexible structure, namely Block-Term tensor decomposition, which greatly reduces the parameters of RNNs and improves their training efficiency. Compared with alternative low-rank approximations, such as tensor-train RNN (TT-RNN), our method, Block-Term RNN (BT-RNN), is not only more concise (when using the same rank), but also able to attain a better approximation to the original RNNs with much fewer parameters. On three challenging tasks, including Action Recognition in Videos, Image Captioning and Image Generation, BT-RNN outperforms TT-RNN and the standard RNN in terms of both prediction accuracy and convergence rate. Specifically, BT-LSTM utilizes 17,388 times fewer parameters than the standard LSTM to achieve an accuracy improvement over 15.6\% in the Action Recognition task on the UCF11 dataset.",,"J Ye, L Wang, G Li, D Chen, S Zhe, X Chu, Z Xu - arXiv preprint arXiv:1712.05134, 2017 - arxiv.org",[],https://arxiv.org/abs/1712.05134,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1712.05134,['https://arxiv.org/pdf/1712.05134'],learning compact recurrent neural networks with block term tensor decomposition,MPO/TT 压缩 / MPS/序列建模,1,,
BT-Nets: Simplifying Deep Neural Networks via Block Term Decomposition,"G Li, J Ye, H Yang, D Chen, S Yan, Z Xu",2017.0,12,"Recently, deep neural networks (DNNs) have been regarded as the state-of-the-art classification methods in a wide range of applications, especially in image classification. Despite the success, the huge number of parameters blocks its deployment to situations with light computing resources. Researchers resort to the redundancy in the weights of DNNs and attempt to find how fewer parameters can be chosen while preserving the accuracy at the same time. Although several promising results have been shown along this research line, most existing methods either fail to significantly compress a well-trained deep network or require a heavy fine-tuning process for the compressed network to regain the original performance. In this paper, we propose the \textit{Block Term} networks (BT-nets) in which the commonly used fully-connected layers (FC-layers) are replaced with block term layers (BT-layers). In BT-layers, the inputs and the outputs are reshaped into two low-dimensional high-order tensors, then block-term decomposition is applied as tensor operators to connect them. We conduct extensive experiments on benchmark datasets to demonstrate that BT-layers can achieve a very large compression ratio on the number of parameters while preserving the representation power of the original FC-layers as much as possible. Specifically, we can get a higher performance while requiring fewer parameters compared with the tensor train method.",,"G Li, J Ye, H Yang, D Chen, S Yan, Z Xu - arXiv preprint arXiv:1712.05689, 2017 - arxiv.org",[],https://arxiv.org/abs/1712.05689,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1712.05689,['https://arxiv.org/pdf/1712.05689'],bt nets simplifying deep neural networks via block term decomposition,MPO/TT 压缩,1,,
Expressive power of recurrent neural networks,"V Khrulkov, A Novikov, I Oseledets",2017.0,9,"Deep neural networks are surprisingly efficient at solving practical tasks, but the theory behind this phenomenon is only starting to catch up with the practice. Numerous works show that depth is the key to this efficiency. A certain class of deep convolutional networks -- namely those that correspond to the Hierarchical Tucker (HT) tensor decomposition -- has been proven to have exponentially higher expressive power than shallow networks. I.e. a shallow network of exponential width is required to realize the same score function as computed by the deep architecture. In this paper, we prove the expressive power theorem (an exponential lower bound on the width of the equivalent shallow network) for a class of recurrent neural networks -- ones that correspond to the Tensor Train (TT) decomposition. This means that even processing an image patch by patch with an RNN can be exponentially more efficient than a (shallow) convolutional network with one hidden layer. Using theoretical results on the relation between the tensor decompositions we compare expressive powers of the HT- and TT-Networks. We also implement the recurrent TT-Networks and provide numerical evidence of their expressivity.",,"V Khrulkov, A Novikov, I Oseledets - arXiv preprint arXiv:1711.00811, 2017 - arxiv.org",[],https://arxiv.org/abs/1711.00811,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,1711.00811,['https://arxiv.org/pdf/1711.00811'],expressive power of recurrent neural networks,MPS/序列建模,1,,
Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz,"A Hallam, E Grant, V Stojevic, S Severini, A G Green",2017.0,6,"This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N).",,"A Hallam, E Grant, V Stojevic, S Severini, A G Green - arXiv preprint arXiv:1711.03357, 2017 - arxiv.org",[],https://arxiv.org/abs/1711.03357,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1711.03357,['https://arxiv.org/pdf/1711.03357'],compact neural networks based on the multiscale entanglement renormalization ansatz,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
Implementing the sine transform of fermionic modes as a tensor network,"H Epple, P Fries, H Hinrichsen",2017.0,0,"Based on the algebraic theory of signal processing, we recursively decompose the discrete sine transform of first kind (DST-I) into small orthogonal block operations. Using a diagrammatic language, we then second-quantize this decomposition to construct a tensor network implementing the DST-I for fermionic modes on a lattice. The complexity of the resulting network is shown to scale as $\frac 54 n \log n$ (not considering swap gates), where $n$ is the number of lattice sites. Our method provides a systematic approach of generalizing Ferris' spectral tensor network for non-trivial boundary conditions.",,"H Epple, P Fries, H Hinrichsen - Phys. Rev. A 96, 032308 (2017)",[],https://arxiv.org/abs/1705.10186,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1705.10186,['https://arxiv.org/pdf/1705.10186'],implementing the sine transform of fermionic modes as a tensor network,MPO/TT 压缩,1,"Phys. Rev. A 96, 032308 (2017)",
MUTAN: Multimodal Tucker Fusion for Visual Question Answering,"H Ben-younes, R Cadene, M Cord, N Thome",2017.0,,"Bilinear models provide an appealing framework for mixing and merging information in Visual Question Answering (VQA) tasks. They help to learn high level associations between question meaning and visual concepts in the image, but they suffer from huge dimensionality issues. We introduce MUTAN, a multimodal tensor-based Tucker decomposition to efficiently parametrize bilinear interactions between visual and textual representations. Additionally to the Tucker framework, we design a low-rank matrix-based decomposition to explicitly constrain the interaction rank. With MUTAN, we control the complexity of the merging scheme while keeping nice interpretable fusion relations. We show how our MUTAN model generalizes some of the latest VQA architectures, providing state-of-the-art results.",,"H Ben-younes, R Cadene, M Cord, N Thome - arXiv preprint arXiv:1705.06676, 2017 - arxiv.org",[],https://arxiv.org/abs/1705.06676,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1705.06676,['https://arxiv.org/pdf/1705.06676'],mutan multimodal tucker fusion for visual question answering,MPO/TT 压缩,1,,
Tensor Fusion Network for Multimodal Sentiment Analysis,"A Zadeh, M Chen, S Poria, E Cambria, L Morency",2017.0,,"Multimodal sentiment analysis is an increasingly popular research area, which extends the conventional language-based definition of sentiment analysis to a multimodal setup where other relevant modalities accompany language. In this paper, we pose the problem of multimodal sentiment analysis as modeling intra-modality and inter-modality dynamics. We introduce a novel model, termed Tensor Fusion Network, which learns both such dynamics end-to-end. The proposed approach is tailored for the volatile nature of spoken language in online videos as well as accompanying gestures and voice. In the experiments, our model outperforms state-of-the-art approaches for both multimodal and unimodal sentiment analysis.",,"A Zadeh, M Chen, S Poria, E Cambria, L Morency - arXiv preprint arXiv:1707.07250, 2017 - arxiv.org",[],https://arxiv.org/abs/1707.07250,arxiv-completion,2026-09-26 (citations:OpenAlex),,1707.07250,['https://arxiv.org/pdf/1707.07250'],tensor fusion network for multimodal sentiment analysis,,1,,
Kronecker Recurrent Units,"C Jose, M Cisse, F Fleuret",2017.0,,"Our work addresses two important issues with recurrent neural networks: (1) they are over-parameterized, and (2) the recurrence matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The latter causes the vanishing and exploding gradient problem. We present a flexible recurrent neural network model called Kronecker Recurrent Units (KRU). KRU achieves parameter efficiency in RNNs through a Kronecker factored recurrent matrix. It overcomes the ill-conditioning of the recurrent matrix by enforcing soft unitary constraints on the factors. Thanks to the small dimensionality of the factors, maintaining these constraints is computationally efficient. Our experimental results on seven standard data-sets reveal that KRU can reduce the number of parameters by three orders of magnitude in the recurrent weight matrix compared to the existing recurrent models, without trading the statistical performance. These results in particular show that while there are advantages in having a high dimensional recurrent space, the capacity of the recurrent part of the model can be dramatically reduced.",,"C Jose, M Cisse, F Fleuret - arXiv preprint arXiv:1705.10142, 2017 - arxiv.org",[],https://arxiv.org/abs/1705.10142,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,1705.10142,['https://arxiv.org/pdf/1705.10142'],kronecker recurrent units,MPS/序列建模,1,,
Tensor Networks in a Nutshell,"J Biamonte, V Bergholm",2017.0,,"Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and pictorially reason about quantum circuits, channels, protocols, open systems and more. Our goal is to explain tensor networks and some associated methods as quickly and as painlessly as possible. Beginning with the key definitions, the graphical tensor network language is presented through examples. We then provide an introduction to matrix product states. We conclude the tutorial with tensor contractions evaluating combinatorial counting problems. The first one counts the number of solutions for Boolean formulae, whereas the second is Penrose's tensor contraction algorithm, returning the number of $3$-edge-colorings of $3$-regular planar graphs.",,"J Biamonte, V Bergholm - arXiv preprint arXiv:1708.00006, 2017 - arxiv.org",[],https://arxiv.org/abs/1708.00006,arxiv-completion,2026-09-26 (citations:OpenAlex),,1708.00006,['https://arxiv.org/pdf/1708.00006'],tensor networks in a nutshell,,1,,
Unsupervised generative modeling using matrix product states,"ZY Han, J Wang, H Fan, L Wang, P Zhang",2018.0,516,"Modeling the probability distribution of complex data using insights from quantum physics is a fresh approach to generative modeling in machine learning, and shows great potential compared to conventional neural network approaches.",25EQKCe7K9QJ,"ZY Han, J Wang, H Fan, L Wang, P Zhang - Physical Review X, 2018 - APS",['https://link.aps.org/pdf/10.1103/PhysRevX.8.031012'],https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.031012,unknown,unknown,MPS 语言模型,1709.01662,['https://link.aps.org/pdf/10.1103/PhysRevX.8.031012'],unsupervised generative modeling using matrix product states,MPS 生成/Born机 / MPS 语言模型 / TTN/MERA/PEPS,3,Physical Review X,
Entanglement entropy: holography and renormalization group,T Nishioka,2018.0,411,"In this review the entanglement and Renyi entropies in quantum field theory are described from different points of view, including the perturbative approach and holographic dualities. The applications of these results to constraining renormalization group flows are presented effectively and illustrated with a variety of examples.",C9eCEm2gPOUJ,"T Nishioka - Reviews of Modern Physics, 2018 - APS",['https://arxiv.org/pdf/1801.10352'],https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.90.035007,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/1801.10352'],entanglement entropy holography and renormalization group,互信息/标度,1,Reviews of Modern Physics,
Wide compression: Tensor ring nets,"W Wang, Y Sun, B Eriksson…",2018.0,256,"Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of parameters and over a thousand layers. The tradeoff is that these large architectures require an enormous amount of memory, storage, and computation, thus limiting their usability. Inspired by the recent tensor ring factorization, we introduce Tensor Ring Networks (TR-Nets), which significantly compress both the fully connected layers and the convolutional layers of deep neural networks. Our results show that our TR-Nets approach is able to compress LeNet-5 by 11× without losing accuracy, and can compress the state-of-the-art Wide ResNet by 243× with only 2.3% degradation in Cifar10 image classification. Overall, this compression scheme shows promise in scientific computing and deep learning, especially for emerging resource-constrained devices such as smartphones, wearables, and IoT devices.",Y26ddrJm_PkJ,"W Wang, Y Sun, B Eriksson… - Proceedings of the …, 2018 - openaccess.thecvf.com",['https://openaccess.thecvf.com/content_cvpr_2018/papers/Wang_Wide_Compression_Tensor_CVPR_2018_paper.pdf'],https://openaccess.thecvf.com/content_cvpr_2018/html/Wang_Wide_Compression_Tensor_CVPR_2018_paper.html,unknown,unknown,MPO/TT 压缩,1802.09052,['https://openaccess.thecvf.com/content_cvpr_2018/papers/Wang_Wide_Compression_Tensor_CVPR_2018_paper.pdf'],wide compression tensor ring nets,MPO/TT 压缩,1,,
Learning relevant features of data with multi-scale tensor networks,EM Stoudenmire,2018.0,215,… The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and the training set size. Computing most of the layers with an …,aodIFCwXE9cJ,"EM Stoudenmire - Quantum Science and Technology, 2018 - iopscience.iop.org",['https://arxiv.org/pdf/1801.00315'],https://iopscience.iop.org/article/10.1088/2058-9565/aaba1a/meta,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/1801.00315'],learning relevant features of data with multi scale tensor networks,互信息/标度,1,,
Experimental machine learning of quantum states,"J Gao, LF Qiao, ZQ Jiao, YC Ma, CQ Hu, RJ Ren…",2018.0,195,… quantum information and machine learning represents a new … a quantum state is characterized by quantum-state tomography… a machine-learning approach to construct a quantum-state …,_QN9krkjE7kJ,"J Gao, LF Qiao, ZQ Jiao, YC Ma, CQ Hu, RJ Ren… - Physical review …, 2018 - APS",['https://arxiv.org/pdf/1712.00456'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.240501,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1712.00456'],experimental machine learning of quantum states,TTN/MERA/PEPS,1,,
Information perspective to probabilistic modeling: Boltzmann machines versus born machines,"S Cheng, J Chen, L Wang",2018.0,156,"… generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states, … Matrix Product States (MPS) …",D2PDMR79VzEJ,"S Cheng, J Chen, L Wang - Entropy, 2018 - mdpi.com",[],https://www.mdpi.com/1099-4300/20/8/583,unknown,unknown,MPS 生成/Born机,1712.04144,[],information perspective to probabilistic modeling boltzmann machines versus born machines,MPS 生成/Born机 / 互信息/标度,2,"Entropy 2018, 20(8), 583",
Machine learning spatial geometry from entanglement features,"YZ You, Z Yang, XL Qi",2018.0,122,"Machine learning is a fast developing area that finds applications in all disciplines of science. Here, the authors demonstrate that the machine learning (in particular deep learning) technique can be applied to understand the emergence of spatial geometry from learning the features of quantum many-body entanglement, an idea that was proposed in a recent study of the holography duality in quantum gravity. This work is the first to successfully demonstrate the idea of ``geometry emerging from learning''.",2oxyM6QXaQkJ,"YZ You, Z Yang, XL Qi - Physical Review B, 2018 - APS",['https://arxiv.org/pdf/1709.01223'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.045153,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1709.01223'],machine learning spatial geometry from entanglement features,TTN/MERA/PEPS,1,Physical review. B./Physical review. B,
A tensor-based Bayesian probabilistic model for citywide personalized travel time estimation,"K Tang, S Chen, Z Liu, AJ Khattak",2018.0,86,… This paper develops a tensor-based Bayesian probabilistic model for citywide and … modeled with a 3-order tensor. This tensor-based modeling approach incorporates both the spatial …,OpJXPDWzf_gJ,"K Tang, S Chen, Z Liu, AJ Khattak - Transportation Research Part C …, 2018 - Elsevier",['https://www.sciencedirect.com/science/article/am/pii/S0968090X18303103'],https://www.sciencedirect.com/science/article/pii/S0968090X18303103,unknown,unknown,MPS/序列建模,,['https://www.sciencedirect.com/science/article/am/pii/S0968090X18303103'],a tensor based bayesian probabilistic model for citywide personalized travel time estimation,MPS/序列建模,1,,
Matrix product operators for sequence to sequence learning,"C Guo, Z Jie, W Lu, D Poletti",2018.0,72,"The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an exponentially large space. It also allows to describe accurately correlations between distant parts of a system, an important ingredient to account for the context in machine learning tasks. Here we introduce a machine learning model in which matrix product operators are trained to implement sequence to sequence prediction, i.e. given a sequence at a time step, it allows one to predict the next sequence. We then apply our algorithm to cellular automata (for which we show exact analytical solutions in terms of matrix product operators), and to nonlinear coupled maps. We show advantages of the proposed algorithm when compared to conditional random fields and bidirectional long short-term memory neural network. To highlight the flexibility of the algorithm, we also show that it can readily perform classification tasks.",O7drpZaK89sJ,"C Guo, Z Jie, W Lu, D Poletti - arXiv preprint arXiv:1803.10908, 2018 - arxiv.org",['https://arxiv.org/pdf/1803.10908'],https://arxiv.org/abs/1803.10908,unknown,unknown,MPS 语言模型,1803.10908,['https://arxiv.org/pdf/1803.10908'],matrix product operators for sequence to sequence learning,MPS 语言模型,1,"Phys. Rev. E 98, 042114 (2018)",
Tensor train neighborhood preserving embedding,"W Wang, V Aggarwal, S Aeron",2018.0,41,"In this paper, we propose a tensor train neighborhood preserving embedding (TTNPE) to embed multidimensional tensor data into low-dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate a novel tradeoff gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior tradeoff in classification, computation, and dimensionality reduction in MNIST handwritten digits, Weizmann face datasets, and financial market datasets.",oUhmZozjgfIJ,"W Wang, V Aggarwal, S Aeron - IEEE Transactions on Signal …, 2018 - ieeexplore.ieee.org",['https://arxiv.org/pdf/1712.00828'],https://ieeexplore.ieee.org/abstract/document/8319501/,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/1712.00828'],tensor train neighborhood preserving embedding,MPO/TT 压缩,1,IEEE Transactions on Signal Processing,
"Ergodicity, entanglement and many-body localization","DA Abanin, E Altman, I Bloch, M Serbyn",2018.0,35,"… We compute topological entanglement entropies of these … I will discuss the renormalization group flow of the irreducible … In modern language, this method can be viewed as a …",5CIY8yRWdxkJ,"DA Abanin, E Altman, I Bloch, M Serbyn - arXiv preprint arXiv …, 2018 - pks.mpg.de",['https://www.pks.mpg.de/~tcqs14/Abstracts_Talks.pdf'],https://www.pks.mpg.de/~tcqs14/Abstracts_Talks.pdf,unknown,unknown,互信息/标度,,['https://www.pks.mpg.de/~tcqs14/Abstracts_Talks.pdf'],ergodicity entanglement and many body localization,互信息/标度,1,arXiv (Cornell University),
LTNN: A layerwise tensorized compression of multilayer neural network,"H Huang, H Yu",2018.0,34,"… neural networks. Furthermore, we define an LTNN if the weight of the neural network can be represented in the tensortrain … be reshaped to a k1 + k2 dimensional tensor by factorizing …",JqLaOdUmjkIJ,"H Huang, H Yu - IEEE transactions on neural networks and …, 2018 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/8480873/,unknown,unknown,MPO/TT 压缩,,[],ltnn a layerwise tensorized compression of multilayer neural network,MPO/TT 压缩,1,,
Tensorial neural networks: Generalization of neural networks and application to model compression,"J Su, J Li, B Bhattacharjee, F Huang",2018.0,26,"We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds to hierarchical nonlinear tensor decomposition. We propose to solve the learning problem using stochastic gradient descent by deriving nontrivial backpropagation rules in generalized tensor algebra we introduce. Our proposed TNNs has three advantages over existing neural networks: (1) TNNs naturally apply to high order input object and thus preserve the multi-dimensional structure in the input, as there is no need to flatten the data. (2) TNNs interpret designs of existing neural network architectures. (3) Mapping a neural network to TNNs with the same expressive power results in a TNN of fewer parameters. TNN based compression of neural network improves existing low-rank approximation based compression methods as TNNs exploit two other types of invariant structures, periodicity and modulation, in addition to the low rankness. Experiments on LeNet-5 (MNIST), ResNet-32 (CIFAR10) and ResNet-50 (ImageNet) demonstrate that our TNN based compression outperforms (5% test accuracy improvement universally on CIFAR10) the state-of-the-art low-rank approximation based compression methods under the same compression rate, besides achieving orders of magnitude faster convergence rates due to the efficiency of TNNs.",_j9UGBRHXm0J,"J Su, J Li, B Bhattacharjee, F Huang - arXiv preprint arXiv:1805.10352, 2018 - arxiv.org",['https://arxiv.org/pdf/1805.10352'],https://arxiv.org/abs/1805.10352,unknown,unknown,MPO/TT 压缩,1805.10352,['https://arxiv.org/pdf/1805.10352'],tensorial neural networks generalization of neural networks and application to model compression,MPO/TT 压缩,1,arXiv (Cornell University),
Entanglement-guided architectures of machine learning by quantum tensor network,"Y Liu, X Zhang, M Lewenstein, SJ Ran",2018.0,24,"It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this question would bring important insights to both fields of machine learning and quantum mechanics. In this work, we implement simple numerical experiments, related to pattern/images classification, in which we represent the classifiers by many-qubit quantum states written in the matrix product states (MPS). Classical machine learning algorithm is applied to these quantum states to learn the classical data. We explicitly show how quantum entanglement (i.e., single-site and bipartite entanglement) can emerge in such represented images. Entanglement characterizes here the importance of data, and such information are practically used to guide the architecture of MPS, and improve the efficiency. The number of needed qubits can be reduced to less than 1/10 of the original number, which is within the access of the state-of-the-art quantum computers. We expect such numerical experiments could open new paths in charactering classical machine learning algorithms, and at the same time shed lights on the generic quantum simulations/computations of machine learning tasks.",gY2gpKgNiCUJ,"Y Liu, X Zhang, M Lewenstein, SJ Ran - arXiv preprint arXiv:1803.09111, 2018 - arxiv.org",['https://arxiv.org/pdf/1803.09111'],https://arxiv.org/abs/1803.09111,unknown,unknown,TTN/MERA/PEPS,1803.09111,['https://arxiv.org/pdf/1803.09111'],entanglement guided architectures of machine learning by quantum tensor network,TTN/MERA/PEPS,1,"Front. Appl. Math. Stat., 06 August 2021",
Renormalization of Entanglement Entropy from topological terms,"G Anastasiou, IJ Araya, R Olea",2018.0,19,"… a renormalization scheme for entanglement entropy of three-… for the renormalized entanglement entropy, which is derived … a Euclidean gravitational action renormalized by the addition …",JHt0NlIZZMYJ,"G Anastasiou, IJ Araya, R Olea - Physical Review D, 2018 - APS",['https://link.aps.org/pdf/10.1103/PhysRevD.97.106011'],https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.106011,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PhysRevD.97.106011'],renormalization of entanglement entropy from topological terms,互信息/标度,1,,
Tensor networks as conformal transformations,"A Milsted, G Vidal",2018.0,14,"Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time evolution and to global scale transformations. In this paper, by exploiting the local structure of the tensor networks, we explain how to also implement local or non-uniform versions of both euclidean time evolution and scale transformations. We demonstrate our proposal with a critical quantum spin chain on a finite circle, where the low energy physics is described by a conformal field theory (CFT), and where non-uniform euclidean time evolution and local scale transformations are conformal transformations acting on the Hilbert space of the CFT. We numerically show, for the critical quantum Ising chain, that the proposed tensor networks indeed transform the low energy states of the periodic spin chain in the same way as the corresponding conformal transformations do in the CFT.",,"A Milsted, G Vidal - arXiv preprint arXiv:1805.12524, 2018 - arxiv.org",[],https://arxiv.org/abs/1805.12524,arxiv-completion,2026-09-26 (citations:OpenAlex),互信息/标度,1805.12524,['https://arxiv.org/pdf/1805.12524'],tensor networks as conformal transformations,互信息/标度,1,,
Compressing End-to-end ASR Networks by Tensor-Train Decomposition.,"T Mori, A Tjandra, S Sakti, S Nakamura",2018.0,13,"… parameters of a neural network can be decomposed and compressed by tensor train in MIDI … , no study has focused on compressing more complex neural networks with tensor-based …",lNcWuZJ3SXIJ,"T Mori, A Tjandra, S Sakti, S Nakamura - Interspeech, 2018 - isca-archive.org",['https://www.isca-archive.org/interspeech_2018/mori18_interspeech.pdf'],https://www.isca-archive.org/interspeech_2018/mori18_interspeech.pdf,unknown,unknown,MPO/TT 压缩,,['https://www.isca-archive.org/interspeech_2018/mori18_interspeech.pdf'],compressing end to end asr networks by tensor train decomposition,MPO/TT 压缩,1,,
Tensor Decomposition for Compressing Recurrent Neural Network,"A Tjandra, S Sakti, S Nakamura",2018.0,6,"In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and inference. In this paper, we are trying to reduce the number of parameters and maintain the expressive power from RNN simultaneously. We utilize several tensor decompositions method including CANDECOMP/PARAFAC (CP), Tucker decomposition and Tensor Train (TT) to re-parameterize the Gated Recurrent Unit (GRU) RNN. We evaluate all tensor-based RNNs performance on sequence modeling tasks with a various number of parameters. Based on our experiment results, TT-GRU achieved the best results in a various number of parameters compared to other decomposition methods.",,"A Tjandra, S Sakti, S Nakamura - arXiv preprint arXiv:1802.10410, 2018 - arxiv.org",[],https://arxiv.org/abs/1802.10410,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1802.10410,['https://arxiv.org/pdf/1802.10410'],tensor decomposition for compressing recurrent neural network,MPO/TT 压缩 / MPS/序列建模,1,,
Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT,"N Bao, G Penington, J Sorce, A C Wall",2018.0,2,"We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs). Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, we build a tensor network by an iterative series of approximations that eliminate redundant degrees of freedom and minimize the bond dimensions of the resulting network. We argue that the bond dimensions of the tensor network will match the areas of the corresponding bulk surfaces. For 'tree' tensor networks (i.e., those that are constructed by discretizing spacetime with non-intersecting Ryu-Takayanagi surfaces), our arguments can be made rigorous using a version of one-shot entanglement distillation in the CFT. Using the known quantum error correcting properties of AdS/CFT, we show that bulk legs can be added to the tensor networks to create holographic quantum error correcting codes. These codes behave similarly to previous holographic tensor network toy models, but describe actual bulk excitations in continuum AdS/CFT. By assuming some natural generalizations of the 'holographic entanglement of purification' conjecture, we are able to construct tensor networks for more general bulk discretizations, leading to finer-grained networks that partition the information content of a Ryu-Takayanagi surface into tensor-factorized subregions. While the granularity of such a tensor network must be set larger than the string/Planck scales, we expect that it can be chosen to lie well below the AdS scale. However, we also prove a no-go theorem which shows that the bulk-to-boundary maps cannot all be isometries in a tensor network with intersecting Ryu-Takayanagi surfaces.",,"N Bao, G Penington, J Sorce, A C Wall - JHEP 2019:69",[],https://arxiv.org/abs/1812.01171,arxiv-completion,2026-09-26 (citations:OpenAlex),互信息/标度,1812.01171,['https://arxiv.org/pdf/1812.01171'],beyond toy models distilling tensor networks in full ads cft,互信息/标度,1,JHEP 2019:69,
Comparative study of Discrete Wavelet Transforms and Wavelet Tensor Train decomposition to feature extraction of FTIR data of medicinal plants,"P Kharyuk, D Nazarenko, I Oseledets",2018.0,2,"Fourier-transform infra-red (FTIR) spectra of samples from 7 plant species were used to explore the influence of preprocessing and feature extraction on efficiency of machine learning algorithms. Wavelet Tensor Train (WTT) and Discrete Wavelet Transforms (DWT) were compared as feature extraction techniques for FTIR data of medicinal plants. Various combinations of signal processing steps showed different behavior when applied to classification and clustering tasks. Best results for WTT and DWT found through grid search were similar, significantly improving quality of clustering as well as classification accuracy for tuned logistic regression in comparison to original spectra. Unlike DWT, WTT has only one parameter to be tuned (rank), making it a more versatile and easier to use as a data processing tool in various signal processing applications.",,"P Kharyuk, D Nazarenko, I Oseledets - arXiv preprint arXiv:1807.07099, 2018 - arxiv.org",[],https://arxiv.org/abs/1807.07099,arxiv-completion,2026-09-26 (citations:OpenAlex),,1807.07099,['https://arxiv.org/pdf/1807.07099'],comparative study of discrete wavelet transforms and wavelet tensor train decomposition to feature extraction of ftir data of medicinal plants,,1,,
Convolutional Neural Networks with Transformed Input based on Robust Tensor Network Decomposition,"J Ong, W Ng, C - J Kuo",2018.0,2,"Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this study, we show that tensor networks can systematically partition structured data, e.g. color images, for distributed storage and communication in privacy-preserving manner. Leveraging the sea of big data and metadata privacy, empirical results show that neighbouring subtensors with implicit information stored in tensor network formats cannot be identified for data reconstruction. This technique complements the existing encryption and randomization techniques which store explicit data representation at one place and highly susceptible to adversarial attacks such as side-channel attacks and de-anonymization. Furthermore, we propose a theory for adversarial examples that mislead convolutional neural networks to misclassification using subspace analysis based on singular value decomposition (SVD). The theory is extended to analyze higher-order tensors using tensor-train SVD (TT-SVD); it helps to explain the level of susceptibility of different datasets to adversarial attacks, the structural similarity of different adversarial attacks including global and localized attacks, and the efficacy of different adversarial defenses based on input transformation. An efficient and adaptive algorithm based on robust TT-SVD is then developed to detect strong and static adversarial attacks.",,"J Ong, W Ng, C - J Kuo - arXiv preprint arXiv:1812.02622, 2018 - arxiv.org",[],https://arxiv.org/abs/1812.02622,arxiv-completion,2026-09-26 (citations:OpenAlex),,1812.02622,['https://arxiv.org/pdf/1812.02622'],convolutional neural networks with transformed input based on robust tensor network decomposition,,2,,
Differentiable Learning of Quantum Circuit Born Machine,"J Liu, L Wang",2018.0,0,"Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. One can efficiently draw samples from the quantum circuits via projective measurements on qubits. However, similar to the leading implicit generative models in deep learning, such as the generative adversarial networks, the quantum circuits cannot provide the likelihood of the generated samples, which poses a challenge to the training. We devise an efficient gradient-based learning algorithm for the quantum circuit Born machine by minimizing the kerneled maximum mean discrepancy loss. We simulated generative modeling of the Bars-and-Stripes dataset and Gaussian mixture distributions using deep quantum circuits. Our experiments show the importance of circuit depth and gradient-based optimization algorithm. The proposed learning algorithm is runnable on near-term quantum device and can exhibit quantum advantages for generative modeling.",,"J Liu, L Wang - Phys. Rev. A 98, 062324 (2018)",[],https://arxiv.org/abs/1804.04168,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,1804.04168,['https://arxiv.org/pdf/1804.04168'],differentiable learning of quantum circuit born machine,MPS 生成/Born机,1,"Phys. Rev. A 98, 062324 (2018)",
Quantum Machine Learning Tensor Network States,"A Kardashin, A Uvarov, J Biamonte",2018.0,0,"Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods used to simulate many-body physics and have a further range of applications in machine learning. Finding and contracting tensor network states is a computational task which quantum computers might be used to accelerate. We present a quantum algorithm which returns a classical description of a rank-$r$ tensor network state satisfying an area law and approximating an eigenvector given black-box access to a unitary matrix. Our work creates a bridge between several contemporary approaches, including tensor networks, the variational quantum eigensolver (VQE), quantum approximate optimization (QAOA), and quantum computation.",,"A Kardashin, A Uvarov, J Biamonte - Frontiers in Physics 8: 586374 (2021)",[],https://arxiv.org/abs/1804.02398,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1804.02398,['https://arxiv.org/pdf/1804.02398'],quantum machine learning tensor network states,MPO/TT 压缩 / 量子/混合LLM / 互信息/标度,1,Frontiers in Physics 8: 586374 (2021),
Towards Quantum Machine Learning with Tensor Networks,"W Huggins, P Patel, K B Whaley, E M Stoudenmire",2018.0,0,"Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.",,"W Huggins, P Patel, K B Whaley, E M Stoudenmire - Quantum Science and Technology, Volume 4, 024001 (2019)",[],https://arxiv.org/abs/1803.11537,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,1803.11537,['https://arxiv.org/pdf/1803.11537'],towards quantum machine learning with tensor networks,MPS 生成/Born机 / 量子/混合LLM,1,"Quantum Science and Technology, Volume 4, 024001 (2019)",
Efficient Low-rank Multimodal Fusion with Modality-Specific Factors,"Z Liu, Y Shen, V B Lakshminarasimhan, P P Liang, A Zadeh, L Morency",2018.0,,"Multimodal research is an emerging field of artificial intelligence, and one of the main research problems in this field is multimodal fusion. The fusion of multimodal data is the process of integrating multiple unimodal representations into one compact multimodal representation. Previous research in this field has exploited the expressiveness of tensors for multimodal representation. However, these methods often suffer from exponential increase in dimensions and in computational complexity introduced by transformation of input into tensor. In this paper, we propose the Low-rank Multimodal Fusion method, which performs multimodal fusion using low-rank tensors to improve efficiency. We evaluate our model on three different tasks: multimodal sentiment analysis, speaker trait analysis, and emotion recognition. Our model achieves competitive results on all these tasks while drastically reducing computational complexity. Additional experiments also show that our model can perform robustly for a wide range of low-rank settings, and is indeed much more efficient in both training and inference compared to other methods that utilize tensor representations.",,"Z Liu, Y Shen, V B Lakshminarasimhan, P P Liang, A Zadeh, L Morency - arXiv preprint arXiv:1806.00064, 2018 - arxiv.org",[],https://arxiv.org/abs/1806.00064,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1806.00064,['https://arxiv.org/pdf/1806.00064'],efficient low rank multimodal fusion with modality specific factors,MPO/TT 压缩,1,,
Reconstructing quantum states with generative models,"J Carrasquilla, G Torlai, RG Melko…",2019.0,474,"… method for density matrix reconstruction based on neural network generative models. The learning … Notably, even though matrix product state (MPS) tomography 16,18,19 has led to …",ykbRWmyXTWwJ,"J Carrasquilla, G Torlai, RG Melko… - Nature Machine …, 2019 - nature.com",['https://arxiv.org/pdf/1810.10584'],https://www.nature.com/articles/s42256-019-0028-1,unknown,unknown,MPS 生成/Born机,,['https://arxiv.org/pdf/1810.10584'],reconstructing quantum states with generative models,MPS 生成/Born机,1,,
Quantum entanglement in deep learning architectures,"Y Levine, O Sharir, N Cohen, A Shashua",2019.0,338,"… such as restricted Boltzmann machines (RBMs) and fully … deep learning architectures, in the form of deep convolutional and recurrent networks, can efficiently represent highly entangled …",Pw40CDdOdhoJ,"Y Levine, O Sharir, N Cohen, A Shashua - Physical review letters, 2019 - APS",['https://arxiv.org/pdf/1803.09780'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.065301,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1803.09780'],quantum entanglement in deep learning architectures,TTN/MERA/PEPS,1,,
Tree tensor networks for generative modeling,"S Cheng, L Wang, T Xiang, P Zhang",2019.0,329,… We have presented a generative model based on tree tensor networks. This model is a direct extension of the matrix product state Born machine [14] and also a generalization of the tree…,aAL4L6VjeU0J,"S Cheng, L Wang, T Xiang, P Zhang - Physical Review B, 2019 - APS",['https://arxiv.org/pdf/1901.02217'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.155131,unknown,unknown,MPS 生成/Born机,,['https://arxiv.org/pdf/1901.02217'],tree tensor networks for generative modeling,MPS 生成/Born机 / TTN/MERA/PEPS,2,,
A tensorized transformer for language modeling,"X Ma, P Zhang, S Zhang, N Duan…",2019.0,273,"Latest development of neural models has connected the encoder and decoder through a self-attention mechanism. In particular, Transformer, which is solely based on self-attention, has led to breakthroughs in Natural Language Processing (NLP) tasks. However, the multi-head attention mechanism, as a key component of Transformer, limits the effective deployment of the model to a resource-limited setting. In this paper, based on the ideas of tensor decomposition and parameters sharing, we propose a novel self-attention model (namely Multi-linear attention) with Block-Term Tensor Decomposition (BTD). We test and verify the proposed attention method on three language modeling tasks (i.e., PTB, WikiText-103 and One-billion) and a neural machine translation task (i.e., WMT-2016 English-German). Multi-linear attention can not only largely compress the model parameters but also obtain performance improvements, compared with a number of language modeling approaches, such as Transformer, Transformer-XL, and Transformer with tensor train decomposition.",orxX2kCPKo0J,"X Ma, P Zhang, S Zhang, N Duan… - Advances in neural …, 2019 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2019/file/dc960c46c38bd16e953d97cdeefdbc68-Paper.pdf'],https://proceedings.neurips.cc/paper_files/paper/8495-a-tensorized-transformer-for-language-modeling,unknown,unknown,MPO/TT 压缩,1906.09777,['https://proceedings.neurips.cc/paper_files/paper/2019/file/dc960c46c38bd16e953d97cdeefdbc68-Paper.pdf'],a tensorized transformer for language modeling,MPO/TT 压缩 / 张量化Transformer,2,arXiv (Cornell University),
Expressive power of tensor-network factorizations for probabilistic modeling,"I Glasser, R Sweke, N Pancotti…",2019.0,206,"Tensor-network techniques have recently proven useful in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods.Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensornetwork factorizations of discrete multivariate probability distributions.These factorizations include non-negative tensor-trains/MPS, which are in correspondence with hidden Markov models, and Born machines, which are naturally related to the probabilistic interpretation of quantum circuits.When used to model probability distributions, they exhibit tractable likelihoods and admit efficient learning algorithms.Interestingly, we prove that there exist probability distributions for which there are unbounded separations between the resource requirements of some of these tensor-network factorizations.Of particular interest, using complex instead of real tensors can lead to an arbitrarily large reduction in the number of parameters of the network.Additionally, we introduce locally purified states (LPS), a new factorization inspired by techniques for the simulation of quantum systems, with provably better expressive power than all other representations considered.The ramifications of this result are explored through numerical experiments.",nDRLkZpVhA0J,"I Glasser, R Sweke, N Pancotti… - Advances in neural …, 2019 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2019/file/b86e8d03fe992d1b0e19656875ee557c-Paper.pdf'],https://proceedings.neurips.cc/paper_files/paper/2019/hash/b86e8d03fe992d1b0e19656875ee557c-Abstract.html,unknown,unknown,MPS/序列建模,1907.03741,['https://proceedings.neurips.cc/paper_files/paper/2019/file/b86e8d03fe992d1b0e19656875ee557c-Paper.pdf'],expressive power of tensor network factorizations for probabilistic modeling,MPS/序列建模,1,MPG.PuRe (Max Planck Society),
Machine learning by unitary tensor network of hierarchical tree structure,"D Liu, SJ Ran, P Wittek, C Peng, RB García…",2019.0,187,"… The tensors in the TTN are updated alternatively to minimize … other tensors are fixed and define the environment tensor E [k,m… a TN with a hierarchical tree structure, called tree TN (TTN). …",GHEZQVpO3ywJ,"D Liu, SJ Ran, P Wittek, C Peng, RB García… - New Journal of …, 2019 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/1367-2630/ab31ef/pdf'],https://iopscience.iop.org/article/10.1088/1367-2630/ab31ef/meta,unknown,unknown,TTN/MERA/PEPS,1710.04833,['https://iopscience.iop.org/article/10.1088/1367-2630/ab31ef/pdf'],machine learning by unitary tensor network of hierarchical tree structure,TTN/MERA/PEPS,1,"New Journal of Physics, 21, 073059 (2019)",
Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion,"L Yuan, C Li, D P Mandic, J Cao, Q Zhao",2019.0,182,"In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.",,"L Yuan, C Li, D P Mandic, J Cao, Q Zhao - Proceedings of the AAAI Conference on Artificial Intelligence, 2019",[],https://doi.org/10.1609/aaai.v33i01.33019151,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,,[],tensor ring decomposition with rank minimization on latent space an efficient approach for tensor completion,MPO/TT 压缩,1,Proceedings of the AAAI Conference on Artificial Intelligence,
TTHRESH: Tensor Compression for Multidimensional Visual Data,"R Ballester‐Ripoll, P Lindström, R Pajarola",2019.0,178,"Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy compression algorithm for multidimensional data over regular grids. It leverages the higher-order singular value decomposition (HOSVD), a generalization of the SVD to three dimensions and higher, together with bit-plane, run-length and arithmetic coding to compress the HOSVD transform coefficients. Our scheme degrades the data particularly smoothly and achieves lower mean squared error than other state-of-the-art algorithms at low-to-medium bit rates, as it is required in data archiving and management for visualization purposes. Further advantages of the proposed algorithm include very fine bit rate selection granularity and the ability to manipulate data at very small cost in the compression domain, for example to reconstruct filtered and/or subsampled versions of all (or selected parts) of the data set.",,"R Ballester‐Ripoll, P Lindström, R Pajarola - IEEE Transactions on Visualization and Computer Graphics",[],https://arxiv.org/abs/1806.05952,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1806.05952,['https://arxiv.org/pdf/1806.05952'],tthresh tensor compression for multidimensional visual data,MPO/TT 压缩,1,IEEE Transactions on Visualization and Computer Graphics,
Compressing recurrent neural networks with tensor ring for action recognition,"Y Pan, J Xu, M Wang, J Ye, F Wang, K Bai…",2019.0,151,"… matrix W by running the linear regression, tensor train decomposition, and tensor ring decomposition, respectively. For tensor train and tensor ring, we first reshape input data to a …",7kILs_3GTmAJ,"Y Pan, J Xu, M Wang, J Ye, F Wang, K Bai… - Proceedings of the AAAI …, 2019 - aaai.org",['https://aaai.org/ojs/index.php/AAAI/article/view/4393/4271'],https://aaai.org/ojs/index.php/AAAI/article/view/4393,unknown,unknown,MPO/TT 压缩,1811.07503,['https://aaai.org/ojs/index.php/AAAI/article/view/4393/4271'],compressing recurrent neural networks with tensor ring for action recognition,MPO/TT 压缩,1,,
TIE: Energy-efficient tensor train-based inference engine for deep neural network,"C Deng, F Sun, X Qian, J Lin, Z Wang…",2019.0,112,… compression becomes a crucial technique to ensure wide deployment of DNNs. This paper advances the state-of-the-art by considering tensor train (… extremely high compression ratio. …,ZwVVjUkn5R4J,"C Deng, F Sun, X Qian, J Lin, Z Wang… - Proceedings of the 46th …, 2019 - dl.acm.org",['https://dl.acm.org/doi/pdf/10.1145/3307650.3322258'],https://dl.acm.org/doi/abs/10.1145/3307650.3322258,unknown,unknown,MPO/TT 压缩,,['https://dl.acm.org/doi/pdf/10.1145/3307650.3322258'],tie energy efficient tensor train based inference engine for deep neural network,MPO/TT 压缩,1,,
Matrix product state–based quantum classifier,"AS Bhatia, MK Saggi, A Kumar, S Jain",2019.0,73,"… In this letter, we have illustrated that a matrix product state quantum classifier can be used to classify quantum data efficiently. We have focused on an … Tensor network language model …",O05tOS1N6qgJ,"AS Bhatia, MK Saggi, A Kumar, S Jain - Neural computation, 2019 - direct.mit.edu",['https://arxiv.org/pdf/1905.01426'],https://direct.mit.edu/neco/article-abstract/31/7/1499/8488,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/1905.01426'],matrix product state based quantum classifier,MPS 语言模型,1,,
TensorNetwork: A Library for Physics and Machine Learning,"C Roberts, A Milsted, M Ganahl, A Zalcman, B Fontaine, Y Zou, J Hidary, G Vidal, S Leichenauer",2019.0,70,"TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other research areas, including machine learning. We demonstrate the use of the API with applications both physics and machine learning, with details appearing in companion papers.",,"C Roberts, A Milsted, M Ganahl, A Zalcman, B Fontaine, Y Zou, J Hidary, G Vidal, S Leichenauer - arXiv preprint arXiv:1905.01330, 2019 - arxiv.org",[],https://arxiv.org/abs/1905.01330,arxiv-completion,2026-09-26 (citations:OpenAlex),,1905.01330,['https://arxiv.org/pdf/1905.01330'],tensornetwork a library for physics and machine learning,,2,,
TensorNetwork for Machine Learning,"S Efthymiou, J Hidary, S Leichenauer",2019.0,62,"We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a way that is parallelizable and well-suited to automatic gradients for optimization. Applying the technique to the MNIST and Fashion-MNIST datasets we find out-of-the-box performance of 98% and 88% accuracy, respectively, using the same tensor network architecture. The TensorNetwork library allows us to seamlessly move from CPU to GPU hardware, and we see a factor of more than 10 improvement in computational speed using a GPU.",,"S Efthymiou, J Hidary, S Leichenauer - arXiv preprint arXiv:1906.06329, 2019 - arxiv.org",[],https://arxiv.org/abs/1906.06329,arxiv-completion,2026-09-26 (citations:OpenAlex),,1906.06329,['https://arxiv.org/pdf/1906.06329'],tensornetwork for machine learning,,1,,
Compression of recurrent neural networks for efficient language modeling,"AM Grachev, DI Ignatov, AV Savchenko",2019.0,55,… compression of neural networks based on different matrix factorization methods. Section 4.3 deals with Tensor … of the methodology to compress RNN-based language models and make …,2rUNtpjyQJ8J,"AM Grachev, DI Ignatov, AV Savchenko - Applied Soft Computing, 2019 - Elsevier",['https://arxiv.org/pdf/1902.02380'],https://www.sciencedirect.com/science/article/pii/S1568494619301851,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/1902.02380'],compression of recurrent neural networks for efficient language modeling,MPO/TT 压缩,1,Applied Soft Computing,
Probabilistic modeling with matrix product states,"J Stokes, J Terilla",2019.0,53,"… a low rank matrix product state (MPS) factorization. Vectors in this model hypothesis class have … For simplicity of presentation, we consider matrix product states with a single fixed bond …",JNIMRdRnuowJ,"J Stokes, J Terilla - Entropy, 2019 - mdpi.com",[],https://www.mdpi.com/1099-4300/21/12/1236,unknown,unknown,MPS 语言模型,1902.06888,[],probabilistic modeling with matrix product states,MPS 生成/Born机 / MPS 语言模型 / MPS/序列建模,3,,
Tensorized Embedding Layers for Efficient Model Compression,"O Hrinchuk, V Khrulkov, L Mirvakhabova, E Orlova, I Oseledets",2019.0,50,"The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing. However, when the vocabulary is large, the corresponding weight matrices can be enormous, which precludes their deployment in a limited resource setting. We introduce a novel way of parametrizing embedding layers based on the Tensor Train (TT) decomposition, which allows compressing the model significantly at the cost of a negligible drop or even a slight gain in performance. We evaluate our method on a wide range of benchmarks in natural language processing and analyze the trade-off between performance and compression ratios for a wide range of architectures, from MLPs to LSTMs and Transformers.",,"O Hrinchuk, V Khrulkov, L Mirvakhabova, E Orlova, I Oseledets - arXiv preprint arXiv:1901.10787, 2019 - arxiv.org",[],https://arxiv.org/abs/1901.10787,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,1901.10787,['https://arxiv.org/pdf/1901.10787'],tensorized embedding layers for efficient model compression,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩,1,,
Mutual information scaling and expressive power of sequence models,H Shen,2019.0,26,"Sequence models assign probabilities to variable-length sequences such as natural language texts. The ability of sequence models to capture temporal dependence can be characterized by the temporal scaling of correlation and mutual information. In this paper, we study the mutual information of recurrent neural networks (RNNs) including long short-term memories and self-attention networks such as Transformers. Through a combination of theoretical study of linear RNNs and empirical study of nonlinear RNNs, we find their mutual information decays exponentially in temporal distance. On the other hand, Transformers can capture long-range mutual information more efficiently, making them preferable in modeling sequences with slow power-law mutual information, such as natural languages and stock prices. We discuss the connection of these results with statistical mechanics. We also point out the non-uniformity problem in many natural language datasets. We hope this work provides a new perspective in understanding the expressive power of sequence models and shed new light on improving the architecture of them.",_2N5Bqidv9MJ,"H Shen - arXiv preprint arXiv:1905.04271, 2019 - arxiv.org",['https://arxiv.org/pdf/1905.04271'],https://arxiv.org/abs/1905.04271,unknown,unknown,互信息/标度,1905.04271,['https://arxiv.org/pdf/1905.04271'],mutual information scaling and expressive power of sequence models,互信息/标度,1,,
Entanglement at a scale and renormalization monotones,N Lashkari,2019.0,24,… We define the entanglement of scaling and the entanglement of recovery as measures of entanglement … We replace the entanglement entropies in CMI with the entanglement of scaling: …,f2Mf7uSU21kJ,"N Lashkari - Journal of High Energy Physics, 2019 - Springer",['https://link.springer.com/content/pdf/10.1007/JHEP01%282019%29219.pdf'],https://link.springer.com/article/10.1007/JHEP01(2019)219,unknown,unknown,互信息/标度,1704.05077,['https://link.springer.com/content/pdf/10.1007/JHEP01%282019%29219.pdf'],entanglement at a scale and renormalization monotones,互信息/标度,1,JHEP 1901(2019) 219,
Learning high-dimensional probability distributions using tree tensor networks,"E Grelier, A Nouy, R Lebrun",2019.0,12,"We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density with respect to a product measure, possibly discrete for handling the case of discrete random variables. After discussing the representation of classical model classes in tree-based tensor formats, we present learning algorithms based on empirical risk minimization using a $L^2$ contrast. These algorithms exploit the multilinear parametrization of the formats to recast the nonlinear minimization problem into a sequence of empirical risk minimization problems with linear models. A suitable parametrization of the tensor in tree-based tensor format allows to obtain a linear model with orthogonal bases, so that each problem admits an explicit expression of the solution and cross-validation risk estimates. These estimations of the risk enable the model selection, for instance when exploiting sparsity in the coefficients of the representation. A strategy for the adaptation of the tensor format (dimension tree and tree-based ranks) is provided, which allows to discover and exploit some specific structures of high-dimensional probability distributions such as independence or conditional independence. We illustrate the performances of the proposed algorithms for the approximation of classical probabilistic models (such as Gaussian distribution, graphical models, Markov chain).",A3ySqLeS62IJ,"E Grelier, A Nouy, R Lebrun - arXiv preprint arXiv:1912.07913, 2019 - arxiv.org",['https://arxiv.org/pdf/1912.07913'],https://arxiv.org/abs/1912.07913,unknown,unknown,MPS/序列建模,1912.07913,"['https://arxiv.org/pdf/1912.07913', 'https://hal.science/hal-03919932v1/file/1912.07913v3.pdf']",learning high dimensional probability distributions using tree tensor networks,MPS/序列建模,2,International Journal for Uncertainty Quantification,
Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning,S Ran,2019.0,4,"It is known that describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, Bayesian tensor network (BTN) is proposed to efficiently capture the conditional probabilities of multiple sets of events with polynomial complexity. BTN is a directed acyclic graphical model that forms a subset of TN. To testify its validity for exponentially many events, BTN is implemented to the image recognition, where the classification is mapped to capturing the conditional probabilities in an exponentially large sample space. Competitive performance is achieved by the BTN with simple tree network structures. Analogous to the tensor network simulations of quantum systems, the validity of the simple-tree BTN implies an ``area law'' of fluctuations in image recognition problems.",,"S Ran - arXiv preprint arXiv:1912.12923, 2019 - arxiv.org",[],https://arxiv.org/abs/1912.12923,arxiv-completion,2026-09-26 (citations:OpenAlex),互信息/标度,1912.12923,['https://arxiv.org/pdf/1912.12923'],bayesian tensor network with polynomial complexity for probabilistic machine learning,互信息/标度,1,,
Machine learning methods in quantum computing theory,"D V Fastovets, Y I Bogdanov, B I Bantysh, V F Lukichev",2019.0,1,"Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. The quantum machine learning includes hybrid methods that involve both classical and quantum algorithms. Quantum approaches can be used to analyze quantum states instead of classical data. On other side, quantum algorithms can exponentially improve classical data science algorithm. Here, we show basic ideas of quantum machine learning. We present several new methods that combine classical machine learning algorithms and quantum computing methods. We demonstrate multiclass tree tensor network algorithm, and its approbation on IBM quantum processor. Also, we introduce neural networks approach to quantum tomography problem. Our tomography method allows us to predict quantum state excluding noise influence. Such classical-quantum approach can be applied in various experiments to reveal latent dependence between input data and output measurement results.",,"D V Fastovets, Y I Bogdanov, B I Bantysh, V F Lukichev - arXiv preprint arXiv:1906.10175, 2019 - arxiv.org",[],https://arxiv.org/abs/1906.10175,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,1906.10175,['https://arxiv.org/pdf/1906.10175'],machine learning methods in quantum computing theory,量子/混合LLM / TTN/MERA/PEPS,1,,
Differentiable Programming Tensor Networks,"H Liao, J Liu, L Wang, T Xiang",2019.0,1,"Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using AD. We present essential techniques to differentiate through the tensor networks contractions, including stable AD for tensor decomposition and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.",,"H Liao, J Liu, L Wang, T Xiang - Phys. Rev. X 9, 031041 (2019)",[],https://arxiv.org/abs/1903.09650,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1903.09650,['https://arxiv.org/pdf/1903.09650'],differentiable programming tensor networks,TTN/MERA/PEPS,1,"Phys. Rev. X 9, 031041 (2019)",
The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine,"B Coyle, D Mills, V Danos, E Kashefi",2019.0,1,"The search for an application of near-term quantum devices is widespread. Quantum Machine Learning is touted as a potential utilisation of such devices, particularly those which are out of the reach of the simulation capabilities of classical computers. In this work, we propose a generative Quantum Machine Learning Model, called the Ising Born Machine (IBM), which we show cannot, in the worst case, and up to suitable notions of error, be simulated efficiently by a classical device. We also show this holds for all the circuit families encountered during training. In particular, we explore quantum circuit learning using non-universal circuits derived from Ising Model Hamiltonians, which are implementable on near term quantum devices. We propose two novel training methods for the IBM by utilising the Stein Discrepancy and the Sinkhorn Divergence cost functions. We show numerically, both using a simulator within Rigetti's Forest platform and on the Aspen-1 16Q chip, that the cost functions we suggest outperform the more commonly used Maximum Mean Discrepancy (MMD) for differentiable training. We also propose an improvement to the MMD by proposing a novel utilisation of quantum kernels which we demonstrate provides improvements over its classical counterpart. We discuss the potential of these methods to learn `hard' quantum distributions, a feat which would demonstrate the advantage of quantum over classical computers, and provide the first formal definitions for what we call `Quantum Learning Supremacy'. Finally, we propose a novel view on the area of quantum circuit compilation by using the IBM to `mimic' target quantum circuits using classical output data only.",,"B Coyle, D Mills, V Danos, E Kashefi - npj Quantum Inf 6, 60 (2020)",[],https://arxiv.org/abs/1904.02214,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,1904.02214,['https://arxiv.org/pdf/1904.02214'],the born supremacy quantum advantage and training of an ising born machine,MPS 生成/Born机 / 量子/混合LLM,1,"npj Quantum Inf 6, 60 (2020)",
A machine learning approach to dynamical properties of quantum many-body systems,"D Hendry, A E Feiguin",2019.0,0,"Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Green's function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional $J_1-J_2$ Heisenberg model. The method is general and can be extended to other variational forms.",,"D Hendry, A E Feiguin - Phys. Rev. B 100, 245123 (2019)",[],https://arxiv.org/abs/1907.01384,arxiv-completion,2026-09-26 (citations:OpenAlex),,1907.01384,['https://arxiv.org/pdf/1907.01384'],a machine learning approach to dynamical properties of quantum many body systems,,1,"Phys. Rev. B 100, 245123 (2019)",
Classical versus Quantum Models in Machine Learning: Insights from a Finance Application,"J Alcazar, V Leyton-Ortega, A Perdomo-Ortiz",2019.0,0,"Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from real-world applications is one of the key milestones towards a quantum ready era. Here, we take a first step towards addressing this challenge by performing a comparison of the widely used classical ML models known as restricted Boltzmann machines (RBMs), against a recently proposed quantum model, now known as quantum circuit Born machines (QCBMs). Both models address the same hard tasks in unsupervised generative modeling, with QCBMs exploiting the probabilistic nature of quantum mechanics and a candidate for near-term quantum computers, as experimentally demonstrated in three different quantum hardware architectures to date. To address the question of the performance of the quantum model on real-world classical data sets, we construct scenarios from a probabilistic version out of the well-known portfolio optimization problem in finance, by using time-series pricing data from asset subsets of the S\&P500 stock market index. It is remarkable to find that, under the same number of resources in terms of parameters for both classical and quantum models, the quantum models seem to have superior performance on typical instances when compared with the canonical training of the RBMs. Our simulations are grounded on a hardware efficient realization of the QCBMs on ion-trap quantum computers, by using their native gate sets, and therefore readily implementable in near-term quantum devices.",,"J Alcazar, V Leyton-Ortega, A Perdomo-Ortiz - arXiv preprint arXiv:1908.10778, 2019 - arxiv.org",[],https://arxiv.org/abs/1908.10778,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,1908.10778,['https://arxiv.org/pdf/1908.10778'],classical versus quantum models in machine learning insights from a finance application,MPS 生成/Born机 / 量子/混合LLM,1,,
Machine Learning Phase Transitions with a Quantum Processor,"A Uvarov, A Kardashin, J Biamonte",2019.0,0,"Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented method recovers. Finally, we propose a nearest-neighbour (checkerboard) quantum neural network. This majority vote quantum classifier is successfully trained to recognize phases of matter with $99\%$ accuracy for the transverse field Ising model and $94\%$ accuracy for the XXZ model. These findings suggest that our merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.",,"A Uvarov, A Kardashin, J Biamonte - Phys. Rev. A 102, 012415 (2020)",[],https://arxiv.org/abs/1906.10155,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,1906.10155,['https://arxiv.org/pdf/1906.10155'],machine learning phase transitions with a quantum processor,量子/混合LLM,1,"Phys. Rev. A 102, 012415 (2020)",
Computing vibrational eigenstates with tree tensor network states (TTNS),H R Larsson,2019.0,0,"We present how to compute vibrational eigenstates with tree tensor network states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group (DMRG). We apply this to compute the vibrational spectrum of acetonitrile (CH$_3$CN) to high accuracy and compare TTNSs with matrix product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme converges much faster than ML-MCTDH-based optimization. For this particular system, we found no major advantage of the more general TTNS over MPS. We highlight that for both TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of required parameters. We furthermore propose a procedure to find good trees.",,"H R Larsson - J. Chem. Phys. 151, 204102 (2019)",[],https://arxiv.org/abs/1909.13831,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,1909.13831,['https://arxiv.org/pdf/1909.13831'],computing vibrational eigenstates with tree tensor network states ttns,TTN/MERA/PEPS,1,"J. Chem. Phys. 151, 204102 (2019)",
"Matrix Product States: Entanglement, symmetries, and state transformations","D Sauerwein, A Molnar, J I Cirac, B Kraus",2019.0,0,"We analyze entanglement in the family of translationally-invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by SLOCC transformations, a central question in entanglement theory. We use that criterion to determine SLOCC classes, and explicitly carry out this classification for the simplest, non-trivial MPS. We also characterize all symmetries of MPS, both global and local (inhomogeneous). We illustrate our results with examples of states that are relevant in different physical contexts.",,"D Sauerwein, A Molnar, J I Cirac, B Kraus - Phys. Rev. Lett. 123, 170504 (2019)",[],https://arxiv.org/abs/1901.07448,arxiv-completion,2026-09-26 (citations:OpenAlex),,1901.07448,['https://arxiv.org/pdf/1901.07448'],matrix product states entanglement symmetries and state transformations,,1,"Phys. Rev. Lett. 123, 170504 (2019)",
Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning,"S Ran, Z Sun, S Fei, G Su, M Lewenstein",2019.0,0,"We propose tensor-network compressed sensing (TNCS) by combining the ideas of compressed sensing, tensor network (TN), and machine learning, which permits novel and efficient quantum communications of realistic data. The strategy is to use the unsupervised TN machine learning algorithm to obtain the entangled state $|Ψ\rangle$ that describes the probability distribution of a huge amount of classical information considered to be communicated. To transfer a specific piece of information with $|Ψ\rangle$, our proposal is to encode such information in the separable state with the minimal distance to the measured state $|Φ\rangle$ that is obtained by partially measuring on $|Ψ\rangle$ in a designed way. To this end, a measuring protocol analogous to the compressed sensing with neural-network machine learning is suggested, where the measurements are designed to minimize uncertainty of information from the probability distribution given by $|Φ\rangle$. In this way, those who have $|Φ\rangle$ can reliably access the information by simply measuring on $|Φ\rangle$. We propose q-sparsity to characterize the sparsity of quantum states and the efficiency of the quantum communications by TNCS. The high q-sparsity is essentially due to the fact that the TN states describing nicely the probability distribution obey the area law of entanglement entropy. Testing on realistic datasets (hand-written digits and fashion images), TNCS is shown to possess high efficiency and accuracy, where the security of communications is guaranteed by the fundamental quantum principles.",,"S Ran, Z Sun, S Fei, G Su, M Lewenstein - Phys. Rev. Research 2, 033293 (2020)",[],https://arxiv.org/abs/1907.10290,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1907.10290,['https://arxiv.org/pdf/1907.10290'],quantum compressed sensing with unsupervised tensor network machine learning,MPO/TT 压缩 / MPS 生成/Born机 / 互信息/标度,1,"Phys. Rev. Research 2, 033293 (2020)",
Compact Trilinear Interaction for Visual Question Answering,"T Do, T Do, H Tran, E Tjiputra, Q D Tran",2019.0,,"In Visual Question Answering (VQA), answers have a great correlation with question meaning and visual contents. Thus, to selectively utilize image, question and answer information, we propose a novel trilinear interaction model which simultaneously learns high level associations between these three inputs. In addition, to overcome the interaction complexity, we introduce a multimodal tensor-based PARALIND decomposition which efficiently parameterizes trilinear interaction between the three inputs. Moreover, knowledge distillation is first time applied in Free-form Opened-ended VQA. It is not only for reducing the computational cost and required memory but also for transferring knowledge from trilinear interaction model to bilinear interaction model. The extensive experiments on benchmarking datasets TDIUC, VQA-2.0, and Visual7W show that the proposed compact trilinear interaction model achieves state-of-the-art results when using a single model on all three datasets.",,"T Do, T Do, H Tran, E Tjiputra, Q D Tran - arXiv preprint arXiv:1909.11874, 2019 - arxiv.org",[],https://arxiv.org/abs/1909.11874,arxiv-completion,2026-09-26 (citations:OpenAlex),,1909.11874,['https://arxiv.org/pdf/1909.11874'],compact trilinear interaction for visual question answering,,1,,
Factorized Higher-Order CNNs with an Application to Spatio-Temporal Emotion Estimation,"J Kossaifi, A Toisoul, A Bulat, Y Panagakis, T Hospedales, M Pantic",2019.0,,"Training deep neural networks with spatio-temporal (i.e., 3D) or multidimensional convolutions of higher-order is computationally challenging due to millions of unknown parameters across dozens of layers. To alleviate this, one approach is to apply low-rank tensor decompositions to convolution kernels in order to compress the network and reduce its number of parameters. Alternatively, new convolutional blocks, such as MobileNet, can be directly designed for efficiency. In this paper, we unify these two approaches by proposing a tensor factorization framework for efficient multidimensional (separable) convolutions of higher-order. Interestingly, the proposed framework enables a novel higher-order transduction, allowing to train a network on a given domain (e.g., 2D images or N-dimensional data in general) and using transduction to generalize to higher-order data such as videos (or (N+K)-dimensional data in general), capturing for instance temporal dynamics while preserving the learnt spatial information. We apply the proposed methodology, coined CP-Higher-Order Convolution (HO-CPConv), to spatio-temporal facial emotion analysis. Most existing facial affect models focus on static imagery and discard all temporal information. This is due to the above-mentioned burden of training 3D convolutional nets and the lack of large bodies of video data annotated by experts. We address both issues with our proposed framework. Initial training is first done on static imagery before using transduction to generalize to the temporal domain. We demonstrate superior performance on three challenging large scale affect estimation datasets, AffectNet, SEWA, and AFEW-VA.",,"J Kossaifi, A Toisoul, A Bulat, Y Panagakis, T Hospedales, M Pantic - arXiv preprint arXiv:1906.06196, 2019 - arxiv.org",[],https://arxiv.org/abs/1906.06196,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1906.06196,['https://arxiv.org/pdf/1906.06196'],factorized higher order cnns with an application to spatio temporal emotion estimation,MPO/TT 压缩,1,,
Variational quantum circuits for deep reinforcement learning,"SYC Chen, CHH Yang, J Qi, PY Chen, X Ma…",2020.0,681,"The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. However, the existing quantum computing platforms are hard to simulate classical deep learning models or problems because of the intractability of deep quantum circuits. Thus, it is necessary to design feasible quantum algorithms for quantum machine learning for noisy intermediate scale quantum (NISQ) devices. This work explores variational quantum circuits for deep reinforcement learning. Specifically, we reshape classical deep reinforcement learning algorithms like experience replay and target network into a representation of variational quantum circuits. Moreover, we use a quantum information encoding scheme to reduce the number of model parameters compared to classical neural networks. To the best of our knowledge, this work is the first proof-of-principle demonstration of variational quantum circuits to approximate the deep Q-value function for decision-making and policy-selection reinforcement learning with experience replay and target network. Besides, our variational quantum circuits can be deployed in many near-term NISQ machines.",DEWnWktcrQkJ,"SYC Chen, CHH Yang, J Qi, PY Chen, X Ma… - IEEE …, 2020 - ieeexplore.ieee.org",['https://ieeexplore.ieee.org/iel7/6287639/8948470/09144562.pdf'],https://ieeexplore.ieee.org/abstract/document/9144562/,unknown,unknown,量子/混合LLM,1907.00397,['https://ieeexplore.ieee.org/iel7/6287639/8948470/09144562.pdf'],variational quantum circuits for deep reinforcement learning,量子/混合LLM,1,IEEE Access,
Encoding of matrix product states into quantum circuits of one-and two-qubit gates,SJ Ran,2020.0,267,"… , our idea is to construct the unitary matrix product operators that optimally disentangle the MPS to a product state. These matrix product operators form the quantum circuit that evolves a …",JGiUU_YbdikJ,"SJ Ran - Physical Review A, 2020 - APS",['https://arxiv.org/pdf/1908.07958'],https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.032310,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/1908.07958'],encoding of matrix product states into quantum circuits of one and two qubit gates,MPS 语言模型,1,,
An overview of neural network compression,JO Neill,2020.0,212,"Overparameterized networks trained to convergence have shown impressive performance in domains such as computer vision and natural language processing. Pushing state of the art on salient tasks within these domains corresponds to these models becoming larger and more difficult for machine learning practitioners to use given the increasing memory and storage requirements, not to mention the larger carbon footprint. Thus, in recent years there has been a resurgence in model compression techniques, particularly for deep convolutional neural networks and self-attention based networks such as the Transformer. Hence, this paper provides a timely overview of both old and current compression techniques for deep neural networks, including pruning, quantization, tensor decomposition, knowledge distillation and combinations thereof. We assume a basic familiarity with deep learning architectures\footnote{For an introduction to deep learning, see ~\citet{goodfellow2016deep}}, namely, Recurrent Neural Networks~\citep[(RNNs)][]{rumelhart1985learning,hochreiter1997long}, Convolutional Neural Networks~\citep{fukushima1980neocognitron}~\footnote{For an up to date overview see~\citet{khan2019survey}} and Self-Attention based networks~\citep{vaswani2017attention}\footnote{For a general overview of self-attention networks, see ~\citet{chaudhari2019attentive}.},\footnote{For more detail and their use in natural language processing, see~\citet{hu2019introductory}}. Most of the papers discussed are proposed in the context of at least one of these DNN architectures.",U_Cufbjjxz8J,"JO Neill - arXiv preprint arXiv:2006.03669, 2020 - arxiv.org",['https://arxiv.org/pdf/2006.03669'],https://arxiv.org/abs/2006.03669,unknown,unknown,MPO/TT 压缩,2006.03669,['https://arxiv.org/pdf/2006.03669'],an overview of neural network compression,MPO/TT 压缩,1,,
Convolutional tensor-train LSTM for spatio-temporal learning,"J Su, W Byeon, J Kossaifi, F Huang…",2020.0,204,"… a novel convolutional tensortrain decomposition, which … compress higher-order ConvLSTM, rather than first-order fully-connected LSTM. We further propose Convolutional Tensor-Train …",LQ_2GjV3s8sJ,"J Su, W Byeon, J Kossaifi, F Huang… - … in Neural …, 2020 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2020/file/9e1a36515d6704d7eb7a30d783400e5d-Paper.pdf'],https://proceedings.neurips.cc/paper_files/paper/2020/hash/9e1a36515d6704d7eb7a30d783400e5d-Abstract.html,unknown,unknown,MPO/TT 压缩,,['https://proceedings.neurips.cc/paper_files/paper/2020/file/9e1a36515d6704d7eb7a30d783400e5d-Paper.pdf'],convolutional tensor train lstm for spatio temporal learning,MPO/TT 压缩,1,,
Generalized Canonical Polyadic Tensor Decomposition,"D K Hong, T G Kolda, J A Duersch",2020.0,149,"Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor decomposition that allows other loss functions besides squared error. For instance, we can use logistic loss or Kullback--Leibler divergence, enabling tensor decomposition for binary or count data. We present a variety of statistically motivated loss functions for various scenarios. We provide a generalized framework for computing gradients and handling missing data that enables the use of standard optimization methods for fitting the model. We demonstrate the flexibility of the GCP decomposition on several real-world examples including interactions in a social network, neural activity in a mouse, and monthly rainfall measurements in India.",,"D K Hong, T G Kolda, J A Duersch - SIAM Review",[],https://arxiv.org/abs/1808.07452,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,1808.07452,['https://arxiv.org/pdf/1808.07452'],generalized canonical polyadic tensor decomposition,MPO/TT 压缩 / MPS 生成/Born机,1,SIAM Review,
Compressing pre-trained language models by matrix decomposition,"MB Noach, Y Goldberg",2020.0,119,"… We presented a way to compress pre-trained large language models fine-tuned for specific tasks, while preserving much of the information contained within them, by using matrix …",nflNwBMfkqcJ,"MB Noach, Y Goldberg - … Joint Conference on Natural Language …, 2020 - aclanthology.org",['https://aclanthology.org/2020.aacl-main.88.pdf'],https://aclanthology.org/2020.aacl-main.88/,unknown,unknown,MPS 语言模型,,['https://aclanthology.org/2020.aacl-main.88.pdf'],compressing pre trained language models by matrix decomposition,MPS 语言模型,1,,
From probabilistic graphical models to generalized tensor networks for supervised learning,"I Glasser, N Pancotti, JI Cirac",2020.0,118,"… the connection between tensor networks and probabilistic graphical models, and … tensor networks where information from a tensor can be copied and reused in other parts of the network…",YdlwwcVxpJcJ,"I Glasser, N Pancotti, JI Cirac - IEEE Access, 2020 - ieeexplore.ieee.org",['https://ieeexplore.ieee.org/iel7/6287639/8948470/09058650.pdf'],https://ieeexplore.ieee.org/abstract/document/9058650/,unknown,unknown,MPS/序列建模,1806.05964,['https://ieeexplore.ieee.org/iel7/6287639/8948470/09058650.pdf'],from probabilistic graphical models to generalized tensor networks for supervised learning,MPS/序列建模 / TTN/MERA/PEPS,2,,
Generative tensor network classification model for supervised machine learning,"ZZ Sun, C Peng, D Liu, SJ Ran, G Su",2020.0,85,"… , we propose a generative tensor network classification (GTNC) model for … generative TN’s; each generative TN is a quantum state defined in E and is trained as the generative model for …",jlr_nWYxhAEJ,"ZZ Sun, C Peng, D Liu, SJ Ran, G Su - Physical Review B, 2020 - APS",['https://arxiv.org/pdf/1903.10742'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.075135,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1903.10742'],generative tensor network classification model for supervised machine learning,TTN/MERA/PEPS,1,,
Deep convolutional neural network compression via coupled tensor decomposition,"W Sun, S Chen, L Huang, HC So…",2020.0,37,"Large neural networks have aroused impressive progress in various real world applications. However, the expensive storage and computational resources requirement for running deep networks make them problematic to be deployed on mobile devices. Recently, matrix and tensor decompositions have been employed for compressing neural networks. In this paper, we develop a simultaneous tensor decomposition technique for network optimization. The shared network structure is first discussed. Sometimes, not only the structure but also the parameters are shared to form a compressed model at the expense of degraded performance. This indicates that the weight tensors between layers within one network contain both identical components and independent components. To utilize this characteristic, two new coupled tensor train decompositions are developed for fully and partly structure sharing cases, and an alternating optimization approach is proposed for low rank tensor computation. Finally, we restore the performance of the neural network model by fine-tuning. The compression ratio of the devised approach can then be calculated. Experimental results are also included to demonstrate the benefits of our algorithm for both applications of image reconstruction and classification, using the well known datasets such as Cifar-10/Cifar-100 and ImageNet and widely used networks such as ResNet. Comparing to the state-of-the-art independent matrix and tensor decomposition based methods, our model can obtain a better network performance under the same compression ratio.",2XkzU-Cy0nIJ,"W Sun, S Chen, L Huang, HC So… - IEEE Journal of Selected …, 2020 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/9261106/,unknown,unknown,MPO/TT 压缩,,[],deep convolutional neural network compression via coupled tensor decomposition,MPO/TT 压缩,1,IEEE Journal of Selected Topics in Signal Processing,
Compressing 3DCNNs based on tensor train decomposition,"D Wang, G Zhao, G Li, L Deng, Y Wu",2020.0,33,"… , neural network compression is a promising approach. In this work, we adopt the tensor train (TT) decomposition, a straightforward and simple in situ training compression method, to …",D0AsQnj7XWkJ,"D Wang, G Zhao, G Li, L Deng, Y Wu - Neural Networks, 2020 - Elsevier",['https://arxiv.org/pdf/1912.03647'],https://www.sciencedirect.com/science/article/pii/S0893608020302690,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/1912.03647'],compressing 3dcnns based on tensor train decomposition,MPO/TT 压缩,1,,
"Tensor train construction from tensor actions, with application to compression of large high order derivative tensors","N Alger, P Chen, O Ghattas",2020.0,20,"… can be compressed into tensor train format with a low tensor train rank, and that the number of tensor actions needed to compress the high order derivative tensors is independent of the …",Q1OsB1yq_UoJ,"N Alger, P Chen, O Ghattas - SIAM Journal on Scientific Computing, 2020 - SIAM",['https://arxiv.org/pdf/2002.06244'],https://epubs.siam.org/doi/abs/10.1137/20M131936X,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/2002.06244'],tensor train construction from tensor actions with application to compression of large high order derivative tensors,MPO/TT 压缩,1,,
Residual matrix product state for machine learning,"YM Meng, J Zhang, P Zhang, C Gao, SJ Ran",2020.0,18,"Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the ""hidden"" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understand of the working mechanisms and improve the performance of both models.",PbZ6EjhD-xoJ,"YM Meng, J Zhang, P Zhang, C Gao, SJ Ran - arXiv preprint arXiv …, 2020 - arxiv.org",['https://arxiv.org/pdf/2012.11841'],https://arxiv.org/abs/2012.11841,unknown,unknown,MPS 语言模型,2012.11841,['https://arxiv.org/pdf/2012.11841'],residual matrix product state for machine learning,MPS 语言模型,1,"SciPost Phys. 14, 142 (2023)",
Tensorcoder: Dimension-wise attention via tensor representation for natural language modeling,"S Zhang, P Zhang, X Ma, J Wei, N Wang…",2020.0,15,"Transformer has been widely-used in many Natural Language Processing (NLP) tasks and the scaled dot-product attention between tokens is a core module of Transformer. This attention is a token-wise design and its complexity is quadratic to the length of sequence, limiting its application potential for long sequence tasks. In this paper, we propose a dimension-wise attention mechanism based on which a novel language modeling approach (namely TensorCoder) can be developed. The dimension-wise attention can reduce the attention complexity from the original $O(N^2d)$ to $O(Nd^2)$, where $N$ is the length of the sequence and $d$ is the dimensionality of head. We verify TensorCoder on two tasks including masked language modeling and neural machine translation. Compared with the original Transformer, TensorCoder not only greatly reduces the calculation of the original model but also obtains improved performance on masked language modeling task (in PTB dataset) and comparable performance on machine translation tasks.",Ha2tA5CcQcMJ,"S Zhang, P Zhang, X Ma, J Wei, N Wang… - arXiv preprint arXiv …, 2020 - arxiv.org",['https://arxiv.org/pdf/2008.01547'],https://arxiv.org/abs/2008.01547,unknown,unknown,张量化Transformer,2008.01547,['https://arxiv.org/pdf/2008.01547'],tensorcoder dimension wise attention via tensor representation for natural language modeling,张量化Transformer,1,arXiv (Cornell University),
Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks,"S Mugel, C Kuchkovsky, E Sanchez, S Fernandez-Lorenzo, J Luis-Hita, E Lizaso, R Orus",2020.0,13,"In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints. This problem is central to quantitative finance. After a detailed introduction to the problem, we implement a number of quantum and quantum-inspired algorithms on different hardware platforms to solve its discrete formulation using real data from daily prices over 8 years of 52 assets, and do a detailed comparison of the obtained Sharpe ratios, profits and computing times. In particular, we implement classical solvers (Gekko, exhaustive), D-Wave Hybrid quantum annealing, two different approaches based on Variational Quantum Eigensolvers on IBM-Q (one of them brand-new and tailored to the problem), and for the first time in this context also a quantum-inspired optimizer based on Tensor Networks. In order to fit the data into each specific hardware platform, we also consider doing a preprocessing based on clustering of assets. From our comparison, we conclude that D-Wave Hybrid and Tensor Networks are able to handle the largest systems, where we do calculations up to 1272 fully-connected qubits for demonstrative purposes. Finally, we also discuss how to mathematically implement other possible real-life constraints, as well as several ideas to further improve the performance of the studied methods.",,"S Mugel, C Kuchkovsky, E Sanchez, S Fernandez-Lorenzo, J Luis-Hita, E Lizaso, R Orus - Phys. Rev. Research 4, 013006 (2022)",[],https://arxiv.org/abs/2007.00017,arxiv-completion,2026-09-26 (citations:OpenAlex),,2007.00017,['https://arxiv.org/pdf/2007.00017'],dynamic portfolio optimization with real datasets using quantum processors and quantum inspired tensor networks,,1,"Phys. Rev. Research 4, 013006 (2022)",
Tensorized transformer for dynamical systems modeling,"A Shalova, I Oseledets",2020.0,11,"The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so probabilistic approaches could give a more general picture of the process. At the same time, high-dimensional probabilities modeling is a challenging and data-intensive task. In this paper, we establish a parallel between the dynamical systems modeling and language modeling tasks. We propose a transformer-based model that incorporates geometrical properties of the data and provide an iterative training algorithm allowing the fine-grid approximation of the conditional probabilities of high-dimensional dynamical systems.",YkSKAM-ZA_AJ,"A Shalova, I Oseledets - arXiv preprint arXiv:2006.03445, 2020 - arxiv.org",['https://arxiv.org/pdf/2006.03445'],https://arxiv.org/abs/2006.03445,unknown,unknown,张量化Transformer,2006.03445,['https://arxiv.org/pdf/2006.03445'],tensorized transformer for dynamical systems modeling,张量化Transformer,1,,
Compressing lstm networks by matrix product operators,"ZF Gao, X Sun, L Gao, J Li, ZY Lu",2020.0,7,"Long Short Term Memory(LSTM) models are the building blocks of many state-of-the-art natural language processing(NLP) and speech enhancement(SE) algorithms. However, there are a large number of parameters in an LSTM model. This usually consumes a large number of resources to train the LSTM model. Also, LSTM models suffer from computational inefficiency in the inference phase. Existing model compression methods (e.g., model pruning) can only discriminate based on the magnitude of model parameters, ignoring the issue of importance distribution based on the model information. Here we introduce the MPO decomposition, which describes the local correlation of quantum states in quantum many-body physics and is used to represent the large model parameter matrix in a neural network, which can compress the neural network by truncating the unimportant information in the weight matrix. In this paper, we propose a matrix product operator(MPO) based neural network architecture to replace the LSTM model. The effective representation of neural networks by MPO can effectively reduce the computational consumption of training LSTM models on the one hand, and speed up the computation in the inference phase of the model on the other hand. We compare the MPO-LSTM model-based compression model with the traditional LSTM model with pruning methods on sequence classification, sequence prediction, and speech enhancement tasks in our experiments. The experimental results show that our proposed neural network architecture based on the MPO approach significantly outperforms the pruning approach.",FzQmOokGU-cJ,"ZF Gao, X Sun, L Gao, J Li, ZY Lu - arXiv preprint arXiv:2012.11943, 2020 - arxiv.org",['https://arxiv.org/pdf/2012.11943'],https://arxiv.org/abs/2012.11943,unknown,unknown,MPS 语言模型,2012.11943,['https://arxiv.org/pdf/2012.11943'],compressing lstm networks by matrix product operators,MPS 语言模型,1,,
Learning phase transition in Ising model with tensor-network Born machines,"A Azizi, K Najafi, M Mohseni…",2020.0,5,"… , a new generative model known as Born Machine has … data based on Born probabilities of quantum state. Leveraging … Matrix Product State (MPS) and indicate that PEPS model on the …",6t-LQstNBIQJ,"A Azizi, K Najafi, M Mohseni… - … Networks in Machine …, 2020 - tensorworkshop.github.io",['https://tensorworkshop.github.io/NeurIPS2020/accepted_papers/NIPS_PEPS.pdf'],https://tensorworkshop.github.io/NeurIPS2020/accepted_papers/NIPS_PEPS.pdf,unknown,unknown,MPS 生成/Born机,,['https://tensorworkshop.github.io/NeurIPS2020/accepted_papers/NIPS_PEPS.pdf'],learning phase transition in ising model with tensor network born machines,MPS 生成/Born机,1,,
Quantum-Classical Machine learning by Hybrid Tensor Networks,"D Liu, J Yao, Z Yao, Q Zhang",2020.0,5,"Tensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks with classical neural networks in a uniform deep learning framework to overcome the limitations of regular tensor networks in machine learning. We first analyze the limitations of regular tensor networks in the applications of machine learning involving the representation power and architecture scalability. We conclude that in fact the regular tensor networks are not competent to be the basic building blocks of deep learning. Then, we discuss the performance of HTN which overcome all the deficiency of regular tensor networks for machine learning. In this sense, we are able to train HTN in the deep learning way which is the standard combination of algorithms such as Back Propagation and Stochastic Gradient Descent. We finally provide two applicable cases to show the potential applications of HTN, including quantum states classification and quantum-classical autoencoder. These cases also demonstrate the great potentiality to design various HTN in deep learning way.",,"D Liu, J Yao, Z Yao, Q Zhang - arXiv preprint arXiv:2005.09428, 2020 - arxiv.org",[],https://arxiv.org/abs/2005.09428,arxiv-completion,2026-09-26 (citations:OpenAlex),,2005.09428,['https://arxiv.org/pdf/2005.09428'],quantum classical machine learning by hybrid tensor networks,,1,,
Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination,"C Hawkins, X Liu, Z Zhang",2020.0,4,"While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a compact neural network from scratch with low memory and low computational cost. Low-rank tensor decomposition is one of the most effective approaches to reduce the memory and computing requirements of large-size neural networks. However, directly training a low-rank tensorized neural network is a very challenging task because it is hard to determine a proper tensor rank {\it a priori}, which controls the model complexity and compression ratio in the training process. This paper presents a novel end-to-end framework for low-rank tensorized training of neural networks. We first develop a flexible Bayesian model that can handle various low-rank tensor formats (e.g., CP, Tucker, tensor train and tensor-train matrix) that compress neural network parameters in training. This model can automatically determine the tensor ranks inside a nonlinear forward model, which is beyond the capability of existing Bayesian tensor methods. We further develop a scalable stochastic variational inference solver to estimate the posterior density of large-scale problems in training. Our work provides the first general-purpose rank-adaptive framework for end-to-end tensorized training. Our numerical results on various neural network architectures show orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the training process. Specifically, on a very large deep learning recommendation system with over $4.2\times 10^9$ model parameters, our method can reduce the variables to only $1.6\times 10^5$ automatically in the training process (i.e., by $2.6\times 10^4$ times) while achieving almost the same accuracy.",,"C Hawkins, X Liu, Z Zhang - arXiv preprint arXiv:2010.08689, 2020 - arxiv.org",[],https://arxiv.org/abs/2010.08689,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2010.08689,['https://arxiv.org/pdf/2010.08689'],towards compact neural networks via end to end training a bayesian tensor approach with automatic rank determination,MPO/TT 压缩 / MPS 生成/Born机,1,,
Dynamic Spatiotemporal Graph Neural Network with Tensor Network,"C Jia, B Wu, X Zhang",2020.0,4,"Dynamic spatial graph construction is a challenge in graph neural network (GNN) for time series data problems. Although some adaptive graphs are conceivable, only a 2D graph is embedded in the network to reflect the current spatial relation, regardless of all the previous situations. In this work, we generate a spatial tensor graph (STG) to collect all the dynamic spatial relations, as well as a temporal tensor graph (TTG) to find the latent pattern along time at each node. These two tensor graphs share the same nodes and edges, which leading us to explore their entangled correlations by Projected Entangled Pair States (PEPS) to optimize the two graphs. We experimentally compare the accuracy and time costing with the state-of-the-art GNN based methods on the public traffic datasets.",,"C Jia, B Wu, X Zhang - arXiv preprint arXiv:2003.08729, 2020 - arxiv.org",[],https://arxiv.org/abs/2003.08729,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2003.08729,['https://arxiv.org/pdf/2003.08729'],dynamic spatiotemporal graph neural network with tensor network,TTN/MERA/PEPS / MPS/序列建模,1,,
Adaptive tensor-train decomposition for neural network compression,"Y Zheng, Y Zhou, Z Zhao, D Yu",2020.0,3,It could be of great difficulty and cost to directly apply complex deep neural network to mobile devices with limited computing and endurance abilities. This paper aims to solve such …,rYlR-DdUQnoJ,"Y Zheng, Y Zhou, Z Zhao, D Yu - International Conference on Parallel and …, 2020 - Springer",['https://www.researchgate.net/profile/Yanwei-Zheng-2/publication/349472298_Adaptive_Tensor-Train_Decomposition_for_Neural_Network_Compression/links/60e64d2730e8e50c01eb5fdf/Adaptive-Tensor-Train-Decomposition-for-Neural-Network-Compression.pdf'],https://link.springer.com/chapter/10.1007/978-3-030-69244-5_6,unknown,unknown,MPO/TT 压缩,,['https://www.researchgate.net/profile/Yanwei-Zheng-2/publication/349472298_Adaptive_Tensor-Train_Decomposition_for_Neural_Network_Compression/links/60e64d2730e8e50c01eb5fdf/Adaptive-Tensor-Train-Decomposition-for-Neural-Network-Compression.pdf'],adaptive tensor train decomposition for neural network compression,MPO/TT 压缩,1,Lecture notes in computer science,
Tensor-to-Vector Regression for Multi-channel Speech Enhancement based on Tensor-Train Network,"J Qi, H Hu, Y Wang, C H Yang, S M Siniscalchi, C Lee",2020.0,3,"We propose a tensor-to-vector regression approach to multi-channel speech enhancement in order to address the issue of input size explosion and hidden-layer size expansion. The key idea is to cast the conventional deep neural network (DNN) based vector-to-vector regression formulation under a tensor-train network (TTN) framework. TTN is a recently emerged solution for compact representation of deep models with fully connected hidden layers. Thus TTN maintains DNN's expressive power yet involves a much smaller amount of trainable parameters. Furthermore, TTN can handle a multi-dimensional tensor input by design, which exactly matches the desired setting in multi-channel speech enhancement. We first provide a theoretical extension from DNN to TTN based regression. Next, we show that TTN can attain speech enhancement quality comparable with that for DNN but with much fewer parameters, e.g., a reduction from 27 million to only 5 million parameters is observed in a single-channel scenario. TTN also improves PESQ over DNN from 2.86 to 2.96 by slightly increasing the number of trainable parameters. Finally, in 8-channel conditions, a PESQ of 3.12 is achieved using 20 million parameters for TTN, whereas a DNN with 68 million parameters can only attain a PESQ of 3.06. Our implementation is available online https://github.com/uwjunqi/Tensor-Train-Neural-Network.",,"J Qi, H Hu, Y Wang, C H Yang, S M Siniscalchi, C Lee - IEEE ICASSP 2020",[],https://arxiv.org/abs/2002.00544,arxiv-completion,2026-09-26 (citations:OpenAlex),,2002.00544,['https://arxiv.org/pdf/2002.00544'],tensor to vector regression for multi channel speech enhancement based on tensor train network,,1,IEEE ICASSP 2020,
A Continuous Variable Born Machine,"I Čepaitė, B Coyle, E Kashefi",2020.0,2,"Generative Modelling has become a promising use case for near term quantum computers. In particular, due to the fundamentally probabilistic nature of quantum mechanics, quantum computers naturally model and learn probability distributions, perhaps more efficiently than can be achieved classically. The Born machine is an example of such a model, easily implemented on near term quantum computers. However, in its original form, the Born machine only naturally represents discrete distributions. Since probability distributions of a continuous nature are commonplace in the world, it is essential to have a model which can efficiently represent them. Some proposals have been made in the literature to supplement the discrete Born machine with extra features to more easily learn continuous distributions, however, all invariably increase the resources required to some extent. In this work, we present the continuous variable Born machine, built on the alternative architecture of continuous variable quantum computing, which is much more suitable for modelling such distributions in a resource-minimal way. We provide numerical results indicating the models ability to learn both quantum and classical continuous distributions, including in the presence of noise.",,"I Čepaitė, B Coyle, E Kashefi - Quantum Mach. Intell. 4, 6 (2022)",[],https://arxiv.org/abs/2011.00904,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2011.00904,['https://arxiv.org/pdf/2011.00904'],a continuous variable born machine,MPS 生成/Born机,1,"Quantum Mach. Intell. 4, 6 (2022)",
Tensor Decompositions in Recursive Neural Networks for Tree-Structured Data,"D Castellana, D Bacciu",2020.0,2,"The paper introduces two new aggregation functions to encode structural knowledge from tree-structured data. They leverage the Canonical and Tensor-Train decompositions to yield expressive context aggregation while limiting the number of model parameters. Finally, we define two novel neural recursive models for trees leveraging such aggregation functions, and we test them on two tree classification tasks, showing the advantage of proposed models when tree outdegree increases.",,"D Castellana, D Bacciu - arXiv preprint arXiv:2006.10619, 2020 - arxiv.org",[],https://arxiv.org/abs/2006.10619,arxiv-completion,2026-09-26 (citations:OpenAlex),,2006.10619,['https://arxiv.org/pdf/2006.10619'],tensor decompositions in recursive neural networks for tree structured data,,1,,
A Fully Tensorized Recurrent Neural Network,"C C Onu, J E Miller, D Precup",2020.0,1,"Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large RNNs in resource-limited settings, while also introducing complications in hyperparameter selection and training. To address these issues, we introduce a ""fully tensorized"" RNN architecture which jointly encodes the separate weight matrices within each recurrent cell using a lightweight tensor-train (TT) factorization. This approach represents a novel form of weight sharing which reduces model size by several orders of magnitude, while still maintaining similar or better performance compared to standard RNNs. Experiments on image classification and speaker verification tasks demonstrate further benefits for reducing inference times and stabilizing model training and hyperparameter selection.",,"C C Onu, J E Miller, D Precup - arXiv preprint arXiv:2010.04196, 2020 - arxiv.org",[],https://arxiv.org/abs/2010.04196,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,2010.04196,['https://arxiv.org/pdf/2010.04196'],a fully tensorized recurrent neural network,MPS/序列建模,1,,
"Connecting Weighted Automata, Tensor Networks and Recurrent Neural Networks through Spectral Learning","T Li, D Precup, G Rabusseau",2020.0,1,"In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks which encompasses a set of optimization techniques for high-order tensors used in quantum physics and numerical analysis. We first present an intrinsic relation between WFA and the tensor train decomposition, a particular form of tensor network. This relation allows us to exhibit a novel low rank structure of the Hankel matrix of a function computed by a WFA and to design an efficient spectral learning algorithm leveraging this structure to scale the algorithm up to very large Hankel matrices.We then unravel a fundamental connection between WFA and second-orderrecurrent neural networks~(2-RNN): in the case of sequences of discrete symbols, WFA and 2-RNN with linear activationfunctions are expressively equivalent. Leveraging this equivalence result combined with the classical spectral learning algorithm for weighted automata, we introduce the first provable learning algorithm for linear 2-RNN defined over sequences of continuous input vectors.This algorithm relies on estimating low rank sub-blocks of the Hankel tensor, from which the parameters of a linear 2-RNN can be provably recovered. The performances of the proposed learning algorithm are assessed in a simulation study on both synthetic and real-world data.",,"T Li, D Precup, G Rabusseau - arXiv preprint arXiv:2010.10029, 2020 - arxiv.org",[],https://arxiv.org/abs/2010.10029,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2010.10029,['https://arxiv.org/pdf/2010.10029'],connecting weighted automata tensor networks and recurrent neural networks through spectral learning,MPS 语言模型 / MPS/序列建模,1,,
Quantum versus Classical Generative Modelling in Finance,"B Coyle, M Henderson, J C J Le, N Kumar, M Paini, E Kashefi",2020.0,,"Finding a concrete use case for quantum computers in the near term is still an open question, with machine learning typically touted as one of the first fields which will be impacted by quantum technologies. In this work, we investigate and compare the capabilities of quantum versus classical models for the task of generative modelling in machine learning. We use a real world financial dataset consisting of correlated currency pairs and compare two models in their ability to learn the resulting distribution - a restricted Boltzmann machine, and a quantum circuit Born machine. We provide extensive numerical results indicating that the simulated Born machine always at least matches the performance of the Boltzmann machine in this task, and demonstrates superior performance as the model scales. We perform experiments on both simulated and physical quantum chips using the Rigetti forest platform, and also are able to partially train the largest instance to date of a quantum circuit Born machine on quantum hardware. Finally, by studying the entanglement capacity of the training Born machines, we find that entanglement typically plays a role in the problem instances which demonstrate an advantage over the Boltzmann machine.",,"B Coyle, M Henderson, J C J Le, N Kumar, M Paini, E Kashefi - arXiv preprint arXiv:2008.00691, 2020 - arxiv.org",[],https://arxiv.org/abs/2008.00691,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2008.00691,['https://arxiv.org/pdf/2008.00691'],quantum versus classical generative modelling in finance,MPS 生成/Born机,1,,
Quantum-inspired Machine Learning on high-energy physics data,"T Felser, M Trenti, L Sestini, A Gianelle, D Zuliani, D Lucchesi, S Montangero",2020.0,,"Tensor Networks, a numerical tool originally designed for simulating quantum many-body systems, have recently been applied to solve Machine Learning problems. Exploiting a tree tensor network, we apply a quantum-inspired machine learning technique to a very important and challenging big data problem in high energy physics: the analysis and classification of data produced by the Large Hadron Collider at CERN. In particular, we present how to effectively classify so-called b-jets, jets originating from b-quarks from proton-proton collisions in the LHCb experiment, and how to interpret the classification results. We exploit the Tensor Network approach to select important features and adapt the network geometry based on information acquired in the learning process. Finally, we show how to adapt the tree tensor network to achieve optimal precision or fast response in time without the need of repeating the learning process. These results pave the way to the implementation of high-frequency real-time applications, a key ingredient needed among others for current and future LHCb event classification able to trigger events at the tens of MHz scale.",,"T Felser, M Trenti, L Sestini, A Gianelle, D Zuliani, D Lucchesi, S Montangero - arXiv preprint arXiv:2004.13747, 2020 - arxiv.org",[],https://arxiv.org/abs/2004.13747,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2004.13747,['https://arxiv.org/pdf/2004.13747'],quantum inspired machine learning on high energy physics data,TTN/MERA/PEPS,1,,
Deep composition of tensor-trains using squared inverse Rosenblatt transports,"T Cui, S Dolgov",2020.0,0,"Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by coupling intractable random variables with tractable reference random variables. This paper generalises the functional tensor-train approximation of the inverse Rosenblatt transport recently developed by Dolgov et al. (Stat Comput 30:603--625, 2020) to a wide class of high-dimensional non-negative functions, such as unnormalised probability density functions. First, we extend the inverse Rosenblatt transform to enable the transport to general reference measures other than the uniform measure. We develop an efficient procedure to compute this transport from a squared tensor-train decomposition which preserves the monotonicity. More crucially, we integrate the proposed order-preserving functional tensor-train transport into a nested variable transformation framework inspired by the layered structure of deep neural networks. The resulting deep inverse Rosenblatt transport significantly expands the capability of tensor approximations and transport maps to random variables with complicated nonlinear interactions and concentrated density functions. We demonstrate the efficiency of the proposed approach on a range of applications in statistical learning and uncertainty quantification, including parameter estimation for dynamical systems and inverse problems constrained by partial differential equations.",,"T Cui, S Dolgov - arXiv preprint arXiv:2007.06968, 2020 - arxiv.org",[],https://arxiv.org/abs/2007.06968,arxiv-completion,2026-09-26 (citations:OpenAlex),,2007.06968,['https://arxiv.org/pdf/2007.06968'],deep composition of tensor trains using squared inverse rosenblatt transports,,1,,
Experimental realization of a quantum image classifier via tensor-network-based machine learning,"K Wang, L Xiao, W Yi, S Ran, P Xue",2020.0,0,"Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical problems. However, quantum machine learning itself is limited by low effective dimensions achievable in state-of-the-art experiments. Here we demonstrate highly successful classifications of real-life images using photonic qubits, combining a quantum tensor-network representation of hand-written digits and entanglement-based optimization. Specifically, we focus on binary classification for hand-written zeroes and ones, whose features are cast into the tensor-network representation, further reduced by optimization based on entanglement entropy and encoded into two-qubit photonic states. We then demonstrate image classification with a high success rate exceeding 98%, through successive gate operations and projective measurements. Although we work with photons, our approach is amenable to other physical realizations such as nitrogen-vacancy centers, nuclear spins and trapped ions, and our scheme can be scaled to efficient multi-qubit encodings of features in the tensor-product representation, thereby setting the stage for quantum-enhanced multi-class classification.",,"K Wang, L Xiao, W Yi, S Ran, P Xue - Photonics Research 9 (12), 12002332 (2021)",[],https://arxiv.org/abs/2003.08551,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2003.08551,['https://arxiv.org/pdf/2003.08551'],experimental realization of a quantum image classifier via tensor network based machine learning,量子/混合LLM / 互信息/标度,1,"Photonics Research 9 (12), 12002332 (2021)",
Hybrid Tensor Decomposition in Neural Network Compression,"B Wu, D Wang, G Zhao, L Deng, G Li",2020.0,0,"Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for computational resources especially the storage consumption is growing due to that the increasing sizes of models are being required for more and more complicated applications. To address this problem, several tensor decomposition methods including tensor-train (TT) and tensor-ring (TR) have been applied to compress DNNs and shown considerable compression effectiveness. In this work, we introduce the hierarchical Tucker (HT), a classical but rarely-used tensor decomposition method, to investigate its capability in neural network compression. We convert the weight matrices and convolutional kernels to both HT and TT formats for comparative study, since the latter is the most widely used decomposition method and the variant of HT. We further theoretically and experimentally discover that the HT format has better performance on compressing weight matrices, while the TT format is more suited for compressing convolutional kernels. Based on this phenomenon we propose a strategy of hybrid tensor decomposition by combining TT and HT together to compress convolutional and fully connected parts separately and attain better accuracy than only using the TT or HT format on convolutional neural networks (CNNs). Our work illuminates the prospects of hybrid tensor decomposition for neural network compression.",,"B Wu, D Wang, G Zhao, L Deng, G Li - arXiv preprint arXiv:2006.15938, 2020 - arxiv.org",[],https://arxiv.org/abs/2006.15938,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2006.15938,['https://arxiv.org/pdf/2006.15938'],hybrid tensor decomposition in neural network compression,MPO/TT 压缩,1,,
Low Tensor Train- and Low Multilinear Rank Approximations for De-speckling and Compression of 3D Optical Coherence Tomography Images,"I Kopriva, F Shi, M Lai, M Štanfel, H Chen, X Chen",2020.0,0,"This paper proposes low tensor-train (TT) rank and low multilinear (ML) rank approximations for de-speckling and compression of 3D optical coherence tomography (OCT) images for a given compression ratio (CR). To this end, we derive the alternating direction method of multipliers based algorithms for the related problems constrained with the low TT- and low ML rank. Rank constraints are implemented through the Schatten-p (Sp) norm, p e {0, 1/2, 2/3, 1}, of unfolded matrices. We provide the proofs of global convergence towards a stationary point for both algorithms. Rank adjusted 3D OCT image tensors are finally approximated through tensor train- and Tucker alternating least squares decompositions. We comparatively validate the low TT- and low ML rank methods on twenty-two 3D OCT images with the JPEG2000 and 3D SPIHT compression methods, as well as with no compression 2D bilateral filtering (BF), 2D median filtering (MF), and enhanced low-rank plus sparse matrix decomposition (ELRpSD) methods. For the CR<10, the low Sp TT rank method with pe{0, 1/2, 2/3} yields either highest or comparable signal-to-noise ratio (SNR), and comparable or better contrast-to-noise ratio (CNR), mean segmentation errors (SEs) of retina layers and expert-based image quality score (EIQS) than original image and image compression methods. It compares favorably in terms of CNR, fairly in terms of SE and EIQS with the no image compression methods. Thus, for CR<10 the low S2/3 TT rank approximation can be considered a good choice for visual inspection based diagnostics. For 2<CR<60, the low S1 ML rank method compares favorably in terms of SE with image compression methods and with 2D BF and ELRpSD. It is slightly inferior to 2D MF. Thus, for 2<CR<60, the low S1 ML rank approximation can be considered a good choice for segmentation based diagnostics either on-site or in the remote mode of operation.",,"I Kopriva, F Shi, M Lai, M Štanfel, H Chen, X Chen - arXiv preprint arXiv:2008.11414, 2020 - arxiv.org",[],https://arxiv.org/abs/2008.11414,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2008.11414,['https://arxiv.org/pdf/2008.11414'],low tensor train and low multilinear rank approximations for de speckling and compression of 3d optical coherence tomography images,MPO/TT 压缩,1,,
On the Compression of Translation Operator Tensors in FMM-FFT-Accelerated SIE Simulators via Tensor Decompositions,"C Qian, A C Yucel",2020.0,0,"Tensor decomposition methodologies are proposed to reduce the memory requirement of translation operator tensors arising in the fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators. These methodologies leverage Tucker, hierarchical Tucker (H-Tucker), and tensor train (TT) decompositions to compress the FFT'ed translation operator tensors stored in three-dimensional (3D) and four-dimensional (4D) array formats. Extensive numerical tests are performed to demonstrate the memory saving achieved by and computational overhead introduced by these methodologies for different simulation parameters. Numerical results show that the H-Tucker-based methodology for 4D array format yields the maximum memory saving while Tucker-based methodology for 3D array format introduces the minimum computational overhead. For many practical scenarios, all methodologies yield a significant reduction in the memory requirement of translation operator tensors while imposing negligible/acceptable computational overhead.",,"C Qian, A C Yucel - arXiv preprint arXiv:2010.00520, 2020 - arxiv.org",[],https://arxiv.org/abs/2010.00520,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2010.00520,['https://arxiv.org/pdf/2010.00520'],on the compression of translation operator tensors in fmm fft accelerated sie simulators via tensor decompositions,MPO/TT 压缩,1,,
Ranks of Tensor Networks for Eigenspace Projections and the Curse of Dimensionality,M Ali,2020.0,0,"The hierarchical (multi-linear) rank of an order-$d$ tensor is key in determining the cost of representing a tensor as a (tree) Tensor Network (TN). In general, it is known that, for a fixed accuracy, a tensor with random entries cannot be expected to be efficiently approximable without the curse of dimensionality, i.e., a complexity growing exponentially with $d$. In this work, we show that the ground state projection (GSP) of a class of unbounded Hamiltonians can be approximately represented as an operator of low effective dimensionality that is independent of the (high) dimension $d$ of the GSP. This allows to approximate the GSP without the curse of dimensionality.",,"M Ali - arXiv preprint arXiv:2012.12953, 2020 - arxiv.org",[],https://arxiv.org/abs/2012.12953,arxiv-completion,2026-09-26 (citations:OpenAlex),,2012.12953,['https://arxiv.org/pdf/2012.12953'],ranks of tensor networks for eigenspace projections and the curse of dimensionality,,1,,
Recurrent Graph Tensor Networks: A Low-Complexity Framework for Modelling High-Dimensional Multi-Way Sequence,"Y L Xu, D P Mandic",2020.0,0,"Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To this end, we develop a multi-linear graph filter framework for approximating the modelling of hidden states in RNNs, which is embedded in a tensor network architecture to improve modelling power and reduce parameter complexity, resulting in a novel Recurrent Graph Tensor Network (RGTN). The proposed framework is validated through several multi-way sequence modelling tasks and benchmarked against traditional RNNs. By virtue of the domain aware information processing of graph filters and the expressive power of tensor networks, we show that the proposed RGTN is capable of not only out-performing standard RNNs, but also mitigating the Curse of Dimensionality associated with traditional RNNs, demonstrating superior properties in terms of performance and complexity.",,"Y L Xu, D P Mandic - arXiv preprint arXiv:2009.08727, 2020 - arxiv.org",[],https://arxiv.org/abs/2009.08727,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,2009.08727,['https://arxiv.org/pdf/2009.08727'],recurrent graph tensor networks a low complexity framework for modelling high dimensional multi way sequence,MPS/序列建模,1,,
Tangent-Space Gradient Optimization of Tensor Network for Machine Learning,"Z Sun, S Ran, G Su",2020.0,0,"The gradient-based optimization method for deep machine learning models suffers from gradient vanishing and exploding problems, particularly when the computational graph becomes deep. In this work, we propose the tangent-space gradient optimization (TSGO) for the probabilistic models to keep the gradients from vanishing or exploding. The central idea is to guarantee the orthogonality between the variational parameters and the gradients. The optimization is then implemented by rotating parameter vector towards the direction of gradient. We explain and testify TSGO in tensor network (TN) machine learning, where the TN describes the joint probability distribution as a normalized state $\left| ψ\right\rangle $ in Hilbert space. We show that the gradient can be restricted in the tangent space of $\left\langle ψ\right.\left| ψ\right\rangle = 1$ hyper-sphere. Instead of additional adaptive methods to control the learning rate in deep learning, the learning rate of TSGO is naturally determined by the angle $θ$ as $η= \tan θ$. Our numerical results reveal better convergence of TSGO in comparison to the off-the-shelf Adam.",,"Z Sun, S Ran, G Su - Phys. Rev. E 102, 012152 (2020)",[],https://arxiv.org/abs/2001.04029,arxiv-completion,2026-09-26 (citations:OpenAlex),,2001.04029,['https://arxiv.org/pdf/2001.04029'],tangent space gradient optimization of tensor network for machine learning,,1,"Phys. Rev. E 102, 012152 (2020)",
Tensor network based machine learning of non-Markovian quantum processes,"C Guo, K Modi, D Poletti",2020.0,0,"We show how to learn structures of generic, non-Markovian, quantum stochastic processes using a tensor network based machine learning algorithm. We do this by representing the process as a matrix product operator (MPO) and train it with a database of local input states at different times and the corresponding time-nonlocal output state. In particular, we analyze a qubit coupled to an environment and predict output state of the system at different time, as well as reconstruct the full system process. We show how the bond dimension of the MPO, a measure of non-Markovianity, depends on the properties of the system, of the environment and of their interaction. Hence, this study opens the way to a possible experimental investigation into the process tensor and its properties.",,"C Guo, K Modi, D Poletti - Phys. Rev. A 102, 062414 (2020)",[],https://arxiv.org/abs/2004.11038,arxiv-completion,2026-09-26 (citations:OpenAlex),,2004.11038,['https://arxiv.org/pdf/2004.11038'],tensor network based machine learning of non markovian quantum processes,,1,"Phys. Rev. A 102, 062414 (2020)",
"Matrix product states and projected entangled pair states: Concepts, symmetries, theorems","JI Cirac, D Perez-Garcia, N Schuch, F Verstraete",2021.0,1386,Many-body wave functions can be described effectively by local tensors in matrix product states and projected entangled pair states. This article reviews how these theories provide not only numerical methods but also insights of a more fundamental nature into the structures of states with global entanglement patterns and topological quantum order.,3QVfQYKr1FwJ,"JI Cirac, D Perez-Garcia, N Schuch, F Verstraete - Reviews of Modern Physics, 2021 - APS",['https://arxiv.org/pdf/2011.12127'],https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93.045003,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/2011.12127'],matrix product states and projected entangled pair states concepts symmetries theorems,MPS 语言模型,1,Reviews of Modern Physics,
Improving multimodal fusion with hierarchical mutual information maximization for multimodal sentiment analysis,"W Han, H Chen, S Poria",2021.0,872,"… In our implementation, we optimize the bounds for two modality pairs— (text, visual) and (text, acoustic). In each pair, we treat text as X and the other modality as Y in (3). We do so be…",VgC5ZRAGTs8J,"W Han, H Chen, S Poria - Proceedings of the 2021 conference on …, 2021 - aclanthology.org",['https://aclanthology.org/2021.emnlp-main.723.pdf'],https://aclanthology.org/2021.emnlp-main.723/,unknown,unknown,互信息/标度,2109.00412,['https://aclanthology.org/2021.emnlp-main.723.pdf'],improving multimodal fusion with hierarchical mutual information maximization for multimodal sentiment analysis,互信息/标度,1,,
Is attention better than matrix decomposition?,"Z Geng, MH Guo, H Chen, X Li, K Wei, Z Lin",2021.0,271,"As an essential ingredient of modern deep learning, attention mechanism, especially self-attention, plays a vital role in the global correlation discovery. However, is hand-crafted attention irreplaceable when modeling the global context? Our intriguing finding is that self-attention is not better than the matrix decomposition (MD) model developed 20 years ago regarding the performance and computational cost for encoding the long-distance dependencies. We model the global context issue as a low-rank recovery problem and show that its optimization algorithms can help design global information blocks. This paper then proposes a series of Hamburgers, in which we employ the optimization algorithms for solving MDs to factorize the input representations into sub-matrices and reconstruct a low-rank embedding. Hamburgers with different MDs can perform favorably against the popular global context module self-attention when carefully coping with gradients back-propagated through MDs. Comprehensive experiments are conducted in the vision tasks where it is crucial to learn the global context, including semantic segmentation and image generation, demonstrating significant improvements over self-attention and its variants.",o8LXcSU7UscJ,"Z Geng, MH Guo, H Chen, X Li, K Wei, Z Lin - arXiv preprint arXiv …, 2021 - arxiv.org",['https://arxiv.org/pdf/2109.04553'],https://arxiv.org/abs/2109.04553,unknown,unknown,张量化Transformer,2109.04553,['https://arxiv.org/pdf/2109.04553'],is attention better than matrix decomposition,张量化Transformer,1,,
Probabilistic transformer for time series analysis,"B Tang, DS Matteson",2021.0,236,… deep probabilistic methods that combine state-space models (… use attention mechanism to model non-Markovian dynamics in … success across a variety of sequence modeling tasks [26…,r9y0Yeieek8J,"B Tang, DS Matteson - Advances in neural information …, 2021 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2021/file/c68bd9055776bf38d8fc43c0ed283678-Paper.pdf'],https://proceedings.neurips.cc/paper_files/paper/2021/hash/c68bd9055776bf38d8fc43c0ed283678-Abstract.html,unknown,unknown,MPS/序列建模,,['https://proceedings.neurips.cc/paper_files/paper/2021/file/c68bd9055776bf38d8fc43c0ed283678-Paper.pdf'],probabilistic transformer for time series analysis,MPS/序列建模,1,,
Tensor Methods in Computer Vision and Deep Learning,"Y Panagakis, J Kossaifi, G G Chrysos, J P Oldfield, M A Nicolaou, A Anandkumar, S P Zafeiriou",2021.0,188,"Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a long history of applications in a wide span of computer vision problems. With the advent of the deep learning paradigm shift in computer vision, tensors have become even more fundamental. Indeed, essential ingredients in modern deep learning architectures, such as convolutions and attention mechanisms, can readily be considered as tensor mappings. In effect, tensor methods are increasingly finding significant applications in deep learning, including the design of memory and compute efficient network architectures, improving robustness to random noise and adversarial attacks, and aiding the theoretical understanding of deep networks. This article provides an in-depth and practical review of tensors and tensor methods in the context of representation learning and deep learning, with a particular focus on visual data analysis and computer vision applications. Concretely, besides fundamental work in tensor-based visual data analysis methods, we focus on recent developments that have brought on a gradual increase in tensor methods, especially in deep learning architectures and their implications in computer vision applications. To further enable the newcomer to grasp such concepts quickly, we provide companion Python notebooks, covering key aspects of this article and implementing them, step-by-step with TensorLy.",,"Y Panagakis, J Kossaifi, G G Chrysos, J P Oldfield, M A Nicolaou, A Anandkumar, S P Zafeiriou - Proceedings of the IEEE",[],https://arxiv.org/abs/2107.03436,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2107.03436,['https://arxiv.org/pdf/2107.03436'],tensor methods in computer vision and deep learning,张量化Transformer / 量子启发综述,1,Proceedings of the IEEE,
Tt-rec: Tensor train compression for deep learning recommendation models,"C Yin, B Acun, CJ Wu, X Liu",2021.0,154,"The memory capacity of embedding tables in deep learning recommendation models (DLRMs) is increasing dramatically from tens of GBs to TBs across the industry. Given the fast growth in DLRMs, novel solutions are urgently needed, in order to enable fast and efficient DLRM innovations. At the same time, this must be done without having to exponentially increase infrastructure capacity demands. In this paper, we demonstrate the promising potential of Tensor Train decomposition for DLRMs (TT-Rec), an important yet under-investigated context. We design and implement optimized kernels (TT-EmbeddingBag) to evaluate the proposed TT-Rec design. TT-EmbeddingBag is 3 times faster than the SOTA TT implementation. The performance of TT-Rec is further optimized with the batched matrix multiplication and caching strategies for embedding vector lookup operations. In addition, we present mathematically and empirically the effect of weight initialization distribution on DLRM accuracy and propose to initialize the tensor cores of TT-Rec following the sampled Gaussian distribution. We evaluate TT-Rec across three important design space dimensions -- memory capacity, accuracy, and timing performance -- by training MLPerf-DLRM with Criteo's Kaggle and Terabyte data sets. TT-Rec achieves 117 times and 112 times model size compression, for Kaggle and Terabyte, respectively. This impressive model size reduction can come with no accuracy nor training time overhead as compared to the uncompressed baseline.",5Tt1KBnZZSEJ,"C Yin, B Acun, CJ Wu, X Liu - Proceedings of Machine …, 2021 - proceedings.mlsys.org",['https://proceedings.mlsys.org/paper_files/paper/2021/file/1c4534ff58dab447545594c4863239b3-Paper.pdf'],https://proceedings.mlsys.org/paper_files/paper/2021/hash/1c4534ff58dab447545594c4863239b3-Abstract.html,unknown,unknown,MPO/TT 压缩,,['https://proceedings.mlsys.org/paper_files/paper/2021/file/1c4534ff58dab447545594c4863239b3-Paper.pdf'],tt rec tensor train compression for deep learning recommendation models,MPO/TT 压缩,1,arXiv (Cornell University),
Towards efficient tensor decomposition-based dnn model compression with optimization framework,"M Yin, Y Sui, S Liao, B Yuan",2021.0,146,"Advanced tensor decomposition, such as tensor train (TT) and tensor ring (TR), has been widely studied for deep neural network (DNN) model compression, especially for recurrent neural networks (RNNs). However, compressing convolutional neural networks (CNNs) using TT/TR always suffers significant accuracy loss. In this paper, we propose a systematic framework for tensor decomposition-based model compression using Alternating Direction Method of Multipliers (ADMM). By formulating TT decomposition-based model compression to an optimization problem with constraints on tensor ranks, we leverage ADMM technique to systemically solve this optimization problem in an iterative way. During this procedure, the entire DNN model is trained in the original structure instead of TT format, but gradually enjoys the desired low tensor rank characteristics. We then decompose this uncompressed model to TT format, and fine-tune it to finally obtain a high-accuracy TT-format DNN model. Our framework is very general, and it works for both CNNs and RNNs, and can be easily modified to fit other tensor decomposition approaches. We evaluate our proposed framework on different DNN models for image classification and video recognition tasks. Experimental results show that our ADMM-based TT-format models demonstrate very high compression performance with high accuracy. Notably, on CIFAR-100, with 2.3× and 2.4× compression ratios, our models have 1.96% and 2.21% higher top-1 accuracy than the original ResNet-20 and ResNet-32, respectively. For compressing ResNet-18 on ImageNet, our model achieves 2.47× FLOPs reduction without accuracy loss.",WsCHIYDJ72oJ,"M Yin, Y Sui, S Liao, B Yuan - 2021 IEEE/CVF Conference on …, 2021 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2107.12422'],https://ieeexplore.ieee.org/abstract/document/9577813/,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/2107.12422'],towards efficient tensor decomposition based dnn model compression with optimization framework,MPO/TT 压缩,1,,
Entangled datasets for quantum machine learning,"L Schatzki, A Arrasmith, PJ Coles, M Cerezo",2021.0,98,"High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.",3fx2hDyWDVkJ,"L Schatzki, A Arrasmith, PJ Coles, M Cerezo - arXiv preprint arXiv …, 2021 - arxiv.org",['https://arxiv.org/pdf/2109.03400'],https://arxiv.org/abs/2109.03400,unknown,unknown,TTN/MERA/PEPS,2109.03400,['https://arxiv.org/pdf/2109.03400'],entangled datasets for quantum machine learning,TTN/MERA/PEPS,1,arXiv (Cornell University),
Supervised learning with projected entangled pair states,"S Cheng, L Wang, P Zhang",2021.0,94,"Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only treelike tensor networks such as the matrix product states and tree tensor networks have been considered, even for modeling two-dimensional data such as images. In this work, we construct supervised learning models for images using the projected entangled pair states (PEPS), a two-dimensional tensor network having a similar structure prior to natural images. Our approach first performs a feature map, which transforms the image data to a product state on a grid, then contracts the product state to a PEPS with trainable parameters to predict image labels. The tensor elements of PEPS are trained by minimizing differences between training labels and predicted labels. The proposed model is evaluated on image classifications using the Modified National Institute of Standards and Technology database (MNIST) and the Fashion-MNIST datasets. We show that our model is significantly superior to existing models using treelike tensor networks. Moreover, using the same input features, our method performs as well as the multilayer perceptron classifier, but with much fewer parameters and is more stable. Our results shed light on potential applications of two-dimensional tensor network models in machine learning.",YqpBptzQS80J,"S Cheng, L Wang, P Zhang - Physical Review B, 2021 - APS",['https://arxiv.org/pdf/2009.09932'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.125117,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2009.09932'],supervised learning with projected entangled pair states,TTN/MERA/PEPS,1,Physical review. B./Physical review. B,
Accurate simulation for finite projected entangled pair states in two dimensions,"WY Liu, YZ Huang, SS Gong, ZC Gu",2021.0,66,"Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing with finite projected entangled pair states, which allows significantly enlarged system size and improves the accuracy of tensor network simulation. We demonstrate our method on the square-lattice antiferromagnetic Heisenberg model up to $32\ifmmode\times\else\texttimes\fi{}32$ sites, as well as a highly frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ model up to $24\ifmmode\times\else\texttimes\fi{}24$ sites. The results, including ground state energy and spin correlations, are in excellent agreement with those of the available quantum Monte Carlo or density matrix renormalization group methods. Therefore, our method substantially advances the calculation of 2D tensor networks for finite systems, and potentially opens a new door towards resolving many challenging strongly correlated quantum many-body problems.",Z33J9XgGDNwJ,"WY Liu, YZ Huang, SS Gong, ZC Gu - Physical Review B, 2021 - APS",['https://arxiv.org/pdf/1908.09359'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.235155,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/1908.09359'],accurate simulation for finite projected entangled pair states in two dimensions,TTN/MERA/PEPS,1,Physical review. B./Physical review. B,
Tensor networks for probabilistic sequence modeling,"J Miller, G Rabusseau, J Terilla",2021.0,59,"Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for probabilistic modeling of sequence data. We first show that u-MPS enable sequence-level parallelism, with length-n sequences able to be evaluated in depth O(log n). We then introduce a novel generative algorithm giving trained u-MPS the ability to efficiently sample from a wide variety of conditional distributions, each one defined by a regular expression. Special cases of this algorithm correspond to autoregressive and fill-in-the-blank sampling, but more complex regular expressions permit the generation of richly structured data in a manner that has no direct analogue in neural generative models. Experiments on sequence modeling with synthetic and real text data show u-MPS outperforming a variety of baselines and effectively generalizing their predictions in the presence of limited data.",_GL0x7s7hF4J,"J Miller, G Rabusseau, J Terilla - … Conference on Artificial …, 2021 - proceedings.mlr.press",['http://proceedings.mlr.press/v130/miller21a/miller21a.pdf'],https://proceedings.mlr.press/v130/miller21a.html,unknown,unknown,MPS/序列建模,2003.01039,['http://proceedings.mlr.press/v130/miller21a/miller21a.pdf'],tensor networks for probabilistic sequence modeling,MPS/序列建模,1,arXiv (Cornell University),
Hybrid convolutional neural network and projected entangled pair states wave functions for quantum many-particle states,"X Liang, SJ Dong, L He",2021.0,55,"… Neural network (NN)-based machine learning (ML) has been applied to solve various physical problems [1,2], such as experiment automation [3], quantum state classification [4–8], …",dVlv33jYN_UJ,"X Liang, SJ Dong, L He - Physical Review B, 2021 - APS",['https://arxiv.org/pdf/2009.14370'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.035138,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2009.14370'],hybrid convolutional neural network and projected entangled pair states wave functions for quantum many particle states,TTN/MERA/PEPS,1,,
Generative machine learning with tensor networks: Benchmarks on near-term quantum computers,"ML Wall, MR Abernathy, G Quiroz",2021.0,54,"Noisy, intermediate-scale quantum (NISQ) computing devices have become an industrial reality in the last few years, and cloud-based interfaces to these devices are enabling the exploration of near-term quantum computing on a range of problems.As NISQ devices are too noisy for many of the algorithms with a known quantum advantage, discovering impactful applications for near-term devices is the subject of intense research interest.We explore a quantum-assisted machine learning (QAML) workflow using NISQ devices through the perspective of tensor networks (TNs), which offer a robust platform for designing resource-efficient and expressive machine learning models to be dispatched on quantum devices.In particular, we lay out a framework for designing and optimizing TN-based QAML models using classical techniques, and then compiling these models to be run on quantum hardware, with demonstrations for generative matrix product state (MPS) models.We put forth a generalized canonical form for MPS models that aids in compilation to quantum devices, and demonstrate greedy heuristics for compiling with a given topology and gate set that outperforms known generic methods in terms of the number of entangling gates, e.g., CNOTs, in some cases by an order of magnitude.We present an exactly solvable benchmark problem for assessing the performance of MPS QAML models and also present an application for the canonical MNIST handwritten digit dataset.The impacts of hardware topology and day-to-day experimental noise fluctuations on model performance are explored by analyzing both raw experimental counts and statistical divergences of inferred distributions.We also present parametric studies of depolarization and readout noise impacts on model performance using hardware simulators.",paY7Ksj1H-YJ,"ML Wall, MR Abernathy, G Quiroz - Physical Review Research, 2021 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.3.023010'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.023010,unknown,unknown,MPS 生成/Born机,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.3.023010'],generative machine learning with tensor networks benchmarks on near term quantum computers,MPS 生成/Born机 / TTN/MERA/PEPS,2,Physical Review Research,
Direct sampling of projected entangled-pair states,"T Vieijra, J Haegeman, F Verstraete, L Vanderstraeten",2021.0,51,"Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers to long-standing questions such as the nature of the phases in the two-dimensional ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. The sampling in these Monte Carlo algorithms is typically performed with Markov chain Monte Carlo algorithms employing local update rules, which often suffer from long autocorrelation times and interdependent samples. We propose a sampling algorithm that generates independent samples from a PEPS, bypassing all problems related to finite autocorrelation times. This algorithm is a generalization of an existing direct sampling algorithm for unitary tensor networks. We introduce an auxiliary probability distribution from which independent samples can be drawn, and combine it with importance sampling in order to evaluate expectation values accurately. We benchmark our algorithm on the classical Ising model and on variational optimization of two-dimensional quantum spin models.",oAUv5SW_9BAJ,"T Vieijra, J Haegeman, F Verstraete, L Vanderstraeten - Physical Review B, 2021 - APS",['https://arxiv.org/pdf/2109.07356'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.235141,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2109.07356'],direct sampling of projected entangled pair states,TTN/MERA/PEPS,1,Physical review. B./Physical review. B,
Enabling lightweight fine-tuning for pre-trained language model compression based on matrix product operators,"P Liu, ZF Gao, WX Zhao, ZY Xie, ZY Lu…",2021.0,50,"Peiyu Liu, Ze-Feng Gao, Wayne Xin Zhao, Zhi-Yuan Xie, Zhong-Yi Lu, Ji-Rong Wen. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.",Ual--BVjv-cJ,"P Liu, ZF Gao, WX Zhao, ZY Xie, ZY Lu… - … on Natural Language …, 2021 - aclanthology.org",['https://aclanthology.org/2021.acl-long.418.pdf'],https://aclanthology.org/2021.acl-long.418/,unknown,unknown,MPS 语言模型,,['https://aclanthology.org/2021.acl-long.418.pdf'],enabling lightweight fine tuning for pre trained language model compression based on matrix product operators,MPO/TT 压缩 / MPS 语言模型,2,,
Tree-tensor-network classifiers for machine learning: From quantum inspired to quantum assisted,"ML Wall, G D'Aguanno",2021.0,50,"… In order to clarify the impact of qubit decoupling on a TTN classifier, it is useful to first describe its impact on a generative circuit given by the adjoint tensors. Namely, the generative …",hwP41TkhrkUJ,"ML Wall, G D'Aguanno - Physical Review A, 2021 - APS",['https://arxiv.org/pdf/2104.02249'],https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.042408,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2104.02249'],tree tensor network classifiers for machine learning from quantum inspired to quantum assisted,TTN/MERA/PEPS,1,,
Skeleton of matrix-product-state-solvable models connecting topological phases of matter,"NG Jones, J Bibo, B Jobst, F Pollmann, A Smith…",2021.0,47,"… These tools are most refined for the case of matrix-product states (MPS) describing one-dimensional systems. In most scenarios, such MPS are approximations to the true ground states. …",eqKgvOcb8XcJ,"NG Jones, J Bibo, B Jobst, F Pollmann, A Smith… - Physical Review …, 2021 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.3.033265'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.033265,unknown,unknown,MPS 语言模型,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.3.033265'],skeleton of matrix product state solvable models connecting topological phases of matter,MPS 语言模型,1,,
"Free versus bound entanglement, a NP-hard problem tackled by machine learning",BC Hiesmayr,2021.0,44,… Via various machine learning algorithms we can confirm that the remaining 6% of … Exploiting machine learning methods we show that those states are more likely to be separable states. …,SomHjBx3tSoJ,"BC Hiesmayr - Scientific Reports, 2021 - nature.com",['https://www.nature.com/articles/s41598-021-98523-6.pdf'],https://www.nature.com/articles/s41598-021-98523-6,unknown,unknown,TTN/MERA/PEPS,,['https://www.nature.com/articles/s41598-021-98523-6.pdf'],free versus bound entanglement a np hard problem tackled by machine learning,TTN/MERA/PEPS,1,,
Entanglement-based feature extraction by tensor network machine learning,"Y Liu, WJ Li, X Zhang, M Lewenstein, G Su…",2021.0,41,"… as matrix product states (MPS). We show how entanglement can interpret machine learning by … –3 ), which significantly improves the efficiency of the MPS machine learning. Our work …",Ik_8MvRz8mMJ,"Y Liu, WJ Li, X Zhang, M Lewenstein, G Su… - Frontiers in Applied …, 2021 - frontiersin.org",['https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.716044/pdf'],https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.716044/full,unknown,unknown,TTN/MERA/PEPS,,['https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.716044/pdf'],entanglement based feature extraction by tensor network machine learning,TTN/MERA/PEPS,1,Frontiers in Applied Mathematics and Statistics,
Towards quantifying information flows: relative entropy in deep neural networks and the renormalization group,"J Erdmenger, KT Grosvenor, R Jefferson",2021.0,41,"We investigate the analogy between the renormalization group (RG) and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by explicitly computing the relative entropy or Kullback-Leibler divergence in both the one- and two-dimensional Ising models under decimation RG, as well as in a feedforward neural network as a function of depth. We observe qualitatively identical behavior characterized by the monotonic increase to a parameter-dependent asymptotic value. On the quantum field theory side, the monotonic increase confirms the connection between the relative entropy and the c-theorem. For the neural networks, the asymptotic behavior may have implications for various information maximization methods in machine learning, as well as for disentangling compactness and generalizability. Furthermore, while both the two-dimensional Ising model and the random neural networks we consider exhibit non-trivial critical points, the relative entropy appears insensitive to the phase structure of either system. In this sense, more refined probes are required in order to fully elucidate the flow of information in these models.",SYw05WyR6OIJ,"J Erdmenger, KT Grosvenor, R Jefferson - arXiv preprint arXiv:2107.06898, 2021 - arxiv.org",['https://arxiv.org/pdf/2107.06898'],https://arxiv.org/abs/2107.06898,unknown,unknown,互信息/标度,2107.06898,['https://arxiv.org/pdf/2107.06898'],towards quantifying information flows relative entropy in deep neural networks and the renormalization group,互信息/标度,1,SciPost Physics,
Nonlinear tensor train format for deep neural network compression,"D Wang, G Zhao, H Chen, Z Liu, L Deng, G Li",2021.0,40,"… compression ratio appears to be not considerable. Therefore, in this work, by researching multiple types of tensor decompositions, we realize that tensor train … nonlinear tensor train (NTT…",nbJK2Srorv8J,"D Wang, G Zhao, H Chen, Z Liu, L Deng, G Li - Neural Networks, 2021 - Elsevier",[],https://www.sciencedirect.com/science/article/pii/S0893608021003415,unknown,unknown,MPO/TT 压缩,,[],nonlinear tensor train format for deep neural network compression,MPO/TT 压缩,1,Neural Networks,
Image search with text feedback by deep hierarchical attention mutual information maximization,"C Gu, J Bu, Z Zhang, Z Yu, D Ma, W Wang",2021.0,39,… estimating mutual information between a single-layer representation in the fusion network and … Extensive experiments on three large-scale benchmark datasets demonstrate that we can …,fnmgou2I27QJ,"C Gu, J Bu, Z Zhang, Z Yu, D Ma, W Wang - Proceedings of the 29th …, 2021 - dl.acm.org",['https://dl.acm.org/doi/pdf/10.1145/3474085.3475619'],https://dl.acm.org/doi/abs/10.1145/3474085.3475619,unknown,unknown,互信息/标度,,['https://dl.acm.org/doi/pdf/10.1145/3474085.3475619'],image search with text feedback by deep hierarchical attention mutual information maximization,互信息/标度,1,,
Computable Rényi mutual information: Area laws and correlations,"SO Scalet, ÁM Alhambra, G Styliaris, JI Cirac",2021.0,36,… We also investigate their behavior on certain tensor network … adjacent subsystems scale only like their mutual boundary and … text we listed several expressions for the mutual information: …,OWL8AAhu8poJ,"SO Scalet, ÁM Alhambra, G Styliaris, JI Cirac - Quantum, 2021 - quantum-journal.org",['https://quantum-journal.org/papers/q-2021-09-14-541/pdf/'],https://quantum-journal.org/papers/q-2021-09-14-541/,unknown,unknown,互信息/标度,2103.01709,['https://quantum-journal.org/papers/q-2021-09-14-541/pdf/'],computable r nyi mutual information area laws and correlations,互信息/标度,1,"Quantum 5, 541 (2021)",
"Quantum tensor networks, stochastic processes, and weighted automata","S Adhikary, S Srinivasan, J Miller…",2021.0,27,"… (where we evaluate probabilities sufficiently away from the end of a sequence). Section 3 presents the known equivalence between uMPS with non-negative parameters, HMMs, and …",MiM_me5S374J,"S Adhikary, S Srinivasan, J Miller… - International …, 2021 - proceedings.mlr.press",['http://proceedings.mlr.press/v130/adhikary21a/adhikary21a.pdf'],http://proceedings.mlr.press/v130/adhikary21a,unknown,unknown,MPS/序列建模,2010.10653,['http://proceedings.mlr.press/v130/adhikary21a/adhikary21a.pdf'],quantum tensor networks stochastic processes and weighted automata,MPS/序列建模,1,International Conference on Artificial Intelligence and Statistics,
TENT: Tensorized encoder transformer for temperature forecasting,"O Bilgin, P Mąka, T Vergutz, S Mehrkanoon",2021.0,27,"Reliable weather forecasting is of great importance in science, business, and society. The best performing data-driven models for weather prediction tasks rely on recurrent or convolutional neural networks, where some of which incorporate attention mechanisms. In this work, we introduce a novel model based on Transformer architecture for weather forecasting. The proposed Tensorial Encoder Transformer (TENT) model is equipped with tensorial attention and thus it exploits the spatiotemporal structure of weather data by processing it in multidimensional tensorial format. We show that compared to the classical encoder transformer, 3D convolutional neural networks, LSTM, and Convolutional LSTM, the proposed TENT model can better learn the underlying complex pattern of the weather data for the studied temperature prediction task. Experiments on two real-life weather datasets are performed. The datasets consist of historical measurements from weather stations in the USA, Canada and Europe. The first dataset contains hourly measurements of weather attributes for 30 cities in the USA and Canada from October 2012 to November 2017. The second dataset contains daily measurements of weather attributes of 18 cities across Europe from May 2005 to April 2020. Two attention scores are introduced based on the obtained tonsorial attention and are visualized in order to shed light on the decision-making process of our model and provide insight knowledge on the most important cities for the target cities.",LB5XIZRXJ_oJ,"O Bilgin, P Mąka, T Vergutz, S Mehrkanoon - arXiv preprint arXiv …, 2021 - arxiv.org",['https://arxiv.org/pdf/2106.14742'],https://arxiv.org/abs/2106.14742,unknown,unknown,张量化Transformer,2106.14742,['https://arxiv.org/pdf/2106.14742'],tent tensorized encoder transformer for temperature forecasting,张量化Transformer,1,,
Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection,"K Kottmann, P Corboz, M Lewenstein…",2021.0,20,"We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state simulations. As a benchmark, the phase diagram of the 2D frustrated bilayer Heisenberg model is analyzed, which exhibits a second-order and two first-order quantum phase transitions. We show that in order to get a good qualitative picture of the transition lines, it suffices to use data from the cost-efficient simple update optimization. Results are further improved by post-selecting ground-states based on their energy at the cost of contracting the tensor network once. Moreover, we show that the mantra of ``more training data leads to better results'' is not true for the learning task at hand and that, in principle, one training example suffices for this learning task. This puts the necessity of neural network optimizations for these learning tasks in question and we show that, at least for the model and data at hand, a simple geometric analysis suffices.",g6tOJXC2JNoJ,"K Kottmann, P Corboz, M Lewenstein… - arXiv preprint arXiv …, 2021 - arxiv.org",['https://arxiv.org/pdf/2105.09089'],https://arxiv.org/abs/2105.09089,unknown,unknown,TTN/MERA/PEPS,2105.09089,['https://arxiv.org/pdf/2105.09089'],unsupervised mapping of phase diagrams of 2d systems from infinite projected entangled pair states via deep anomaly detection,TTN/MERA/PEPS,1,"SciPost Phys. 11, 025 (2021)",
On the renormalization of entanglement entropy,"JY Pang, JW Chen",2021.0,18,"We show, using strong subadditivity and Lorentz covariance, that in three-dimensional space-time the entanglement entropy of a circle is a concave function. This implies the decrease of the coefficient of the area term and the increase of the constant term in the entropy between the ultraviolet and infrared fixed points. This is in accordance with recent holographic $c$ theorems and with conjectures about the renormalization group flow of the partition function of a three sphere ($F$ theorem). The irreversibility of the renormalization group flow in three dimensions would follow from the argument provided there is an intrinsic definition for the constant term in the entropy at fixed points. We discuss the difficulties in generalizing this result for spheres in higher dimensions.",jpOaTL7D5scJ,"JY Pang, JW Chen - AAPPS Bulletin, 2021 - Springer",['https://link.springer.com/content/pdf/10.1007/s43673-021-00032-1.pdf'],https://link.springer.com/article/10.1007/s43673-021-00032-1,unknown,unknown,互信息/标度,,['https://link.springer.com/content/pdf/10.1007/s43673-021-00032-1.pdf'],on the renormalization of entanglement entropy,互信息/标度,1,"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
Probabilistic graphical models and tensor networks: a hybrid framework,"J Miller, G Roeder, TD Bradley",2021.0,13,"We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling framework for simulating complex quantum systems. The graphical calculus of PGMs and TNs exhibits many similarities, with discrete undirected graphical models (UGMs) being a special case of TNs. However, more general probabilistic TN models such as Born machines (BMs) employ complex-valued hidden states to produce novel forms of correlation among the probabilities. While representing a new modeling resource for capturing structure in discrete probability distributions, this behavior also renders the direct application of standard PGM tools impossible. We aim to bridge this gap by introducing a hybrid PGM-TN formalism that integrates quantum-like correlations into PGM models in a principled manner, using the physically-motivated concept of decoherence. We first prove that applying decoherence to the entirety of a BM model converts it into a discrete UGM, and conversely, that any subgraph of a discrete UGM can be represented as a decohered BM. This method allows a broad family of probabilistic TN models to be encoded as partially decohered BMs, a fact we leverage to combine the representational strengths of both model families. We experimentally verify the performance of such hybrid models in a sequential modeling task, and identify promising uses of our method within the context of existing applications of graphical models.",aI-ZFrgNmWkJ,"J Miller, G Roeder, TD Bradley - arXiv preprint arXiv:2106.15666, 2021 - arxiv.org",['https://arxiv.org/pdf/2106.15666'],https://arxiv.org/abs/2106.15666,unknown,unknown,MPS/序列建模,2106.15666,['https://arxiv.org/pdf/2106.15666'],probabilistic graphical models and tensor networks a hybrid framework,MPS/序列建模,1,,
TextTN: Probabilistic encoding of language on tensor network,"P Zhang, J Zhang, X Ma, S Rao, G Tian, J Wang",2021.0,11,"… a tensor network architecture to encode and classify a sentence of words in a TN’s probabilistic manner. For a sentence with n words (ie, S=(w1,...,wn)), the tensor representation of the …",i9HBW362AxoJ,"P Zhang, J Zhang, X Ma, S Rao, G Tian, J Wang - 2021 - openreview.net",['https://openreview.net/pdf?id=uUTx2LOBMV'],https://openreview.net/forum?id=uUTx2LOBMV,unknown,unknown,MPS/序列建模,,['https://openreview.net/pdf?id=uUTx2LOBMV'],texttn probabilistic encoding of language on tensor network,MPS/序列建模,1,,
Matrix product states for inference in discrete probabilistic models,"R Bonnevie, MN Schmidt",2021.0,10,"… functionality of the matrix product state model when used as a variational approximation for tensor-shaped distributions. Throughout, we will use a stochastic block model (Nowicki and …",jLJR4_zrYbwJ,"R Bonnevie, MN Schmidt - Journal of Machine Learning Research, 2021 - jmlr.org",['http://www.jmlr.org/papers/volume22/18-431/18-431.pdf'],http://www.jmlr.org/papers/v22/18-431.html,unknown,unknown,MPS 语言模型,,['http://www.jmlr.org/papers/volume22/18-431/18-431.pdf'],matrix product states for inference in discrete probabilistic models,MPS 语言模型,1,,
QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks,"J Qi, C H Yang, P Chen",2021.0,10,"The advent of noisy intermediate-scale quantum (NISQ) computers raises a crucial challenge to design quantum neural networks for fully quantum learning tasks. To bridge the gap, this work proposes an end-to-end learning framework named QTN-VQC, by introducing a trainable quantum tensor network (QTN) for quantum embedding on a variational quantum circuit (VQC). The architecture of QTN is composed of a parametric tensor-train network for feature extraction and a tensor product encoding for quantum embedding. We highlight the QTN for quantum embedding in terms of two perspectives: (1) we theoretically characterize QTN by analyzing its representation power of input features; (2) QTN enables an end-to-end parametric model pipeline, namely QTN-VQC, from the generation of quantum embedding to the output measurement. Our experiments on the MNIST dataset demonstrate the advantages of QTN for quantum embedding over other quantum embedding approaches.",,"J Qi, C H Yang, P Chen - Quantum Tensor Networks in Machine Learning Workshop, NeurIPS 2021",[],https://arxiv.org/abs/2110.03861,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2110.03861,['https://arxiv.org/pdf/2110.03861'],qtn vqc an end to end learning framework for quantum neural networks,量子/混合LLM / 量子启发综述,1,"Quantum Tensor Networks in Machine Learning Workshop, NeurIPS 2021",
Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification,"F Kong, X Liu, R Henao",2021.0,10,"Tiny object classification problem exists in many machine learning applications like medical imaging or remote sensing, where the object of interest usually occupies a small region of the whole image. It is challenging to design an efficient machine learning model with respect to tiny object of interest. Current neural network structures are unable to deal with tiny object efficiently because they are mainly developed for images featured by large scale objects. However, in quantum physics, there is a great theoretical foundation guiding us to analyze the target function for image classification regarding to specific objects size ratio. In our work, we apply Tensor Networks to solve this arising tough machine learning problem. First, we summarize the previous work that connects quantum spin model to image classification and bring the theory into the scenario of tiny object classification. Second, we propose using 2D multi-scale entanglement renormalization ansatz (MERA) to classify tiny objects in image. In the end, our experimental results indicate that tensor network models are effective for tiny object classification problem and potentially will beat state-of-the-art. Our codes will be available online https://github.com/timqqt/MERA_Image_Classification.",,"F Kong, X Liu, R Henao - https://tensorworkshop.github.io/NeurIPS2020/CFP.html",[],https://arxiv.org/abs/2101.03154,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2101.03154,['https://arxiv.org/pdf/2101.03154'],quantum tensor network in machine learning an application to tiny object classification,量子/混合LLM / TTN/MERA/PEPS,1,https://tensorworkshop.github.io/NeurIPS2020/CFP.html,
TensorLy-Quantum: Quantum Machine Learning with Tensor Methods,"T L Patti, J Kossaifi, S F Yelin, A Anandkumar",2021.0,5,"Simulation is essential for developing quantum hardware and algorithms. However, simulating quantum circuits on classical hardware is challenging due to the exponential scaling of quantum state space. While factorized tensors can greatly reduce this overhead, tensor network-based simulators are relatively few and often lack crucial functionalities. To address this deficiency, we created TensorLy-Quantum, a Python library for quantum circuit simulation that adopts the PyTorch API. Our library leverages the optimized tensor methods of the existing TensorLy ecosystem to represent, simulate, and manipulate large-scale quantum circuits. Through compact tensor representations and efficient operations, TensorLy-Quantum can scale to hundreds of qubits on a single GPU and thousands of qubits on multiple GPUs. TensorLy-Quantum is open-source and accessible at https://github.com/tensorly/quantum",,"T L Patti, J Kossaifi, S F Yelin, A Anandkumar - arXiv preprint arXiv:2112.10239, 2021 - arxiv.org",[],https://arxiv.org/abs/2112.10239,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2112.10239,['https://arxiv.org/pdf/2112.10239'],tensorly quantum quantum machine learning with tensor methods,量子/混合LLM,1,,
Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions,"M Bachmayr, A Nouy, R Schneider",2021.0,5,"This paper is concerned with convergence estimates for fully discrete tree tensor network approximations of high-dimensional functions from several model classes. For functions having standard or mixed Sobolev regularity, new estimates generalizing and refining known results are obtained, based on notions of linear widths of multivariate functions. In the main results of this paper, such techniques are applied to classes of functions with compositional structure, which are known to be particularly suitable for approximation by deep neural networks. As shown here, such functions can also be approximated by tree tensor networks without a curse of dimensionality -- however, subject to certain conditions, in particular on the depth of the underlying tree. In addition, a constructive encoding of compositional functions in tree tensor networks is given.",,"M Bachmayr, A Nouy, R Schneider - Pure and Applied Functional Analysis, Volume 8, Number 2, 405-428, 2023",[],https://arxiv.org/abs/2112.01474,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2112.01474,['https://arxiv.org/pdf/2112.01474'],approximation by tree tensor networks in high dimensions sobolev and compositional functions,TTN/MERA/PEPS,1,"Pure and Applied Functional Analysis, Volume 8, Number 2, 405-428, 2023",
GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models,"J Alcazar, M G Vakili, C B Kalayci, A Perdomo-Ortiz",2021.0,3,"We introduce a new framework that leverages machine learning models known as generative models to solve optimization problems. Our Generator-Enhanced Optimization (GEO) strategy is flexible to adopt any generative model, from quantum to quantum-inspired or classical, such as Generative Adversarial Networks, Variational Autoencoders, or Quantum Circuit Born Machines, to name a few. Here, we focus on a quantum-inspired version of GEO relying on tensor-network Born machines and referred to hereafter as TN-GEO. We present two prominent strategies for using TN-GEO. The first uses data points previously evaluated by any quantum or classical optimizer, and we show how TN-GEO improves the performance of the classical solver as a standalone strategy in hard-to-solve instances. The second strategy uses TN-GEO as a standalone solver, i.e., when no previous observations are available. Here, we show its superior performance when the goal is to find the best minimum given a fixed budget for the number of function calls. This might be ideal in situations where the cost function evaluation can be very expensive. To illustrate our results, we run these benchmarks in the context of the portfolio optimization problem by constructing instances from the S\&P 500 and several other financial stock indexes. We also comprehensively compare state-of-the-art algorithms in a generalized version of the portfolio optimization problem. The results show that TN-GEO is among the best compared to these state-of-the-art algorithms; a remarkable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. We see this as an important step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models.",,"J Alcazar, M G Vakili, C B Kalayci, A Perdomo-Ortiz - arXiv preprint arXiv:2101.06250, 2021 - arxiv.org",[],https://arxiv.org/abs/2101.06250,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2101.06250,['https://arxiv.org/pdf/2101.06250'],geo enhancing combinatorial optimization with classical and quantum generative models,MPS 生成/Born机,1,,
A tensorized spectral attention mechanism for efficient natural language processing,"YL Xu, K Konstantinidis, S Li…",2021.0,2,"… tensorized embedding benefits from the power of multi-linear algebra and the associated tensor decomposition … training large-scale attention-based models (eg transformers), resulting …",t-_NBhWvb2MJ,"YL Xu, K Konstantinidis, S Li… - … on Quantum Tensor …, 2021 - tensorworkshop.github.io",['https://tensorworkshop.github.io/NeurIPS2021/accepted_papers/Tensorized_Spectral_Attention.pdf'],https://tensorworkshop.github.io/NeurIPS2021/accepted_papers/Tensorized_Spectral_Attention.pdf,unknown,unknown,张量化Transformer,,['https://tensorworkshop.github.io/NeurIPS2021/accepted_papers/Tensorized_Spectral_Attention.pdf'],a tensorized spectral attention mechanism for efficient natural language processing,张量化Transformer,1,,
Matrix Product State Representations for Machine Learning,"E Howard, IS Chowdhury, I Nagle",2021.0,2,"… Matrix Product States (MPS), with the aim to show that machine learning methods are a powerful tool for quantum state … , with a particular proof for Ising model. We also study the upper …",o7JBT8ypzvYJ,"E Howard, IS Chowdhury, I Nagle - Computer Science On-line …, 2021 - Springer",[],https://link.springer.com/chapter/10.1007/978-3-030-77445-5_43,unknown,unknown,MPS 语言模型,,[],matrix product state representations for machine learning,MPS 语言模型,1,,
Generative Quantum Learning of Joint Probability Distribution Functions,"E Y Zhu, S Johri, D Bacon, M Esencan, J Kim, M Muir, N Murgai, J Nguyen, N Pisenti, A Schouela, K Sosnova, K Wright",2021.0,2,"Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this work, we design quantum machine learning algorithms to model copulas. We show that any copula can be naturally mapped to a multipartite maximally entangled state. A variational ansatz we christen as a `qopula' creates arbitrary correlations between variables while maintaining the copula structure starting from a set of Bell pairs for two variables, or GHZ states for multiple variables. As an application, we train a Quantum Generative Adversarial Network (QGAN) and a Quantum Circuit Born Machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables for historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to 8 qubits and show that our results outperform those obtained through equivalent classical generative learning. Further, we present theoretical arguments for exponential advantage in our model's expressivity over classical models based on communication and computational complexity arguments.",,"E Y Zhu, S Johri, D Bacon, M Esencan, J Kim, M Muir, N Murgai, J Nguyen, N Pisenti, A Schouela, K Sosnova, K Wright - Phys. Rev. Research 4, 043092 (2022)",[],https://arxiv.org/abs/2109.06315,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2109.06315,['https://arxiv.org/pdf/2109.06315'],generative quantum learning of joint probability distribution functions,MPS 生成/Born机 / 量子/混合LLM,1,"Phys. Rev. Research 4, 043092 (2022)",
Quantum Machine Learning for Radio Astronomy,"M Kordzanganeh, A Utting, A Scaife",2021.0,2,"In this work we introduce a novel approach to the pulsar classification problem in time-domain radio astronomy using a Born machine, often referred to as a quantum neural network. Using a single-qubit architecture, we show that the pulsar classification problem maps well to the Bloch sphere and that comparable accuracies to more classical machine learning approaches are achievable. We introduce a novel single-qubit encoding for the pulsar data used in this work and show that this performs comparably to a multi-qubit QAOA encoding.",,"M Kordzanganeh, A Utting, A Scaife - arXiv preprint arXiv:2112.02655, 2021 - arxiv.org",[],https://arxiv.org/abs/2112.02655,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2112.02655,['https://arxiv.org/pdf/2112.02655'],quantum machine learning for radio astronomy,MPS 生成/Born机 / 量子/混合LLM,1,,
Semi-tensor Product-based TensorDecomposition for Neural Network Compression,"H Zhao, Y Liu, X Huang, C Zhu",2021.0,1,"The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper, the semi-tensor product is used to generalize classical matrix product-based mode product to semi-tensor mode product. As it permits the connection of two factors with different dimensionality, more flexible and compact tensor decompositions can be obtained with smaller sizes of factors. Tucker decomposition, Tensor Train (TT) and Tensor Ring (TR) are common decomposition for low rank compression of deep neural networks. The semi-tensor product is applied to these tensor decompositions to obtained their generalized versions, i.e., semi-tensor Tucker decomposition (STTu), semi-tensor train(STT) and semi-tensor ring (STR). Experimental results show the STTu, STT and STR achieve higher compression factors than the conventional tensor decompositions with the same accuracy but less training times in ResNet and WideResNetcompression. With 2% accuracy degradation, the TT-RN (rank = 14) and the TR-WRN (rank = 16) only obtain 3 times and99t times compression factors while the STT-RN (rank = 14) and the STR-WRN (rank = 16) achieve 9 times and 179 times compression factors, respectively.",,"H Zhao, Y Liu, X Huang, C Zhu - arXiv preprint arXiv:2109.15200, 2021 - arxiv.org",[],https://arxiv.org/abs/2109.15200,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2109.15200,['https://arxiv.org/pdf/2109.15200'],semi tensor product based tensordecomposition for neural network compression,MPO/TT 压缩,1,,
Matrix Product State Pre-Training for Quantum Machine Learning,"J Dborin, F Barratt, V Wimalaweera, L Wright, A G Green",2021.0,1,"Hybrid Quantum-Classical algorithms are a promising candidate for developing uses for NISQ devices. In particular, Parametrised Quantum Circuits (PQCs) paired with classical optimizers have been used as a basis for quantum chemistry and quantum optimization problems. Training PQCs relies on methods to overcome the fact that the gradients of PQCs vanish exponentially in the size of the circuits used. Tensor network methods are being increasingly used as a classical machine learning tool, as well as a tool for studying quantum systems. We introduce a circuit pre-training method based on matrix product state machine learning methods, and demonstrate that it accelerates training of PQCs for both supervised learning, energy minimization, and combinatorial optimization.",,"J Dborin, F Barratt, V Wimalaweera, L Wright, A G Green - arXiv preprint arXiv:2106.05742, 2021 - arxiv.org",[],https://arxiv.org/abs/2106.05742,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2106.05742,['https://arxiv.org/pdf/2106.05742'],matrix product state pre training for quantum machine learning,量子/混合LLM,1,,
Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus,"C Zhao, X Gao",2021.0,0,"In this paper, we propose a general scheme to analyze the gradient vanishing phenomenon, also known as the barren plateau phenomenon, in training quantum neural networks with the ZX-calculus. More precisely, we extend the barren plateaus theorem from unitary 2-design circuits to any parameterized quantum circuits under certain reasonable assumptions. The main technical contribution of this paper is representing certain integrations as ZX-diagrams and computing them with the ZX-calculus. The method is used to analyze four concrete quantum neural networks with different structures. It is shown that, for the hardware efficient ansatz and the MPS-inspired ansatz, there exist barren plateaus, while for the QCNN ansatz and the tree tensor network ansatz, there exists no barren plateau.",,"C Zhao, X Gao - Quantum 5, 466 (2021)",[],https://arxiv.org/abs/2102.01828,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2102.01828,['https://arxiv.org/pdf/2102.01828'],analyzing the barren plateau phenomenon in training quantum neural networks with the zx calculus,量子/混合LLM / TTN/MERA/PEPS,1,"Quantum 5, 466 (2021)",
Convolutional Neural Network Compression through Generalized Kronecker Product Decomposition,"M G A Hameed, M S Tahaei, A Mosleh, V P Nia",2021.0,0,"Modern Convolutional Neural Network (CNN) architectures, despite their superiority in solving various problems, are generally too large to be deployed on resource constrained edge devices. In this paper, we reduce memory usage and floating-point operations required by convolutional layers in CNNs. We compress these layers by generalizing the Kronecker Product Decomposition to apply to multidimensional tensors, leading to the Generalized Kronecker Product Decomposition (GKPD). Our approach yields a plug-and-play module that can be used as a drop-in replacement for any convolutional layer. Experimental results for image classification on CIFAR-10 and ImageNet datasets using ResNet, MobileNetv2 and SeNet architectures substantiate the effectiveness of our proposed approach. We find that GKPD outperforms state-of-the-art decomposition methods including Tensor-Train and Tensor-Ring as well as other relevant compression methods such as pruning and knowledge distillation.",,"M G A Hameed, M S Tahaei, A Mosleh, V P Nia - arXiv preprint arXiv:2109.14710, 2021 - arxiv.org",[],https://arxiv.org/abs/2109.14710,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2109.14710,['https://arxiv.org/pdf/2109.14710'],convolutional neural network compression through generalized kronecker product decomposition,MPO/TT 压缩,1,,
F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits,"C Leadbeater, L Sharrock, B Coyle, M Benedetti",2021.0,0,"Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit Born machine. In particular, we consider training a quantum circuit Born machine using $f$-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any $f$-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the Born machine. The first is based on $f$-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing $f$-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback-Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another $f$-divergence, namely, the Pearson divergence.",,"C Leadbeater, L Sharrock, B Coyle, M Benedetti - Entropy 2021, 23(10), 1281",[],https://arxiv.org/abs/2110.04253,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2110.04253,['https://arxiv.org/pdf/2110.04253'],f divergences and cost function locality in generative modelling with quantum circuits,MPS 生成/Born机,1,"Entropy 2021, 23(10), 1281",
Active learning of tree tensor networks using optimal least-squares,"C Haberstich, A Nouy, G Perrin",2021.0,0,"In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that generates a sequence of nested tensor subspaces based on a generalization of principal component analysis for multivariate functions. An optimal least-squares method is used for computing projections onto the generated tensor subspaces, using samples generated from a distribution depending on the previously generated subspaces. We provide an error bound in expectation for the obtained approximation. Practical strategies are proposed for adapting the feature spaces and ranks to achieve a prescribed error. Also, we propose an algorithm that progressively constructs the dimension tree by suitable pairings of variables, that allows to further reduce the number of samples necessary to reach that error. Numerical examples illustrate the performance of the proposed algorithms and show that stable approximations are obtained with a number of samples close to the number of free parameters of the estimated tensor networks.",,"C Haberstich, A Nouy, G Perrin - arXiv preprint arXiv:2104.13436, 2021 - arxiv.org",[],https://arxiv.org/abs/2104.13436,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2104.13436,['https://arxiv.org/pdf/2104.13436'],active learning of tree tensor networks using optimal least squares,TTN/MERA/PEPS / MPS/序列建模,1,,
Born Machines for Periodic and Open XY Quantum Spin Chains,"A M Gomez, S F Yelin, K Najafi",2021.0,0,"Quantum phase transitions are ubiquitous in quantum many body systems. The quantum fluctuations that occur at very low temperatures are known to be responsible for driving the system across different phases as a function of an external control parameter. The XY Hamiltonian with a transverse field is a basic model that manifests two distinct quantum phase transitions, including spontaneous $Z_2$ symmetry breaking from an ordered to a disordered state. While programmable quantum devices have shown great success in investigating the various exotic quantum phases of matter, in parallel, the quest for harnessing machine learning tools in learning quantum phases of matter is ongoing. In this paper, we present a numerical study of the power of a quantum-inspired generative model known as the Born machine in learning quantum phases of matter. Data obtained from the system under open and periodic boundary conditions is considered. Our results indicate that a Born machine based on matrix product states can successfully capture the quantum state across various phases of the XY Hamiltonian and close to a critical point, despite the existence of long-range correlations. We further impose boundary conditions on the Born machine and show that matching the boundary condition of the Born machine and that of the training data improves performance when limited data is available and a small bond dimension is employed.",,"A M Gomez, S F Yelin, K Najafi - arXiv preprint arXiv:2112.05326, 2021 - arxiv.org",[],https://arxiv.org/abs/2112.05326,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2112.05326,['https://arxiv.org/pdf/2112.05326'],born machines for periodic and open xy quantum spin chains,MPS 生成/Born机,1,,
Neural Tangent Kernel of Matrix Product States: Convergence and Applications,"E Guo, D Draper",2021.0,0,"In this work, we study the Neural Tangent Kernel (NTK) of Matrix Product States (MPS) and the convergence of its NTK in the infinite bond dimensional limit. We prove that the NTK of MPS asymptotically converges to a constant matrix during the gradient descent (training) process (and also the initialization phase) as the bond dimensions of MPS go to infinity by the observation that the variation of the tensors in MPS asymptotically goes to zero during training in the infinite limit. By showing the positive-definiteness of the NTK of MPS, the convergence of MPS during the training in the function space (space of functions represented by MPS) is guaranteed without any extra assumptions of the data set. We then consider the settings of (supervised) Regression with Mean Square Error (RMSE) and (unsupervised) Born Machines (BM) and analyze their dynamics in the infinite bond dimensional limit. The ordinary differential equations (ODEs) which describe the dynamics of the responses of MPS in the RMSE and BM are derived and solved in the closed-form. For the Regression, we consider Mercer Kernels (Gaussian Kernels) and find that the evolution of the mean of the responses of MPS follows the largest eigenvalue of the NTK. Due to the orthogonality of the kernel functions in BM, the evolution of different modes (samples) decouples and the ""characteristic time"" of convergence in training is obtained.",,"E Guo, D Draper - arXiv preprint arXiv:2111.14046, 2021 - arxiv.org",[],https://arxiv.org/abs/2111.14046,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2111.14046,['https://arxiv.org/pdf/2111.14046'],neural tangent kernel of matrix product states convergence and applications,MPS 生成/Born机,1,,
On the closedness and geometry of tensor network state sets,"T Barthel, J Lu, G Friesecke",2021.0,0,"Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. We discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states (TTNS), and the multiscale entanglement renormalization ansatz (MERA) are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled-pair states (PEPS) are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.",,"T Barthel, J Lu, G Friesecke - Lett. Math. Phys. 112, 72 (2022)",[],https://arxiv.org/abs/2108.00031,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2108.00031,['https://arxiv.org/pdf/2108.00031'],on the closedness and geometry of tensor network state sets,TTN/MERA/PEPS,1,"Lett. Math. Phys. 112, 72 (2022)",
Symmetries and local transformations of translationally invariant Matrix Product States,"M Hebenstreit, D Sauerwein, A Molnar, J I Cirac, B Kraus",2021.0,,"We determine the local symmetries and local transformation properties of translationally invariant matrix product states (MPS). We focus on physical dimension $d=2$ and bond dimension $D=3$ and use the procedure introduced in D. Sauerwein et al., Phys. Rev. Lett. 123, 170504 (2019) to determine all (including non--global) symmetries of those states. We identify and classify the stochastic local transformations (SLOCC) that are allowed among MPS. We scrutinize two very distinct sets of MPS and show the big diversity (also compared to the case $D=2$) occurring in both, their symmetries and the possible SLOCC transformations. These results reflect the variety of local properties of MPS, even if restricted to translationally invariant states with low bond dimension. Finally, we show that states with non-trivial local symmetries are of measure zero for $d = 2$ and $D > 3$.",,"M Hebenstreit, D Sauerwein, A Molnar, J I Cirac, B Kraus - arXiv preprint arXiv:2111.02457, 2021 - arxiv.org",[],https://arxiv.org/abs/2111.02457,arxiv-completion,2026-09-26 (citations:OpenAlex),,2111.02457,['https://arxiv.org/pdf/2111.02457'],symmetries and local transformations of translationally invariant matrix product states,,1,,
TedNet: A Pytorch Toolkit for Tensor Decomposition Networks,"Y Pan, M Wang, Z Xu",2021.0,,"Tensor Decomposition Networks (TDNs) prevail for their inherent compact architectures. To give more researchers a flexible way to exploit TDNs, we present a Pytorch toolkit named TedNet. TedNet implements 5 kinds of tensor decomposition(i.e., CANDECOMP/PARAFAC (CP), Block-Term Tucker (BTT), Tucker-2, Tensor Train (TT) and Tensor Ring (TR) on traditional deep neural layers, the convolutional layer and the fully-connected layer. By utilizing the basic layers, it is simple to construct a variety of TDNs. TedNet is available at https://github.com/tnbar/tednet.",,"Y Pan, M Wang, Z Xu - arXiv preprint arXiv:2104.05018, 2021 - arxiv.org",[],https://arxiv.org/abs/2104.05018,arxiv-completion,2026-09-26 (citations:OpenAlex),,2104.05018,['https://arxiv.org/pdf/2104.05018'],tednet a pytorch toolkit for tensor decomposition networks,,1,,
Tensor Yard: One-Shot Algorithm of Hardware-Friendly Tensor-Train Decomposition for Convolutional Neural Networks,"A Taskynov, V Korviakov, I Mazurenko, Y Xiong",2021.0,0,"Nowadays Deep Learning became widely used in many economic, technical and scientific areas of human interest. It is clear that efficiency of solutions based on Deep Neural Networks should consider not only quality metric for the target task, but also latency and constraints of target platform design should be taken into account. In this paper we present novel hardware-friendly Tensor-Train decomposition implementation for Convolutional Neural Networks together with Tensor Yard - one-shot training algorithm which optimizes an order of decomposition of network layers. These ideas allow to accelerate ResNet models on Ascend 310 NPU devices without significant loss of accuracy. For example we accelerate ResNet-101 by 14.6% with drop by 0.5 of top-1 ImageNet accuracy.",,"A Taskynov, V Korviakov, I Mazurenko, Y Xiong - arXiv preprint arXiv:2108.04029, 2021 - arxiv.org",[],https://arxiv.org/abs/2108.04029,arxiv-completion,2026-09-26 (citations:OpenAlex),,2108.04029,['https://arxiv.org/pdf/2108.04029'],tensor yard one shot algorithm of hardware friendly tensor train decomposition for convolutional neural networks,,1,,
Tensor-Train Recurrent Neural Networks for Interpretable Multi-Way Financial Forecasting,"Y L Xu, G G Calvi, D P Mandic",2021.0,0,"Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential increase in the number of parameters imposes a computational bottleneck. The necessity to equip RNNs with the ability to deal with the curse of dimensionality, such as through the parameter compression ability inherent to tensors, has led to the development of the Tensor-Train RNN (TT-RNN). Despite achieving promising results in many applications, the full potential of the TT-RNN is yet to be explored in the context of interpretable financial modelling, a notoriously challenging task characterized by multi-modal data with low signal-to-noise ratio. To address this issue, we investigate the potential of TT-RNN in the task of financial forecasting of currencies. We show, through the analysis of TT-factors, that the physical meaning underlying tensor decomposition, enables the TT-RNN model to aid the interpretability of results, thus mitigating the notorious ""black-box"" issue associated with neural networks. Furthermore, simulation results highlight the regularization power of TT decomposition, demonstrating the superior performance of TT-RNN over its uncompressed RNN counterpart and other tensor forecasting methods.",,"Y L Xu, G G Calvi, D P Mandic - arXiv preprint arXiv:2105.04983, 2021 - arxiv.org",[],https://arxiv.org/abs/2105.04983,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2105.04983,['https://arxiv.org/pdf/2105.04983'],tensor train recurrent neural networks for interpretable multi way financial forecasting,MPO/TT 压缩 / MPS/序列建模,1,,
The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning,"Z Liu, L Yu, L - Duan, D Deng",2021.0,0,"Tensor networks are efficient representations of high-dimensional tensors with widespread applications in quantum many-body physics. Recently, they have been adapted to the field of machine learning, giving rise to an emergent research frontier that has attracted considerable attention. Here, we study the trainability of tensor-network based machine learning models by exploring the landscapes of different loss functions, with a focus on the matrix product states (also called tensor trains) architecture. In particular, we rigorously prove that barren plateaus (i.e., exponentially vanishing gradients) prevail in the training process of the machine learning algorithms with global loss functions. Whereas, for local loss functions the gradients with respect to variational parameters near the local observables do not vanish as the system size increases. Therefore, the barren plateaus are absent in this case and the corresponding models could be efficiently trainable. Our results reveal a crucial aspect of tensor-network based machine learning in a rigorous fashion, which provide a valuable guide for both practical applications and theoretical studies in the future.",,"Z Liu, L Yu, L - Duan, D Deng - arXiv preprint arXiv:2108.08312, 2021 - arxiv.org",[],https://arxiv.org/abs/2108.08312,arxiv-completion,2026-09-26 (citations:OpenAlex),,2108.08312,['https://arxiv.org/pdf/2108.08312'],the presence and absence of barren plateaus in tensor network based machine learning,,1,,
Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr$_2$RuO$_4$,"X Cao, Y Lu, P Hansmann, M W Haverkort",2021.0,0,"We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diagonal Green's functions. For the archetypal correlated Hund's metal Sr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra related to the van Hove singularity and the high-energy atomic multiplet excitations can be faithfully resolved. In particular, we show that while the spin-orbit coupling has only minor effects on the orbital-diagonal one-particle spectral functions, it has a more profound impact on the low-energy spin and orbital response functions.",,"X Cao, Y Lu, P Hansmann, M W Haverkort - Phys. Rev. B 104, 115119 (2021)",[],https://arxiv.org/abs/2103.05545,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2103.05545,['https://arxiv.org/pdf/2103.05545'],tree tensor network real time multiorbital impurity solver spin orbit coupling and correlation functions in sr 2 ruo 4,TTN/MERA/PEPS,1,"Phys. Rev. B 104, 115119 (2021)",
Kronecker Decomposition for GPT Compression,"A Edalati, M Tahaei, A Rashid, V P Nia, J J Clark, M Rezagholizadeh",2021.0,,"GPT is an auto-regressive Transformer-based pre-trained language model which has attracted a lot of attention in the natural language processing (NLP) domain due to its state-of-the-art performance in several downstream tasks. The success of GPT is mostly attributed to its pre-training on huge amount of data and its large number of parameters (from ~100M to billions of parameters). Despite the superior performance of GPT (especially in few-shot or zero-shot setup), this overparameterized nature of GPT can be very prohibitive for deploying this model on devices with limited computational power or memory. This problem can be mitigated using model compression techniques; however, compressing GPT models has not been investigated much in the literature. In this work, we use Kronecker decomposition to compress the linear mappings of the GPT-22 model. Our Kronecker GPT-2 model (KnGPT2) is initialized based on the Kronecker decomposed version of the GPT-2 model and then is undergone a very light pre-training on only a small portion of the training data with intermediate layer knowledge distillation (ILKD). Finally, our KnGPT2 is fine-tuned on down-stream tasks using ILKD as well. We evaluate our model on both language modeling and General Language Understanding Evaluation benchmark tasks and show that with more efficient pre-training and similar number of parameters, our KnGPT2 outperforms the existing DistilGPT2 model significantly.",,"A Edalati, M Tahaei, A Rashid, V P Nia, J J Clark, M Rezagholizadeh - arXiv preprint arXiv:2110.08152, 2021 - arxiv.org",[],https://arxiv.org/abs/2110.08152,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2110.08152,['https://arxiv.org/pdf/2110.08152'],kronecker decomposition for gpt compression,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩,1,,
Towards Extremely Compact RNNs for Video Recognition with Fully Decomposed Hierarchical Tucker Structure,"M Yin, S Liao, X Liu, X Wang, B Yuan",2021.0,,"Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges. Although various prior works have been proposed to reduce the RNN model sizes, executing RNN models in resource-restricted environments is still a very challenging problem. In this paper, we propose to develop extremely compact RNN models with fully decomposed hierarchical Tucker (FDHT) structure. The HT decomposition does not only provide much higher storage cost reduction than the other tensor decomposition approaches but also brings better accuracy performance improvement for the compact RNN models. Meanwhile, unlike the existing tensor decomposition-based methods that can only decompose the input-to-hidden layer of RNNs, our proposed fully decomposition approach enables the comprehensive compression for the entire RNN models with maintaining very high accuracy. Our experimental results on several popular video recognition datasets show that our proposed fully decomposed hierarchical tucker-based LSTM (FDHT-LSTM) is extremely compact and highly efficient. To the best of our knowledge, FDHT-LSTM, for the first time, consistently achieves very high accuracy with only few thousand parameters (3,132 to 8,808) on different datasets. Compared with the state-of-the-art compressed RNN models, such as TT-LSTM, TR-LSTM and BT-LSTM, our FDHT-LSTM simultaneously enjoys both order-of-magnitude (3,985x to 10,711x) fewer parameters and significant accuracy improvement (0.6% to 12.7%).",,"M Yin, S Liao, X Liu, X Wang, B Yuan - arXiv preprint arXiv:2104.05758, 2021 - arxiv.org",[],https://arxiv.org/abs/2104.05758,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2104.05758,['https://arxiv.org/pdf/2104.05758'],towards extremely compact rnns for video recognition with fully decomposed hierarchical tucker structure,MPO/TT 压缩 / MPS/序列建模,1,,
Enhancing generative models via quantum correlations,"X Gao, ER Anschuetz, ST Wang, JI Cirac, MD Lukin",2022.0,176,"Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning.Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models.We show theoretically that such quantum-inspired correlations provide a powerful resource for generative modeling.In particular, we provide an unconditional proof of separation in expressive power between a class of widely used generative models, known as Bayesian networks, and its minimal quantum-inspired extension.We show that this expressivity enhancement is associated with quantum nonlocality and quantum contextuality.Furthermore, we numerically test this separation on standard machine-learning data sets and show that it holds for practical problems.The possibility of quantum-inspired enhancement demonstrated in this work not only sheds light on the design of useful quantum machine-learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.",vuYnTLPNCooJ,"X Gao, ER Anschuetz, ST Wang, JI Cirac, MD Lukin - Physical Review X, 2022 - APS",['https://link.aps.org/pdf/10.1103/PhysRevX.12.021037'],https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.021037,unknown,unknown,MPS 生成/Born机,,['https://link.aps.org/pdf/10.1103/PhysRevX.12.021037'],enhancing generative models via quantum correlations,MPS 生成/Born机,1,Physical Review X,
Tensor program optimization with probabilistic programs,"J Shao, X Zhou, S Feng, B Hou, R Lai…",2022.0,108,"… There are many general-purpose probabilistic languages, such as Church [17], Stan [8], … probabilistic language for tensor program optimization with specializations such as tensor …",WwNXreLT4twJ,"J Shao, X Zhou, S Feng, B Hou, R Lai… - Advances in …, 2022 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2022/file/e894eafae43e68b4c8dfdacf742bcbf3-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2022/hash/e894eafae43e68b4c8dfdacf742bcbf3-Abstract-Conference.html,unknown,unknown,MPS/序列建模,2205.13603,['https://proceedings.neurips.cc/paper_files/paper/2022/file/e894eafae43e68b4c8dfdacf742bcbf3-Paper-Conference.pdf'],tensor program optimization with probabilistic programs,MPS/序列建模,1,,
Entanglement phase transitions in random stabilizer tensor networks,"ZC Yang, Y Li, MPA Fisher, X Chen",2022.0,58,"… , and extract universal operator scaling dimensions via … mutual information for RSTNs with different bond dimensions as a function of η, where we find that the curves for tensor networks …",AFg9dMTPM94J,"ZC Yang, Y Li, MPA Fisher, X Chen - Physical Review B, 2022 - APS",['https://arxiv.org/pdf/2107.12376'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.104306,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/2107.12376'],entanglement phase transitions in random stabilizer tensor networks,互信息/标度,1,,
Testing matrix product states,"M Soleimanifar, J Wright",2022.0,49,"Matrix product states (MPS) are a class of physically-relevant quantum states which arise in the study of quantum many-body systems. A quantum state comprised of n qudits is said to be an MPS of bond dimension r if the reduced density matrix ψ1, …, k has rank r for each k ∊ {1, …, n}. When r = 1, this corresponds to the set of product states, i.e. states of the form |ψ1〉 ⊗ ⃛ ⊗ |ψn), which possess no entanglement. For larger values of r, this yields a more expressive class of quantum states, which are allowed to possess limited amounts of entanglement. Devising schemes for testing the amount of entanglement in quantum systems has played a crucial role in quantum computing and information theory. In this work, we study the problem of testing whether an unknown state |ψ〉 is an MPS in the property testing model. In this model, one is given m identical copies of |ψ〉, and the goal is to determine whether |ψ〉 is an MPS of bond dimension r or whether |ψ〉 is far from all such states. For the case of product states, we study the product test, a simple two-copy test previously analyzed by Harrow and Montanaro [17], and a key ingredient in their proof that QMA(2) = QMA(k) for k ≥ 2. We give a new and simpler analysis of the product test which achieves an optimal bound for a wide range of parameters, answering open problems in [17] and [23]. For the case of r ≥ 2, we give an efficient algorithm for testing whether |ψ〉 is an MPS of bond dimension r using m = O(nr2) copies, independent of the dimensions of the qudits, and we show that Ω(n1/2) copies are necessary for this task. This lower bound shows that a dependence on the number of qudits n is necessary, in sharp contrast to the case of product states where a constant number of copies suffices.",qBWv36oefDAJ,"M Soleimanifar, J Wright - Proceedings of the 2022 Annual ACM-SIAM …, 2022 - SIAM",['https://arxiv.org/pdf/2201.01824'],https://epubs.siam.org/doi/abs/10.1137/1.9781611977073.68,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/2201.01824'],testing matrix product states,MPS 语言模型,1,Society for Industrial and Applied Mathematics eBooks,
Multi-View Tensor Graph Neural Networks Through Reinforced Aggregation,"X Zhao, Q Dai, J X Wu, H M Peng, M Liu, X Bai, J Tan, S Wang",2022.0,49,"Graph Neural Networks (GNNs) have yielded fruitful results in learning multi-view graph data. However, it is challenging for existing GNNs to capture the potential correlation information (PCI) among the graph structure features of multiple views. It is also challenging to adaptively identify valuable neighbors for node feature fusion in different views. To this end, we propose a novelReinforcedTensorGraphNeuralNetwork (RTGNN) framework to more effectively perform multi-view graph representation learning through reinforcing inter- and intra-graph aggregation. Specifically, RTGNN first uses tensor decomposition to extract the graph structure features (GSFs) of each view in the common feature space. These GSFs contain the PCI of multiple views and alleviate fusion conflicts that may be caused by differences between view feature spaces in cross-view feature fusion. Since fusing the features of all neighbor nodes may harm the features of the center node, we filter the irrelevant neighbors to improve the performance of intra-graph aggregation in each view. Concretely, a reinforcement learning (RL)-guided scheme is developed to automatically calculate the optimal filtering threshold for each view, avoiding tedious manual updates and infeasible back propagation updates. Experimental results and analysis on five datasets show that RTGNN surpasses the best multi-view graph representation baselines and achieves the maximum 14.26% performance improvement in terms of F1. The code link ishttps://github.com/RingBDStack/RTGNN.",,"X Zhao, Q Dai, J X Wu, H M Peng, M Liu, X Bai, J Tan, S Wang - IEEE Transactions on Knowledge and Data Engineering, 2022",[],https://doi.org/10.1109/tkde.2022.3142179,arxiv-completion,2026-09-26 (citations:OpenAlex),,,[],multi view tensor graph neural networks through reinforced aggregation,,1,IEEE Transactions on Knowledge and Data Engineering,
A -Tensor-Aided Multiscale Transformer for Remaining Useful Life Prediction in IIoT,"L Ren, Z Jia, X Wang, J Dong…",2022.0,44,"… First, we propose a novel tensorized representation of time… The T2-tensors and the tensor decomposed transformer model … However, the attention mechanism of the transformer only …",c8nmQc7ubDEJ,"L Ren, Z Jia, X Wang, J Dong… - IEEE Transactions on …, 2022 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/9756042/,unknown,unknown,张量化Transformer,,[],a tensor aided multiscale transformer for remaining useful life prediction in iiot,张量化Transformer,1,,
Mutual information scaling for tensor network machine learning,"I Convy, W Huggins, H Liao…",2022.0,40,"… how entanglement scaling relates to tensor network methods in … mutual information (MI), which provides a generalized measure of correlation. We show that when using tensor networks …",OUv2dgWFclIJ,"I Convy, W Huggins, H Liao… - … learning: science and …, 2022 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/2632-2153/ac44a9/pdf'],https://iopscience.iop.org/article/10.1088/2632-2153/ac44a9/meta,unknown,unknown,互信息/标度,2103.00105,['https://iopscience.iop.org/article/10.1088/2632-2153/ac44a9/pdf'],mutual information scaling for tensor network machine learning,互信息/标度,1,Mach. Learn.: Sci. Technol. 3 015017 (2022),
Entanglement quantification from collective measurements processed by machine learning,"J Roik, K Bartkiewicz, A Černoch, K Lemr",2022.0,35,"… Machine learning has penetrated many areas of science, helping with finding complex models based on large data sets [46]. Artificial neural networks (ANNs) are particularly well suited …",U17WEDkKEz0J,"J Roik, K Bartkiewicz, A Černoch, K Lemr - Physics Letters A, 2022 - Elsevier",[],https://www.sciencedirect.com/science/article/pii/S0375960122003528,unknown,unknown,TTN/MERA/PEPS,2203.01607,[],entanglement quantification from collective measurements processed by machine learning,TTN/MERA/PEPS,1,,
Generative modeling with projected entangled-pair states,"T Vieijra, L Vanderstraeten, F Verstraete",2022.0,35,"We argue and demonstrate that projected entangled-pair states (PEPS) outperform matrix product states significantly for the task of generative modeling of datasets with an intrinsic two-dimensional structure such as images. Our approach builds on a recently introduced algorithm for sampling PEPS, which allows for the efficient optimization and sampling of the distributions.",QE96dM1ghhcJ,"T Vieijra, L Vanderstraeten, F Verstraete - arXiv preprint arXiv:2202.08177, 2022 - arxiv.org",['https://arxiv.org/pdf/2202.08177'],https://arxiv.org/abs/2202.08177,unknown,unknown,MPS 生成/Born机,2202.08177,['https://arxiv.org/pdf/2202.08177'],generative modeling with projected entangled pair states,MPS 生成/Born机 / TTN/MERA/PEPS,2,,
Born machine model based on matrix product state quantum circuit,"LH Gong, LZ Xiang, SH Liu, NR Zhou",2022.0,33,"… A new class of quantum generative models, Born machines directly utilize the probability interpretation of the wave function to approximate the probability distribution of target data [13], […",cAK76-TR5ZoJ,"LH Gong, LZ Xiang, SH Liu, NR Zhou - Physica A: Statistical Mechanics …, 2022 - Elsevier",[],https://www.sciencedirect.com/science/article/pii/S0378437122000322,unknown,unknown,MPS 生成/Born机,,[],born machine model based on matrix product state quantum circuit,MPS 生成/Born机,1,Physica A Statistical Mechanics and its Applications,
Conditional Born machine for Monte Carlo event generation,"O Kiss, M Grossi, E Kajomovitz, S Vallecorsa",2022.0,33,"… The present paper focuses on generative modeling in quantum machine learning (QML), … regime, generative models are often expressed as neural networks. For instance, generative …",gd9j_09MplEJ,"O Kiss, M Grossi, E Kajomovitz, S Vallecorsa - Physical Review A, 2022 - APS",['https://link.aps.org/pdf/10.1103/PhysRevA.106.022612'],https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.022612,unknown,unknown,MPS 生成/Born机,,['https://link.aps.org/pdf/10.1103/PhysRevA.106.022612'],conditional born machine for monte carlo event generation,MPS 生成/Born机,1,,
Language design as information renormalization,"AJ Gallego, R Orús",2022.0,29,"… ie, the Shannon entropy of the reduced probability distribution for the block of n words is larger than the entanglement entropy of the block. This relation, combined with Eq. (34), implies …",Z42oCZXvC68J,"AJ Gallego, R Orús - SN Computer Science, 2022 - Springer",['https://arxiv.org/pdf/1708.01525'],https://link.springer.com/article/10.1007/s42979-021-01002-y,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/1708.01525'],language design as information renormalization,互信息/标度,1,,
Toward compact transformers for end-to-end object detection with decomposed chain tensor structure,"P Zhen, X Yan, W Wang, T Hou, H Wei…",2022.0,20,"… a tensorized compression method for the detection transformer. By rearranging the weight matrices into high-order tensors and adopting a low-rank tensor factorization, … -head attention (…",_azQ1U59f1IJ,"P Zhen, X Yan, W Wang, T Hou, H Wei… - IEEE Transactions on …, 2022 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/9895435/,unknown,unknown,张量化Transformer,,[],toward compact transformers for end to end object detection with decomposed chain tensor structure,张量化Transformer,1,,
Deeply tensor compressed transformers for end-to-end object detection,"P Zhen, Z Gao, T Hou, Y Cheng, HB Chen",2022.0,19,"DEtection TRansformer (DETR) is a recently proposed method that streamlines the detection pipeline and achieves competitive results against two-stage detectors such as Faster-RCNN. The DETR models get rid of complex anchor generation and post-processing procedures thereby making the detection pipeline more intuitive. However, the numerous redundant parameters in transformers make the DETR models computation and storage intensive, which seriously hinder them to be deployed on the resources-constrained devices. In this paper, to obtain a compact end-to-end detection framework, we propose to deeply compress the transformers with low-rank tensor decomposition. The basic idea of the tensor-based compression is to represent the large-scale weight matrix in one network layer with a chain of low-order matrices. Furthermore, we propose a gated multi-head attention (GMHA) module to mitigate the accuracy drop of the tensor-compressed DETR models. In GMHA, each attention head has an independent gate to determine the passed attention value. The redundant attention information can be suppressed by adopting the normalized gates. Lastly, to obtain fully compressed DETR models, a low-bitwidth quantization technique is introduced for further reducing the model storage size. Based on the proposed methods, we can achieve significant parameter and model size reduction while maintaining high detection performance. We conduct extensive experiments on the COCO dataset to validate the effectiveness of our tensor-compressed (tensorized) DETR models. The experimental results show that we can attain 3.7 times full model compression with 482 times feed forward network (FFN) parameter reduction and only 0.6 points accuracy drop.",-JrFFke0BZYJ,"P Zhen, Z Gao, T Hou, Y Cheng, HB Chen - Proceedings of the AAAI …, 2022 - ojs.aaai.org",['https://ojs.aaai.org/index.php/AAAI/article/download/20397/20156'],https://ojs.aaai.org/index.php/AAAI/article/view/20397,unknown,unknown,张量化Transformer,,['https://ojs.aaai.org/index.php/AAAI/article/download/20397/20156'],deeply tensor compressed transformers for end to end object detection,张量化Transformer,1,Proceedings of the AAAI Conference on Artificial Intelligence,
Explainable natural language processing with matrix product states,"J Tangpanitanon, C Mangkang, P Bhadola…",2022.0,19,"Abstract Despite empirical successes of recurrent neural networks (RNNs) in natural language processing (NLP), theoretical understanding of RNNs is still limited due to intrinsically complex non-linear computations. We systematically analyze RNNs’ behaviors in a ubiquitous NLP task, the sentiment analysis of movie reviews, via the mapping between a class of RNNs called recurrent arithmetic circuits (RACs) and a matrix product state. Using the von-Neumann entanglement entropy (EE) as a proxy for information propagation, we show that single-layer RACs possess a maximum information propagation capacity, reflected by the saturation of the EE. Enlarging the bond dimension beyond the EE saturation threshold does not increase model prediction accuracies, so a minimal model that best estimates the data statistics can be inferred. Although the saturated EE is smaller than the maximum EE allowed by the area law, our minimal model still achieves ∼ 99 % training accuracies in realistic sentiment analysis data sets. Thus, low EE is not a warrant against the adoption of single-layer RACs for NLP. Contrary to a common belief that long-range information propagation is the main source of RNNs’ successes, we show that single-layer RACs harness high expressiveness from the subtle interplay between the information propagation and the word vector embeddings. Our work sheds light on the phenomenology of learning in RACs, and more generally on the explainability of RNNs for NLP, using tools from many-body quantum physics.",yATlHDmqel4J,"J Tangpanitanon, C Mangkang, P Bhadola… - New Journal of …, 2022 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/1367-2630/ac6232/pdf'],https://iopscience.iop.org/article/10.1088/1367-2630/ac6232/meta,unknown,unknown,MPS 语言模型,2112.08628,['https://iopscience.iop.org/article/10.1088/1367-2630/ac6232/pdf'],explainable natural language processing with matrix product states,MPS 语言模型,1,New Journal of Physics,
Heat: Hardware-efficient automatic tensor decomposition for transformer compression,"J Gu, B Keller, J Kossaifi, A Anandkumar…",2022.0,15,"Transformers have attained superior performance in natural language processing and computer vision. Their self-attention and feedforward layers are overparameterized, limiting inference speed and energy efficiency. Tensor decomposition is a promising technique to reduce parameter redundancy by leveraging tensor algebraic properties to express the parameters in a factorized form. Prior efforts used manual or heuristic factorization settings without hardware-aware customization, resulting in poor hardware efficiencies and large performance degradation. In this work, we propose a hardware-aware tensor decomposition framework, dubbed HEAT, that enables efficient exploration of the exponential space of possible decompositions and automates the choice of tensorization shape and decomposition rank with hardware-aware co-optimization. We jointly investigate tensor contraction path optimizations and a fused Einsum mapping strategy to bridge the gap between theoretical benefits and real hardware efficiency improvement. Our two-stage knowledge distillation flow resolves the trainability bottleneck and thus significantly boosts the final accuracy of factorized Transformers. Overall, we experimentally show that our hardware-aware factorized BERT variants reduce the energy-delay product by 5.7x with less than 1.1% accuracy loss and achieve a better efficiency-accuracy Pareto frontier than hand-tuned and heuristic baselines.",d-UsOM3CNMQJ,"J Gu, B Keller, J Kossaifi, A Anandkumar… - arXiv preprint arXiv …, 2022 - arxiv.org",['https://arxiv.org/pdf/2211.16749'],https://arxiv.org/abs/2211.16749,unknown,unknown,张量化Transformer,2211.16749,['https://arxiv.org/pdf/2211.16749'],heat hardware efficient automatic tensor decomposition for transformer compression,张量化Transformer,1,arXiv (Cornell University),
Convolutional neural network compression via tensor-train decomposition on permuted weight tensor with automatic rank determination,"M Gabor, R Zdunek",2022.0,14,… neural network compression method using direct tensor-train decomposition on the permuted kernel weight tensor … proposed compression method was applied to four neural networks: …,LHiKyiyxLuUJ,"M Gabor, R Zdunek - International Conference on Computational Science, 2022 - Springer",['https://www.iccs-meeting.org/archive/iccs2022/papers/133520635.pdf'],https://link.springer.com/chapter/10.1007/978-3-031-08757-8_54,unknown,unknown,MPO/TT 压缩,,['https://www.iccs-meeting.org/archive/iccs2022/papers/133520635.pdf'],convolutional neural network compression via tensor train decomposition on permuted weight tensor with automatic rank determination,MPO/TT 压缩,1,,
Power of Quantum Generative Learning,"Y Du, Z Tu, B Wu, X Yuan, D Tao",2022.0,11,"The intrinsic probabilistic nature of quantum mechanics invokes endeavors of designing quantum generative learning models (QGLMs). Despite the empirical achievements, the foundations and the potential advantages of QGLMs remain largely obscure. To narrow this knowledge gap, here we explore the generalization property of QGLMs, the capability to extend the model from learned to unknown data. We consider two prototypical QGLMs, quantum circuit Born machines and quantum generative adversarial networks, and explicitly give their generalization bounds. The result identifies superiorities of QGLMs over classical methods when quantum devices can directly access the target distribution and quantum kernels are employed. We further employ these generalization bounds to exhibit potential advantages in quantum state preparation and Hamiltonian learning. Numerical results of QGLMs in loading Gaussian distribution and estimating ground states of parameterized Hamiltonians accord with the theoretical analysis. Our work opens the avenue for quantitatively understanding the power of quantum generative learning models.",,"Y Du, Z Tu, B Wu, X Yuan, D Tao - arXiv preprint arXiv:2205.04730, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.04730,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2205.04730,['https://arxiv.org/pdf/2205.04730'],power of quantum generative learning,MPS 生成/Born机,1,,
Urban tree generator: spatio-temporal and generative deep learning for urban tree localization and modeling: A. Firoze et al.,"A Firoze, B Benes, D Aliaga",2022.0,10,"… rules and our procedural modeling system, it trains generative networks for four … generative modeling engine produces a tree distribution map for each cluster. Finally, from the map tree …",G-yC-VJ7zigJ,"A Firoze, B Benes, D Aliaga - The Visual Computer, 2022 - Springer",['https://par.nsf.gov/servlets/purl/10358340'],https://link.springer.com/article/10.1007/s00371-022-02526-x,unknown,unknown,TTN/MERA/PEPS,,['https://par.nsf.gov/servlets/purl/10358340'],urban tree generator spatio temporal and generative deep learning for urban tree localization and modeling a firoze et al,TTN/MERA/PEPS,1,,
Ensemble of tensor train decomposition and quantization methods for deep learning model compression,"OA Ademola, P Eduard, L Mairo",2022.0,8,… The performance of the compressed models varies with the compression techniques. In this … of tensor train decomposition and 8-bit quantization methods for compressing large CNN …,fRFV4tKt3-MJ,"OA Ademola, P Eduard, L Mairo - … on Neural Networks (IJCNN), 2022 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/9892626/,unknown,unknown,MPO/TT 压缩,,[],ensemble of tensor train decomposition and quantization methods for deep learning model compression,MPO/TT 压缩,1,,
Learning generative models for active inference using tensor networks,"ST Wauthier, B Vanhecke, T Verbelen…",2022.0,7,"… Later, we show how a tensor network agent behaves when planning under sophisticated … Examples of other possible networks are: tree tensor networks (TTN) and projected entangled …",j9igsm5CWS0J,"ST Wauthier, B Vanhecke, T Verbelen… - International Workshop on …, 2022 - Springer",['https://arxiv.org/pdf/2208.08713'],https://link.springer.com/chapter/10.1007/978-3-031-28719-0_20,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2208.08713'],learning generative models for active inference using tensor networks,TTN/MERA/PEPS,1,,
Recent Advances for Quantum Neural Networks in Generative Learning,"J Tian, X Sun, Y Du, S Zhao, Q Liu, K Zhang, W Yi, W Huang, C Wang, X Wu, M Hsieh, T Liu, W Yang, D Tao",2022.0,7,"Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relation and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.",,"J Tian, X Sun, Y Du, S Zhao, Q Liu, K Zhang, W Yi, W Huang, C Wang, X Wu, M Hsieh, T Liu, W Yang, D Tao - arXiv preprint arXiv:2206.03066, 2022 - arxiv.org",[],https://arxiv.org/abs/2206.03066,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2206.03066,['https://arxiv.org/pdf/2206.03066'],recent advances for quantum neural networks in generative learning,MPS 生成/Born机 / 量子/混合LLM / 量子启发综述,1,,
Generalization Metrics for Practical Quantum Advantage in Generative Models,"K Gili, M Mauri, A Perdomo-Ortiz",2022.0,6,"As the quantum computing community gravitates towards understanding the practical benefits of quantum computers, having a clear definition and evaluation scheme for assessing practical quantum advantage in the context of specific applications is paramount. Generative modeling, for example, is a widely accepted natural use case for quantum computers, and yet has lacked a concrete approach for quantifying success of quantum models over classical ones. In this work, we construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Using the sample-based approach proposed here, any generative model, from state-of-the-art classical generative models such as GANs to quantum models such as Quantum Circuit Born Machines, can be evaluated on the same ground on a concrete well-defined framework. In contrast to other sample-based metrics for probing practical generalization, we leverage constrained optimization problems (e.g., cardinality-constrained problems) and use these discrete datasets to define specific metrics capable of unambiguously measuring the quality of the samples and the model's generalization capabilities for generating data beyond the training set but still within the valid solution space. Additionally, our metrics can diagnose trainability issues such as mode collapse and overfitting, as we illustrate when comparing GANs to quantum-inspired models built out of tensor networks. Our simulation results show that our quantum-inspired models have up to a $68 \times$ enhancement in generating unseen unique and valid samples compared to GANs, and a ratio of 61:2 for generating samples with better quality than those observed in the training set. We foresee these metrics as valuable tools for rigorously defining practical quantum advantage in the domain of generative modeling.",,"K Gili, M Mauri, A Perdomo-Ortiz - arXiv preprint arXiv:2201.08770, 2022 - arxiv.org",[],https://arxiv.org/abs/2201.08770,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2201.08770,['https://arxiv.org/pdf/2201.08770'],generalization metrics for practical quantum advantage in generative models,MPS 生成/Born机,1,,
Generalization and Overfitting in Matrix Product State Machine Learning Architectures,"A Strashko, E M Stoudenmire",2022.0,6,"While overfitting and, more generally, double descent are ubiquitous in machine learning, increasing the number of parameters of the most widely used tensor network, the matrix product state (MPS), has generally lead to monotonic improvement of test performance in previous studies. To better understand the generalization properties of architectures parameterized by MPS, we construct artificial data which can be exactly modeled by an MPS and train the models with different number of parameters. We observe model overfitting for one-dimensional data, but also find that for more complex data overfitting is less significant, while with MNIST image data we do not find any signatures of overfitting. We speculate that generalization properties of MPS depend on the properties of data: with one-dimensional data (for which the MPS ansatz is the most suitable) MPS is prone to overfitting, while with more complex data which cannot be fit by MPS exactly, overfitting may be much less significant.",,"A Strashko, E M Stoudenmire - arXiv preprint arXiv:2208.04372, 2022 - arxiv.org",[],https://arxiv.org/abs/2208.04372,arxiv-completion,2026-09-26 (citations:OpenAlex),,2208.04372,['https://arxiv.org/pdf/2208.04372'],generalization and overfitting in matrix product state machine learning architectures,,1,,
Distilled Low Rank Neural Radiance Field with Quantization for Light Field Compression,"J Shi, C Guillemot",2022.0,5,"We propose in this paper a Quantized Distilled Low-Rank Neural Radiance Field (QDLR-NeRF) representation for the task of light field compression. While existing compression methods encode the set of light field sub-aperture images, our proposed method learns an implicit scene representation in the form of a Neural Radiance Field (NeRF), which also enables view synthesis. To reduce its size, the model is first learned under a Low-Rank (LR) constraint using a Tensor Train (TT) decomposition within an Alternating Direction Method of Multipliers (ADMM) optimization framework. To further reduce the model's size, the components of the tensor train decomposition need to be quantized. However, simultaneously considering the optimization of the NeRF model with both the low-rank constraint and rate-constrained weight quantization is challenging. To address this difficulty, we introduce a network distillation operation that separates the low-rank approximation and the weight quantization during network training. The information from the initial LR-constrained NeRF (LR-NeRF) is distilled into a model of much smaller dimension (DLR-NeRF) based on the TT decomposition of the LR-NeRF. We then learn an optimized global codebook to quantize all TT components, producing the final QDLR-NeRF. Experimental results show that our proposed method yields better compression efficiency compared to state-of-the-art methods, and it additionally has the advantage of allowing the synthesis of any light field view with high quality.",,"J Shi, C Guillemot - arXiv preprint arXiv:2208.00164, 2022 - arxiv.org",[],https://arxiv.org/abs/2208.00164,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2208.00164,['https://arxiv.org/pdf/2208.00164'],distilled low rank neural radiance field with quantization for light field compression,MPO/TT 压缩,1,,
Privacy-preserving machine learning with tensor networks,"A Pozas-Kerstjens, S Hernández-Santana, J R P Monturiol, M C López, G Scarpa, C E González-Guillén, D Pérez-García",2022.0,5,"Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.",,"A Pozas-Kerstjens, S Hernández-Santana, J R P Monturiol, M C López, G Scarpa, C E González-Guillén, D Pérez-García - Quantum 8, 1425 (2024)",[],https://arxiv.org/abs/2202.12319,arxiv-completion,2026-09-26 (citations:OpenAlex),,2202.12319,['https://arxiv.org/pdf/2202.12319'],privacy preserving machine learning with tensor networks,,1,"Quantum 8, 1425 (2024)",
Do Quantum Circuit Born Machines Generalize?,"K Gili, M Hibat-Allah, M Mauri, C Ballance, A Perdomo-Ortiz",2022.0,4,"In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as Quantum Circuit Born Machines (QCBMs) have been almost entirely evaluated on their capability to learn a given target distribution with high accuracy. While this aspect may be ideal for some tasks, it limits the scope of a generative model's assessment to its ability to memorize data rather than generalize. As a result, there has been little understanding of a model's generalization performance and the relation between such capability and the resource requirements, e.g., the circuit depth and the amount of training data. In this work, we leverage upon a recently proposed generalization evaluation framework to begin addressing this knowledge gap. We first investigate the QCBM's learning process of a cardinality-constrained distribution and see an increase in generalization performance while increasing the circuit depth. In the 12-qubit example presented here, we observe that with as few as 30% of the valid data in the training set, the QCBM exhibits the best generalization performance toward generating unseen and valid data. Lastly, we assess the QCBM's ability to generalize not only to valid samples, but to high-quality bitstrings distributed according to an adequately re-weighted distribution. We see that the QCBM is able to effectively learn the reweighted dataset and generate unseen samples with higher quality than those in the training set. To the best of our knowledge, this is the first work in the literature that presents the QCBM's generalization performance as an integral evaluation metric for quantum generative models, and demonstrates the QCBM's ability to generalize to high-quality, desired novel samples.",,"K Gili, M Hibat-Allah, M Mauri, C Ballance, A Perdomo-Ortiz - arXiv preprint arXiv:2207.13645, 2022 - arxiv.org",[],https://arxiv.org/abs/2207.13645,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2207.13645,['https://arxiv.org/pdf/2207.13645'],do quantum circuit born machines generalize,MPS 生成/Born机,1,,
"On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond","M Stoian, R Milbradt, C B Mendl",2022.0,4,"The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a polynomial-time algorithm, by drawing connections to database join ordering. The result relies on the adjacent sequence interchange property of the contraction cost, which enables a global decision of the contraction order based on local comparisons. Based on that, we specify a modified version of the IKKBZ database join ordering algorithm to find the optimal tree tensor network linear contraction order. Finally, we extend our algorithm as a heuristic to general contraction orders and arbitrary tensor network topologies.",,"M Stoian, R Milbradt, C B Mendl - SIAM J. Sci. Comput. 46, B647-B668 (2024)",[],https://arxiv.org/abs/2209.12332,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2209.12332,['https://arxiv.org/pdf/2209.12332'],on the optimal linear contraction order of tree tensor networks and beyond,TTN/MERA/PEPS / MPS/序列建模,1,"SIAM J. Sci. Comput. 46, B647-B668 (2024)",
Reconstructing Quantum States Using Basis-Enhanced Born Machines,"A M Gomez, S F Yelin, K Najafi",2022.0,4,"Rapid improvement in quantum hardware has opened the door to complex problems, but the precise characterization of quantum systems itself remains a challenge. To address this obstacle, novel tomography schemes have been developed that employ generative machine learning models, enabling quantum state reconstruction from limited classical data. In particular, quantum-inspired Born machines provide a natural way to encode measured data into a model of a quantum state. Born machines have shown great success in learning from classical data; however, the full potential of a Born machine in learning from quantum measurement has thus far been unrealized. To this end, we devise a complex-valued basis-enhanced Born machine and show that it can reconstruct pure quantum states using projective measurements from only two Pauli measurement bases. We implement the basis-enhanced Born machine to learn the ground states across the phase diagram of a 1D chain of Rydberg atoms, reconstructing quantum states deep in ordered phases and even at critical points with quantum fidelities surpassing 99%. The model accurately predicts quantum correlations and different observables, and system sizes as large as 37 qubits are considered. Quantum states across the phase diagram of a 1D XY spin chain are also successfully reconstructed using this scheme. Our method only requires simple Pauli measurements with a sample complexity that scales quadratically with system size, making it amenable to experimental implementation.",,"A M Gomez, S F Yelin, K Najafi - arXiv preprint arXiv:2206.01273, 2022 - arxiv.org",[],https://arxiv.org/abs/2206.01273,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2206.01273,['https://arxiv.org/pdf/2206.01273'],reconstructing quantum states using basis enhanced born machines,MPS 生成/Born机,1,,
Machine learning applications for noisy intermediate-scale quantum computers,B Coyle,2022.0,3,"Quantum machine learning has proven to be a fruitful area in which to search for potential applications of quantum computers. This is particularly true for those available in the near term, so called noisy intermediate-scale quantum (NISQ) devices. In this Thesis, we develop and study three quantum machine learning applications suitable for NISQ computers, ordered in terms of increasing complexity of data presented to them. These algorithms are variational in nature and use parameterised quantum circuits (PQCs) as the underlying quantum machine learning model. The first application area is quantum classification using PQCs, where the data is classical feature vectors and their corresponding labels. Here, we study the robustness of certain data encoding strategies in such models against noise present in a quantum computer. The second area is generative modelling using quantum computers, where we use quantum circuit Born machines to learn and sample from complex probability distributions. We discuss and present a framework for quantum advantage for such models, propose gradient-based training methods and demonstrate these both numerically and on the Rigetti quantum computer up to 28 qubits. For our final application, we propose a variational algorithm in the area of approximate quantum cloning, where the data becomes quantum in nature. For the algorithm, we derive differentiable cost functions, prove theoretical guarantees such as faithfulness, and incorporate state of the art methods such as quantum architecture search. Furthermore, we demonstrate how this algorithm is useful in discovering novel implementable attacks on quantum cryptographic protocols, focusing on quantum coin flipping and key distribution as examples.",,"B Coyle - arXiv preprint arXiv:2205.09414, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.09414,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2205.09414,['https://arxiv.org/pdf/2205.09414'],machine learning applications for noisy intermediate scale quantum computers,MPS 生成/Born机 / 量子/混合LLM / 量子启发综述,1,,
Hypoformer: Hybrid Decomposition Transformer for Edge-friendly Neural Machine Translation,"S Li, P Zhang, G Gan, X Lv, B Wang, V J Wei, X Jiang",2022.0,3,"Transformer has been demonstrated effective in Neural Machine Translation (NMT).However, it is memory-consuming and time-consuming in edge devices, resulting in some difficulties for real-time feedback.To compress and accelerate Transformer, we propose a Hybrid Tensor-Train (HTT) decomposition, which retains full rank and meanwhile reduces operations and parameters.A Transformer using HTT, named Hypoformer, consistently and notably outperforms the recent lightweight SOTA methods on three standard translation tasks under different parameter and speed scales.In extreme low resource scenarios, Hypoformer has a 7.1 point absolute improvement in BLEU and 1.27× speedup than the vanilla Transformer on the IWSLT'14 De-En task.",,"S Li, P Zhang, G Gan, X Lv, B Wang, V J Wei, X Jiang - arXiv, 2022",[],https://doi.org/10.18653/v1/2022.emnlp-main.475,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,,[],hypoformer hybrid decomposition transformer for edge friendly neural machine translation,张量化Transformer / MPO/TT 压缩,1,,
Entangling Solid Solutions: Machine Learning of Tensor Networks for Materials Property Prediction,"DE Sommer, ST Dunham",2022.0,2,"Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning architectures. A large class of atomic structure representations based on expansions of smoothed atomic densities have been shown to correspond to specific choices of basis sets in an abstract many-body Hilbert space. Concurrently, tensor network structures, conventionally the purview of quantum many-body physics and quantum information, have been successfully applied in supervised and unsupervised learning tasks in computer vision and natural language processing. In this work, we argue that architectures based on tensor networks are well-suited to machine learning on Hilbert-space representations of atomic structures. This is demonstrated on supervised learning tasks involving widely available datasets of density functional theory calculations of metal and semiconductor alloys. In particular, we show that certain standard tensor network topologies exhibit strong generalizability even on small training datasets while being parametrically efficient. We further relate this generalizability to the presence of complex entanglement in the trained tensor networks. We also discuss connections to learning with generalized structural kernels and related strategies for compressing large input feature spaces.",6QN6fwQkgbUJ,"DE Sommer, ST Dunham - arXiv preprint arXiv:2203.09613, 2022 - arxiv.org",['https://arxiv.org/pdf/2203.09613'],https://arxiv.org/abs/2203.09613,unknown,unknown,TTN/MERA/PEPS,2203.09613,['https://arxiv.org/pdf/2203.09613'],entangling solid solutions machine learning of tensor networks for materials property prediction,TTN/MERA/PEPS,1,,
Hybrid quantum ResNet for car classification and its hyperparameter optimization,"A Sagingalieva, M Kordzanganeh, A Kurkin, A Melnikov, D Kuhmistrov, M Perelshtein, A Melnikov, A Skolik, D V Dollen",2022.0,2,"Image recognition is one of the primary applications of machine learning algorithms. Nevertheless, machine learning models used in modern image recognition systems consist of millions of parameters that usually require significant computational time to be adjusted. Moreover, adjustment of model hyperparameters leads to additional overhead. Because of this, new developments in machine learning models and hyperparameter optimization techniques are required. This paper presents a quantum-inspired hyperparameter optimization technique and a hybrid quantum-classical machine learning model for supervised learning. We benchmark our hyperparameter optimization method over standard black-box objective functions and observe performance improvements in the form of reduced expected run times and fitness in response to the growth in the size of the search space. We test our approaches in a car image classification task and demonstrate a full-scale implementation of the hybrid quantum ResNet model with the tensor train hyperparameter optimization. Our tests show a qualitative and quantitative advantage over the corresponding standard classical tabular grid search approach used with a deep neural network ResNet34. A classification accuracy of 0.97 was obtained by the hybrid model after 18 iterations, whereas the classical model achieved an accuracy of 0.92 after 75 iterations.",,"A Sagingalieva, M Kordzanganeh, A Kurkin, A Melnikov, D Kuhmistrov, M Perelshtein, A Melnikov, A Skolik, D V Dollen - Quantum Mach. Intell. 5(2), 38 (2023)",[],https://arxiv.org/abs/2205.04878,arxiv-completion,2026-09-26 (citations:OpenAlex),,2205.04878,['https://arxiv.org/pdf/2205.04878'],hybrid quantum resnet for car classification and its hyperparameter optimization,,1,"Quantum Mach. Intell. 5(2), 38 (2023)",
Near-Term Advances in Quantum Natural Language Processing,"D Widdows, A Alexander, D Zhu, C Zimmerman, A Majumder",2022.0,2,"This paper describes experiments showing that some tasks in natural language processing (NLP) can already be performed using quantum computers, though so far only with small datasets. We demonstrate various approaches to topic classification. The first uses an explicit word-based approach, in which word-topic scoring weights are implemented as fractional rotations of individual qubit, and a new phrase is classified based on the accumulation of these weights in a scoring qubit using entangling controlled-NOT gates. This is compared with more scalable quantum encodings of word embedding vectors, which are used in the computation of kernel values in a quantum support vector machine: this approach achieved an average of 62% accuracy on classification tasks involving over 10000 words, which is the largest such quantum computing experiment to date. We describe a quantum probability approach to bigram modeling that can be applied to sequences of words and formal concepts, investigating a generative approximation to these distributions using a quantum circuit Born machine, and an approach to ambiguity resolution in verb-noun composition using single-qubit rotations for simple nouns and 2-qubit controlled-NOT gates for simple verbs. The smaller systems described have been run successfully on physical quantum computers, and the larger ones have been simulated. We show that statistically meaningful results can be obtained using real datasets, but this is much more difficult to predict than with easier artificial language examples used previously in developing quantum NLP systems. Other approaches to quantum NLP are compared, partly with respect to contemporary issues including informal language, fluency, and truthfulness.",,"D Widdows, A Alexander, D Zhu, C Zimmerman, A Majumder - Annals of Mathematics and Artificial Intelligence (2024)",[],https://arxiv.org/abs/2206.02171,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2206.02171,['https://arxiv.org/pdf/2206.02171'],near term advances in quantum natural language processing,MPS 语言模型 / MPS 生成/Born机 / 量子/混合LLM / MPS/序列建模,2,Annals of Mathematics and Artificial Intelligence (2024),
A quantum-inspired tensor network method for constrained combinatorial optimization problems,"T Hao, X Huang, C Jia, C Peng",2022.0,2,"Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.",,"T Hao, X Huang, C Jia, C Peng - Frontiers in Physics, Volume 10, Article 906590 (2022)",[],https://arxiv.org/abs/2203.15246,arxiv-completion,2026-09-26 (citations:OpenAlex),量子启发综述,2203.15246,['https://arxiv.org/pdf/2203.15246'],a quantum inspired tensor network method for constrained combinatorial optimization problems,量子启发综述,1,"Frontiers in Physics, Volume 10, Article 906590 (2022)",
Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learning,"F Barratt, J Dborin, L Wright",2022.0,2,"Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks suffer from initialization problems resulting in exploding or vanishing gradients and require extensive hyperparameter tuning. Efforts to overcome these problems usually depend on specific network architectures, or ad hoc prescriptions. In this paper we address the problems of initialization and hyperparameter tuning, making it possible to train tensor networks using established machine learning techniques. We introduce a `copy node' method that successfully initializes arbitrary tensor networks, in addition to a gradient based regularization technique for bond dimensions. We present numerical results that show that the combination of techniques presented here produces quantum inspired tensor network models with far fewer parameters, while improving generalization performance.",,"F Barratt, J Dborin, L Wright - Second Workshop on Quantum Tensor Networks in Machine Learning, 35th Conference on Neural Information Processing Systems (NeurIPS 2021)",[],https://arxiv.org/abs/2203.03366,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2203.03366,['https://arxiv.org/pdf/2203.03366'],improvements to gradient descent methods for quantum tensor network machine learning,量子/混合LLM,1,"Second Workshop on Quantum Tensor Networks in Machine Learning, 35th Conference on Neural Information Processing Systems (NeurIPS 2021)",
Decohering Tensor Network Quantum Machine Learning Models,"H Liao, I Convy, Z Yang, K B Whaley",2022.0,1,"Tensor network quantum machine learning (QML) models are promising applications on near-term quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished performance can be compensated for by adding ancillas to the models and accordingly increasing the virtual bond dimension of the models. We investigate here the competition between decoherence and adding ancillas on the classification performance of two models, with an analysis of the decoherence effect from the perspective of regression. We present numerical evidence that the fully-decohered unitary tree tensor network (TTN) with two ancillas performs at least as well as the non-decohered unitary TTN, suggesting that it is beneficial to add at least two ancillas to the unitary TTN regardless of the amount of decoherence may be consequently introduced.",,"H Liao, I Convy, Z Yang, K B Whaley - Quantum Mach. Intell. 5, 7 (2023)",[],https://arxiv.org/abs/2209.01195,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2209.01195,['https://arxiv.org/pdf/2209.01195'],decohering tensor network quantum machine learning models,量子/混合LLM / TTN/MERA/PEPS / 量子启发综述,1,"Quantum Mach. Intell. 5, 7 (2023)",
Quantum-Aided Meta-Learning for Bayesian Binary Neural Networks via Born Machines,"I Nikoloska, O Simeone",2022.0,1,"Near-term noisy intermediate-scale quantum circuits can efficiently implement implicit probabilistic models in discrete spaces, supporting distributions that are practically infeasible to sample from using classical means. One of the possible applications of such models, also known as Born machines, is probabilistic inference, which is at the core of Bayesian methods. This paper studies the use of Born machines for the problem of training binary Bayesian neural networks. In the proposed approach, a Born machine is used to model the variational distribution of the binary weights of the neural network, and data from multiple tasks is used to reduce training data requirements on new tasks. The method combines gradient-based meta-learning and variational inference via Born machines, and is shown in a prototypical regression problem to outperform conventional joint learning strategies.",,"I Nikoloska, O Simeone - arXiv preprint arXiv:2203.17089, 2022 - arxiv.org",[],https://arxiv.org/abs/2203.17089,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2203.17089,['https://arxiv.org/pdf/2203.17089'],quantum aided meta learning for bayesian binary neural networks via born machines,MPS 生成/Born机,1,,
Tensor Network States with Low-Rank Tensors,"H Chen, T Barthel",2022.0,1,"Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential to polynomial in $N$, and this has become a popular approach for machine learning. We introduce the idea of imposing low-rank constraints on the tensors that compose the tensor network. With this modification, the time and space complexities for the network optimization can be substantially reduced while maintaining high accuracy. We detail this idea for tree tensor network states (TTNS) and projected entangled-pair states. Simulations of spin models on Cayley trees with low-rank TTNS exemplify the effect of rank constraints on the expressive power. We find that choosing the tensor rank $r$ to be on the order of the bond dimension $m$, is sufficient to obtain high-accuracy groundstate approximations and to substantially outperform standard TTNS computations. Thus low-rank tensor networks are a promising route for the simulation of quantum matter and machine learning on large data sets.",,"H Chen, T Barthel - arXiv preprint arXiv:2205.15296, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.15296,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2205.15296,['https://arxiv.org/pdf/2205.15296'],tensor network states with low rank tensors,MPO/TT 压缩 / 量子/混合LLM / TTN/MERA/PEPS,2,,
Tensor-network-assisted variational quantum algorithm,"J Huang, W He, Y Zhang, Y Wu, B Wu, X Yuan",2022.0,1,"Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a classical tensor-network operator with a quantum circuit to effectively increase the circuit's expressivity without requiring a physically deeper circuit. We present a framework for tensor-network-assisted variational quantum algorithms that can solve quantum many-body problems using shallower quantum circuits. We demonstrate the efficiency of this approach by considering two examples of unitary matrix-product operators and unitary tree tensor networks, showing that they can both be implemented efficiently. Through numerical simulations, we show that the expressivity of these circuits is greatly enhanced with the assistance of tensor networks. We apply our method to two-dimensional Ising models and one-dimensional time-crystal Hamiltonian models with up to 16 qubits and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits.",,"J Huang, W He, Y Zhang, Y Wu, B Wu, X Yuan - Phys. Rev. A 108, 052407 (2023)",[],https://arxiv.org/abs/2212.10421,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2212.10421,['https://arxiv.org/pdf/2212.10421'],tensor network assisted variational quantum algorithm,TTN/MERA/PEPS,1,"Phys. Rev. A 108, 052407 (2023)",
Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations,"S Bai, Y Tang, S Ran",2022.0,1,"Given an image of a white shoe drawn on a blackboard, how are the white pixels deemed (say by human minds) to be informative for recognizing the shoe without any labeling information on the pixels? Here we investigate such a ``white shoe'' recognition problem from the perspective of tensor network (TN) machine learning and quantum entanglement. Utilizing a generative TN that captures the probability distribution of the features as quantum amplitudes, we propose an unsupervised recognition scheme of informative features with the variations of entanglement entropy (EE) caused by designed measurements. In this way, a given sample, where the values of its features are statistically meaningless, is mapped to the variations of EE that statistically characterize the gain of information. We show that the EE variations identify the features that are critical to recognize this specific sample, and the EE itself reveals the information distribution of the probabilities represented by the TN model. The signs of the variations further reveal the entanglement structures among the features. We test the validity of our scheme on a toy dataset of strip images, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset of the pictures of fashion articles, and the images of brain cells. Our scheme opens the avenue to the quantum-inspired and interpreted unsupervised learning, which can be applied to, e.g., image segmentation and object detection.",,"S Bai, Y Tang, S Ran - Chinese Physics Letters 39, 100701 (2022)",[],https://arxiv.org/abs/2207.06031,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2207.06031,['https://arxiv.org/pdf/2207.06031'],unsupervised recognition of informative features via tensor network machine learning and quantum entanglement variations,MPS 生成/Born机 / 互信息/标度 / 量子启发综述,1,"Chinese Physics Letters 39, 100701 (2022)",
Verifying Fairness in Quantum Machine Learning,"J Guan, W Fang, M Ying",2022.0,0,"Due to the beyond-classical capability of quantum computing, quantum machine learning is applied independently or embedded in classical models for decision making, especially in the field of finance. Fairness and other ethical issues are often one of the main concerns in decision making. In this work, we define a formal framework for the fairness verification and analysis of quantum machine learning decision models, where we adopt one of the most popular notions of fairness in the literature based on the intuition -- any two similar individuals must be treated similarly and are thus unbiased. We show that quantum noise can improve fairness and develop an algorithm to check whether a (noisy) quantum machine learning model is fair. In particular, this algorithm can find bias kernels of quantum data (encoding individuals) during checking. These bias kernels generate infinitely many bias pairs for investigating the unfairness of the model. Our algorithm is designed based on a highly efficient data structure -- Tensor Networks -- and implemented on Google's TensorFlow Quantum. The utility and effectiveness of our algorithm are confirmed by the experimental results, including income prediction and credit scoring on real-world data, for a class of random (noisy) quantum decision models with 27 qubits ($2^{27}$-dimensional state space) tripling ($2^{18}$ times more than) that of the state-of-the-art algorithms for verifying quantum machine learning models.",,"J Guan, W Fang, M Ying - arXiv preprint arXiv:2207.11173, 2022 - arxiv.org",[],https://arxiv.org/abs/2207.11173,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2207.11173,['https://arxiv.org/pdf/2207.11173'],verifying fairness in quantum machine learning,量子/混合LLM,1,,
A practical overview of image classification with variational tensor-network quantum circuits,"D Guala, S Zhang, E Cruz, C A Riofrío, J Klepsch, J M Arrazola",2022.0,0,"Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to design variational circuits is to base the circuit architecture on tensor networks. Here, we comprehensively describe tensor-network quantum circuits and how to implement them in simulations. This includes leveraging circuit cutting, a technique used to evaluate circuits with more qubits than those available on current quantum devices. We then illustrate the computational requirements and possible applications by simulating various tensor-network quantum circuits with PennyLane, an open-source python library for differential programming of quantum computers. Finally, we demonstrate how to apply these circuits to increasingly complex image processing tasks, completing this overview of a flexible method to design circuits that can be applied to industrially-relevant machine learning tasks.",,"D Guala, S Zhang, E Cruz, C A Riofrío, J Klepsch, J M Arrazola - arXiv preprint arXiv:2209.11058, 2022 - arxiv.org",[],https://arxiv.org/abs/2209.11058,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2209.11058,['https://arxiv.org/pdf/2209.11058'],a practical overview of image classification with variational tensor network quantum circuits,量子/混合LLM,1,,
Computing time-periodic steady-state currents via the time evolution of tensor network states,"N E Strand, H Vroylandt, T R Gingrich",2022.0,,"We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group (DMRG) algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted in a companion letter, but the approach extends naturally to other interacting lattice models with time-dependent driving. Though trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy could be more favorable.",,"N E Strand, H Vroylandt, T R Gingrich - J. Chem. Phys., 157, 054104, 2022",[],https://arxiv.org/abs/2201.04107,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2201.04107,['https://arxiv.org/pdf/2201.04107'],computing time periodic steady state currents via the time evolution of tensor network states,TTN/MERA/PEPS,1,"J. Chem. Phys., 157, 054104, 2022",
Exploiting Low-Rank Tensor-Train Deep Neural Networks Based on Riemannian Gradient Descent With Illustrations of Speech Processing,"J Qi, C H Yang, P Chen, J Tejedor",2022.0,0,"This work focuses on designing low complexity hybrid tensor networks by considering trade-offs between the model complexity and practical performance. Firstly, we exploit a low-rank tensor-train deep neural network (TT-DNN) to build an end-to-end deep learning pipeline, namely LR-TT-DNN. Secondly, a hybrid model combining LR-TT-DNN with a convolutional neural network (CNN), which is denoted as CNN+(LR-TT-DNN), is set up to boost the performance. Instead of randomly assigning large TT-ranks for TT-DNN, we leverage Riemannian gradient descent to determine a TT-DNN associated with small TT-ranks. Furthermore, CNN+(LR-TT-DNN) consists of convolutional layers at the bottom for feature extraction and several TT layers at the top to solve regression and classification problems. We separately assess the LR-TT-DNN and CNN+(LR-TT-DNN) models on speech enhancement and spoken command recognition tasks. Our empirical evidence demonstrates that the LR-TT-DNN and CNN+(LR-TT-DNN) models with fewer model parameters can outperform the TT-DNN and CNN+(TT-DNN) counterparts.",,"J Qi, C H Yang, P Chen, J Tejedor - arXiv preprint arXiv:2203.06031, 2022 - arxiv.org",[],https://arxiv.org/abs/2203.06031,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2203.06031,['https://arxiv.org/pdf/2203.06031'],exploiting low rank tensor train deep neural networks based on riemannian gradient descent with illustrations of speech processing,MPO/TT 压缩,1,,
"Investigating Quantum Many-Body Systems with Tensor Networks, Machine Learning and Quantum Computers",K Kottmann,2022.0,0,"We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM.",,"K Kottmann - arXiv preprint arXiv:2210.11130, 2022 - arxiv.org",[],https://arxiv.org/abs/2210.11130,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2210.11130,['https://arxiv.org/pdf/2210.11130'],investigating quantum many body systems with tensor networks machine learning and quantum computers,MPS 生成/Born机 / 量子/混合LLM / TTN/MERA/PEPS,1,,
Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions,"A V Mahankali, D P Woodruff, Z Zhang",2022.0,,"We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks. For tensor train decomposition, we give a bicriteria $(1 + \eps)$-approximation algorithm with a small bicriteria rank and $O(q \cdot \nnz(A))$ running time, up to lower order terms, which improves over the additive error algorithm of \cite{huber2017randomized}. We also show how to convert the algorithm of \cite{huber2017randomized} into a relative error algorithm, but their algorithm necessarily has a running time of $O(qr^2 \cdot \nnz(A)) + n \cdot \poly(qk/\eps)$ when converted to a $(1 + \eps)$-approximation algorithm with bicriteria rank $r$. To the best of our knowledge, our work is the first to achieve polynomial time relative error approximation for tensor train decomposition. Our key technique is a method for obtaining subspace embeddings with a number of rows polynomial in $q$ for a matrix which is the flattening of a tensor train of $q$ tensors. We extend our algorithm to tree tensor networks. In addition, we extend our algorithm to tensor networks with arbitrary graphs (which we refer to as general tensor networks), by using a result of \cite{ms08_simulating_quantum_tensor_contraction} and showing that a general tensor network of rank $k$ can be contracted to a binary tree network of rank $k^{O(°(G)\tw(G))}$, allowing us to reduce to the case of tree tensor networks. Finally, we give new fixed-parameter tractable algorithms for the tensor train, Tucker, and CP decompositions, which are simpler than those of \cite{swz19_tensor_low_rank} since they do not make use of polynomial system solvers. Our technique of Gaussian subspace embeddings with exactly $k$ rows (and thus exponentially small success probability) may be of independent interest.",,"A V Mahankali, D P Woodruff, Z Zhang - arXiv preprint arXiv:2207.07417, 2022 - arxiv.org",[],https://arxiv.org/abs/2207.07417,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2207.07417,['https://arxiv.org/pdf/2207.07417'],near linear time and fixed parameter tractable algorithms for tensor decompositions,TTN/MERA/PEPS,1,,
Quaternion Tensor Train Rank Minimization with Sparse Regularization in a Transformed Domain for Quaternion Tensor Completion,"J Miao, K I Kou, L Yang, D Cheng",2022.0,0,"The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (>3) tensors. On the other hand, recently, quaternions have proven to be a very suitable framework for encoding color pixels, and have obtained outstanding performance in various color image processing tasks. In this paper, the quaternion tensor train (QTT) decomposition is presented, and based on that the quaternion TT-rank (QTT-rank) is naturally defined, which are the generalizations of their counterparts in the real number field. In addition, to utilize the local sparse prior of the quaternion tensor, a general and flexible transform framework is defined. Combining both the global low-rank and local sparse priors of the quaternion tensor, we propose a novel quaternion tensor completion model, i.e., QTT-rank minimization with sparse regularization in a transformed domain. Specifically, we use the quaternion weighted nuclear norm (QWNN) of mode-n canonical unfolding quaternion matrices to characterize the global low-QTT-rankness, and the l1-norm of the quaternion tensor in a transformed domain to characterize the local sparse property. Moreover, to enable the QTT-rank minimization to handle color images and better handle color videos, we generalize KA, a tensor augmentation method, to quaternion tensors and define quaternion KA (QKA), which is a helpful pretreatment step for QTT-rank based optimization problems. The numerical experiments on color images and color videos inpainting tasks indicate the advantages of the proposed method over the state-of-the-art ones.",,"J Miao, K I Kou, L Yang, D Cheng - arXiv preprint arXiv:2209.02964, 2022 - arxiv.org",[],https://arxiv.org/abs/2209.02964,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2209.02964,['https://arxiv.org/pdf/2209.02964'],quaternion tensor train rank minimization with sparse regularization in a transformed domain for quaternion tensor completion,MPO/TT 压缩,1,,
Sample-efficient Quantum Born Machine through Coding Rate Reduction,P Zhai,2022.0,0,"The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate classically. As data samples are generated quantum-mechanically, QCBMs encompass a unique optimization landscape. However, pioneering works on QCBMs do not consider the practical scenario where only small batch sizes are allowed during training. QCBMs trained with a statistical two-sample test objective in the image space require large amounts of projective measurements to approximate the model distribution well, unpractical for large-scale quantum systems due to the exponential scaling of the probability space. QCBMs trained adversarially against a deep neural network discriminator are proof-of-concept models that face mode collapse. In this work we investigate practical learning of QCBMs. We use the information-theoretic \textit{Maximal Coding Rate Reduction} (MCR$^2$) metric as a second moment matching tool and study its effect on mode collapse in QCBMs. We compute the sampling based gradient of MCR$^2$ with respect to quantum circuit parameters with or without an explicit feature mapping. We experimentally show that matching up to the second moment alone is not sufficient for training the quantum generator, but when combined with the class probability estimation loss, MCR$^2$ is able to resist mode collapse. In addition, we show that adversarially trained neural network kernel for infinite moment matching is also effective against mode collapse. On the Bars and Stripes dataset, our proposed techniques alleviate mode collapse to a larger degree than previous QCBM training schemes, moving one step closer towards practicality and scalability.",,"P Zhai - arXiv preprint arXiv:2211.10418, 2022 - arxiv.org",[],https://arxiv.org/abs/2211.10418,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2211.10418,['https://arxiv.org/pdf/2211.10418'],sample efficient quantum born machine through coding rate reduction,MPS 生成/Born机,1,,
Tensor networks in machine learning,"R Sengupta, S Adhikary, I Oseledets, J Biamonte",2022.0,0,"A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear maps. This is reminiscent to how a Boolean function might be decomposed into a gate array: this represents a special case of tensor decomposition, in which the tensor entries are replaced by 0, 1 and the factorisation becomes exact. The collection of associated techniques are called, tensor network methods: the subject developed independently in several distinct fields of study, which have more recently become interrelated through the language of tensor networks. The tantamount questions in the field relate to expressability of tensor networks and the reduction of computational overheads. A merger of tensor networks with machine learning is natural. On the one hand, machine learning can aid in determining a factorization of a tensor network approximating a data set. On the other hand, a given tensor network structure can be viewed as a machine learning model. Herein the tensor network parameters are adjusted to learn or classify a data-set. In this survey we recover the basics of tensor networks and explain the ongoing effort to develop the theory of tensor networks in machine learning.",,"R Sengupta, S Adhikary, I Oseledets, J Biamonte - arXiv preprint arXiv:2207.02851, 2022 - arxiv.org",[],https://arxiv.org/abs/2207.02851,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2207.02851,['https://arxiv.org/pdf/2207.02851'],tensor networks in machine learning,TTN/MERA/PEPS / 量子启发综述,1,,
Tensor-Train Compression of Discrete Element Method Simulation Data,"S De, E Corona, P Jayakumar, S Veerapaneni",2022.0,0,"We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its effectiveness in compressing both raw (e.g. particle position and velocity) and derived (e.g. stress and strain) datasets. We show that geometry-driven ""tensorization"" coupled with the TT decomposition (known as quantized TT) yields a hierarchical compression scheme, achieving high compression ratios for key variables in these DEM datasets.",,"S De, E Corona, P Jayakumar, S Veerapaneni - arXiv preprint arXiv:2210.08399, 2022 - arxiv.org",[],https://arxiv.org/abs/2210.08399,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2210.08399,['https://arxiv.org/pdf/2210.08399'],tensor train compression of discrete element method simulation data,MPO/TT 压缩,1,,
Tuning the entanglement growth in matrix-product-state evolution of quantum systems by nonunitary similarity transformations,"H Nuomin, F Song, P Zhang, D N Beratan",2022.0,0,"The possibility of using similarity transformations to alter dynamical entanglement growth in matrix-product-state simulations of quantum systems is explored. By appropriately choosing the similarity transformation, the entanglement growth rate is suppressed, improving the efficiency of numerical simulations of quantum systems. The transformation can be applied to general quantum-many-body systems.",,"H Nuomin, F Song, P Zhang, D N Beratan - arXiv preprint arXiv:2202.09925, 2022 - arxiv.org",[],https://arxiv.org/abs/2202.09925,arxiv-completion,2026-09-26 (citations:OpenAlex),,2202.09925,['https://arxiv.org/pdf/2202.09925'],tuning the entanglement growth in matrix product state evolution of quantum systems by nonunitary similarity transformations,,1,,
Using tensor network states for multi-particle Brownian ratchets,"N E Strand, H Vroylandt, T R Gingrich",2022.0,,"The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet's current. To surmount the many-body problem, we employ the time-dependent variational principle with a binary tree tensor network, methods discussed at length in a companion paper. Rather than propagating individual trajectories, the tensor network approach propagates a distribution over many-body configurations via a controllable variational approximation. The calculations, which reproduce Gillespie trajectory sampling, identify and explain a shift in the frequency of maximum current to higher driving frequency as the lattice occupancy increases.",,"N E Strand, H Vroylandt, T R Gingrich - J. Chem. Phys., 156, 221103, 2022",[],https://arxiv.org/abs/2201.03531,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2201.03531,['https://arxiv.org/pdf/2201.03531'],using tensor network states for multi particle brownian ratchets,TTN/MERA/PEPS,1,"J. Chem. Phys., 156, 221103, 2022",
MorphTE: Injecting Morphology in Tensorized Embeddings,"G Gan, P Zhang, S Li, X Lu, B Wang",2022.0,,"In the era of deep learning, word embeddings are essential when dealing with text tasks. However, storing and accessing these embeddings requires a large amount of space. This is not conducive to the deployment of these models on resource-limited devices. Combining the powerful compression capability of tensor products, we propose a word embedding compression method with morphological augmentation, Morphologically-enhanced Tensorized Embeddings (MorphTE). A word consists of one or more morphemes, the smallest units that bear meaning or have a grammatical function. MorphTE represents a word embedding as an entangled form of its morpheme vectors via the tensor product, which injects prior semantic and grammatical knowledge into the learning of embeddings. Furthermore, the dimensionality of the morpheme vector and the number of morphemes are much smaller than those of words, which greatly reduces the parameters of the word embeddings. We conduct experiments on tasks such as machine translation and question answering. Experimental results on four translation datasets of different languages show that MorphTE can compress word embedding parameters by about 20 times without performance loss and significantly outperforms related embedding compression methods.",,"G Gan, P Zhang, S Li, X Lu, B Wang - arXiv preprint arXiv:2210.15379, 2022 - arxiv.org",[],https://arxiv.org/abs/2210.15379,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2210.15379,['https://arxiv.org/pdf/2210.15379'],morphte injecting morphology in tensorized embeddings,MPO/TT 压缩,1,,
KronA: Parameter Efficient Tuning with Kronecker Adapter,"A Edalati, M Tahaei, I Kobyzev, V P Nia, J J Clark, M Rezagholizadeh",2022.0,,"Fine-tuning a Pre-trained Language Model (PLM) on a specific downstream task has been a well-known paradigm in Natural Language Processing. However, with the ever-growing size of PLMs, training the entire model on several downstream tasks becomes very expensive and resource-hungry. Recently, different Parameter Efficient Tuning (PET) techniques are proposed to improve the efficiency of fine-tuning PLMs. One popular category of PET methods is the low-rank adaptation methods which insert learnable truncated SVD modules into the original model either sequentially or in parallel. However, low-rank decomposition suffers from limited representation power. In this work, we address this problem using the Kronecker product instead of the low-rank representation. We introduce KronA, a Kronecker product-based adapter module for efficient fine-tuning of Transformer-based PLMs. We apply the proposed methods for fine-tuning T5 on the GLUE benchmark to show that incorporating the Kronecker-based modules can outperform state-of-the-art PET methods.",,"A Edalati, M Tahaei, I Kobyzev, V P Nia, J J Clark, M Rezagholizadeh - arXiv preprint arXiv:2212.10650, 2022 - arxiv.org",[],https://arxiv.org/abs/2212.10650,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2212.10650,['https://arxiv.org/pdf/2212.10650'],krona parameter efficient tuning with kronecker adapter,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩,1,,
A Unified Weight Initialization Paradigm for Tensorial Convolutional Neural Networks,"Y Pan, Z Su, A Liu, J Wang, N Li, Z Xu",2022.0,,"Tensorial Convolutional Neural Networks (TCNNs) have attracted much research attention for their power in reducing model parameters or enhancing the generalization ability. However, exploration of TCNNs is hindered even from weight initialization methods. To be specific, general initialization methods, such as Xavier or Kaiming initialization, usually fail to generate appropriate weights for TCNNs. Meanwhile, although there are ad-hoc approaches for specific architectures (e.g., Tensor Ring Nets), they are not applicable to TCNNs with other tensor decomposition methods (e.g., CP or Tucker decomposition). To address this problem, we propose a universal weight initialization paradigm, which generalizes Xavier and Kaiming methods and can be widely applicable to arbitrary TCNNs. Specifically, we first present the Reproducing Transformation to convert the backward process in TCNNs to an equivalent convolution process. Then, based on the convolution operators in the forward and backward processes, we build a unified paradigm to control the variance of features and gradients in TCNNs. Thus, we can derive fan-in and fan-out initialization for various TCNNs. We demonstrate that our paradigm can stabilize the training of TCNNs, leading to faster convergence and better results.",,"Y Pan, Z Su, A Liu, J Wang, N Li, Z Xu - arXiv preprint arXiv:2205.15307, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.15307,arxiv-completion,2026-09-26 (citations:OpenAlex),,2205.15307,['https://arxiv.org/pdf/2205.15307'],a unified weight initialization paradigm for tensorial convolutional neural networks,,1,,
Exploring Extreme Parameter Compression for Pre-trained Language Models,"Y Ren, B Wang, L Shang, X Jiang, Q Liu",2022.0,,"Recent work explored the potential of large-scale Transformer-based pre-trained models, especially Pre-trained Language Models (PLMs) in natural language processing. This raises many concerns from various perspectives, e.g., financial costs and carbon emissions. Compressing PLMs like BERT with negligible performance loss for faster inference and cheaper deployment has attracted much attention. In this work, we aim to explore larger compression ratios for PLMs, among which tensor decomposition is a potential but under-investigated one. Two decomposition and reconstruction protocols are further proposed to improve the effectiveness and efficiency during compression. Our compressed BERT with ${1}/{7}$ parameters in Transformer layers performs on-par with, sometimes slightly better than the original BERT in GLUE benchmark. A tiny version achieves $96.7\%$ performance of BERT-base with $ {1}/{48} $ encoder parameters (i.e., less than 2M parameters excluding the embedding layer) and $2.7 \times$ faster on inference. To show that the proposed method is orthogonal to existing compression methods like knowledge distillation, we also explore the benefit of the proposed method on a distilled BERT.",,"Y Ren, B Wang, L Shang, X Jiang, Q Liu - arXiv preprint arXiv:2205.10036, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.10036,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2205.10036,['https://arxiv.org/pdf/2205.10036'],exploring extreme parameter compression for pre trained language models,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩 / 量子启发综述,1,,
High-Order Pooling for Graph Neural Networks with Tensor Decomposition,"C Hua, G Rabusseau, J Tang",2022.0,,"Graph Neural Networks (GNNs) are attracting growing attention due to their effectiveness and flexibility in modeling a variety of graph-structured data. Exiting GNN architectures usually adopt simple pooling operations (eg. sum, average, max) when aggregating messages from a local neighborhood for updating node representation or pooling node representations from the entire graph to compute the graph representation. Though simple and effective, these linear operations do not model high-order non-linear interactions among nodes. We propose the Tensorized Graph Neural Network (tGNN), a highly expressive GNN architecture relying on tensor decomposition to model high-order non-linear node interactions. tGNN leverages the symmetric CP decomposition to efficiently parameterize permutation-invariant multilinear maps for modeling node interactions. Theoretical and empirical analysis on both node and graph classification tasks show the superiority of tGNN over competitive baselines. In particular, tGNN achieves the most solid results on two OGB node classification datasets and one OGB graph classification dataset.",,"C Hua, G Rabusseau, J Tang - arXiv preprint arXiv:2205.11691, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.11691,arxiv-completion,2026-09-26 (citations:OpenAlex),,2205.11691,['https://arxiv.org/pdf/2205.11691'],high order pooling for graph neural networks with tensor decomposition,,1,,
Nimble GNN Embedding with Tensor-Train Decomposition,"C Yin, D Zheng, I Nisa, C Faloutos, G Karypis, R Vuduc",2022.0,,"This paper describes a new method for representing embedding tables of graph neural networks (GNNs) more compactly via tensor-train (TT) decomposition. We consider the scenario where (a) the graph data that lack node features, thereby requiring the learning of embeddings during training; and (b) we wish to exploit GPU platforms, where smaller tables are needed to reduce host-to-GPU communication even for large-memory GPUs. The use of TT enables a compact parameterization of the embedding, rendering it small enough to fit entirely on modern GPUs even for massive graphs. When combined with judicious schemes for initialization and hierarchical graph partitioning, this approach can reduce the size of node embedding vectors by 1,659 times to 81,362 times on large publicly available benchmark datasets, achieving comparable or better accuracy and significant speedups on multi-GPU systems. In some cases, our model without explicit node features on input can even match the accuracy of models that use node features.",,"C Yin, D Zheng, I Nisa, C Faloutos, G Karypis, R Vuduc - arXiv preprint arXiv:2206.10581, 2022 - arxiv.org",[],https://arxiv.org/abs/2206.10581,arxiv-completion,2026-09-26 (citations:OpenAlex),,2206.10581,['https://arxiv.org/pdf/2206.10581'],nimble gnn embedding with tensor train decomposition,,1,,
Permutation Search of Tensor Network Structures via Local Sampling,"C Li, J Zeng, Z Tao, Q Zhao",2022.0,,"Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we consider a practical variant of TN-SS, dubbed TN permutation search (TN-PS), in which we search for good mappings from tensor modes onto TN vertices (core tensors) for compact TN representations. We conduct a theoretical investigation of TN-PS and propose a practically-efficient algorithm to resolve the problem. Theoretically, we prove the counting and metric properties of search spaces of TN-PS, analyzing for the first time the impact of TN structures on these unique properties. Numerically, we propose a novel meta-heuristic algorithm, in which the searching is done by randomly sampling in a neighborhood established in our theory, and then recurrently updating the neighborhood until convergence. Numerical results demonstrate that the new algorithm can reduce the required model size of TNs in extensive benchmarks, implying the improvement in the expressive power of TNs. Furthermore, the computational cost for the new algorithm is significantly less than that in~\cite{li2020evolutionary}.",,"C Li, J Zeng, Z Tao, Q Zhao - arXiv preprint arXiv:2206.06597, 2022 - arxiv.org",[],https://arxiv.org/abs/2206.06597,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,2206.06597,['https://arxiv.org/pdf/2206.06597'],permutation search of tensor network structures via local sampling,MPS/序列建模,1,,
Position: Tensor Networks are a Valuable Asset for Green AI,"E Memmel, C Menzen, J Schuurmans, F Wesel, K Batselier",2022.0,,"For the first time, this position paper introduces a fundamental link between tensor networks (TNs) and Green AI, highlighting their synergistic potential to enhance both the inclusivity and sustainability of AI research. We argue that TNs are valuable for Green AI due to their strong mathematical backbone and inherent logarithmic compression potential. We undertake a comprehensive review of the ongoing discussions on Green AI, emphasizing the importance of sustainability and inclusivity in AI research to demonstrate the significance of establishing the link between Green AI and TNs. To support our position, we first provide a comprehensive overview of efficiency metrics proposed in Green AI literature and then evaluate examples of TNs in the fields of kernel machines and deep learning using the proposed efficiency metrics. This position paper aims to incentivize meaningful, constructive discussions by bridging fundamental principles of Green AI and TNs. We advocate for researchers to seriously evaluate the integration of TNs into their research projects, and in alignment with the link established in this paper, we support prior calls encouraging researchers to treat Green AI principles as a research priority.",,"E Memmel, C Menzen, J Schuurmans, F Wesel, K Batselier - arXiv preprint arXiv:2205.12961, 2022 - arxiv.org",[],https://arxiv.org/abs/2205.12961,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2205.12961,['https://arxiv.org/pdf/2205.12961'],position tensor networks are a valuable asset for green ai,MPO/TT 压缩 / 量子启发综述,1,,
Optimizing Tensor Network Contraction Using Reinforcement Learning,"E A Meirom, H Maron, S Mannor, G Chechik",2022.0,,"Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit requires computing the contraction of a large network of tensors. The order (path) of contraction can have a drastic effect on the computing cost, but finding an efficient order is a challenging combinatorial optimization problem. We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges and obtain significant improvements over state-of-the-art techniques in three varieties of circuits, including the largest scale networks used in contemporary QC.",,"E A Meirom, H Maron, S Mannor, G Chechik - arXiv preprint arXiv:2204.09052, 2022 - arxiv.org",[],https://arxiv.org/abs/2204.09052,arxiv-completion,2026-09-26 (citations:OpenAlex),,2204.09052,['https://arxiv.org/pdf/2204.09052'],optimizing tensor network contraction using reinforcement learning,,1,,
Losparse: Structured compression of large language models based on low-rank and sparse approximation,"Y Li, Y Yu, Q Zhang, C Liang, P He…",2023.0,205,"… in various natural language tasks, but they are often prohibitively large, requiring … models, we propose LoSparse (Low-Rank and Sparse approximation), a novel model compression tech…",qoeYdaGAk5IJ,"Y Li, Y Yu, Q Zhang, C Liang, P He… - International …, 2023 - proceedings.mlr.press",['https://proceedings.mlr.press/v202/li23ap/li23ap.pdf'],https://proceedings.mlr.press/v202/li23ap.html,unknown,unknown,MPO/TT 压缩,2306.11222,['https://proceedings.mlr.press/v202/li23ap/li23ap.pdf'],losparse structured compression of large language models based on low rank and sparse approximation,MPO/TT 压缩,1,,
Tensor networks meet neural networks: A survey and future perspectives,"M Wang, Y Pan, Z Xu, G Li, X Yang, D Mandic…",2023.0,88,"Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial complexity. As a result, they have attracted significant attention in the fields of quantum physics and machine learning. Meanwhile, NNs have displayed exceptional performance in various applications, e.g., computer vision, natural language processing, and robotics research. Interestingly, although these two types of networks originate from different observations, they are inherently linked through the typical multilinearity structure underlying both TNs and NNs, thereby motivating a significant number of developments regarding combinations of TNs and NNs. In this paper, we refer to these combinations as tensorial neural networks~(TNNs) and present an introduction to TNNs from both data processing and model architecture perspectives. From the data perspective, we explore the capabilities of TNNs in multi-source fusion, multimodal pooling, data compression, multi-task training, and quantum data processing. From the model perspective, we examine TNNs' integration with various architectures, including Convolutional Neural Networks, Recurrent Neural Networks, Graph Neural Networks, Transformers, Large Language Models, and Quantum Neural Networks. Furthermore, this survey also explores methods for improving TNNs, examines flexible toolboxes for implementing TNNs, and documents TNN development while highlighting potential future directions. To the best of our knowledge, this is the first comprehensive survey that bridges the connections among NNs and TNs. We provide a curated list of TNNs at https://github.com/tnbar/awesome-tensorial-neural-networks.",QI0H8PJP_8MJ,"M Wang, Y Pan, Z Xu, G Li, X Yang, D Mandic… - arXiv preprint arXiv …, 2023 - arxiv.org",['https://arxiv.org/pdf/2302.09019'],https://arxiv.org/abs/2302.09019,unknown,unknown,MPS/序列建模,2302.09019,['https://arxiv.org/pdf/2302.09019'],tensor networks meet neural networks a survey and future perspectives,MPO/TT 压缩 / MPS/序列建模,2,,
Tensorgpt: Efficient compression of large language models based on tensor-train decomposition,"M Xu, YL Xu, DP Mandic",2023.0,84,"High-dimensional token embeddings underpin Large Language Models (LLMs), as they can capture subtle semantic information and significantly enhance the modelling of complex language patterns. However, this high dimensionality also introduces considerable model parameters and prohibitively high model storage and memory requirements, which is particularly unaffordable for low-end devices. Targeting no extra training data and insufficient computation cases, we propose a training-free model compression approach based on the Tensor-Train Decomposition (TTD), whereby each pre-trained token embedding is converted into a lower-dimensional Matrix Product State (MPS). We then comprehensively investigate the low-rank structures extracted by this approach, in terms of the compression ratio, the language task performance, and latency on a typical low-end device (i.e. Raspberry Pi). Taking GPT family models (i.e. GPT-2 and CerebrasGPT) as case studies, our approach theoretically results in $46.89\%$ fewer parameters of the entire model, with a compression ratio $39.38\times$ - $65.64\times$ for the embedding layers. With different hyperparameter choices, the model compressed with our approach can achieve a comparable language task performance to the original model with around $2.0\times$ embedding layer compression. This empirically proves the existence of low-rank structure in GPT family models, and demonstrates that about half of the parameters in the embedding layers are redundant.",HWfZ1S1dO9kJ,"M Xu, YL Xu, DP Mandic - arXiv preprint arXiv:2307.00526, 2023 - arxiv.org",['https://arxiv.org/pdf/2307.00526'],https://arxiv.org/abs/2307.00526,unknown,unknown,MPO/TT 压缩,2307.00526,['https://arxiv.org/pdf/2307.00526'],tensorgpt efficient compression of large language models based on tensor train decomposition,MPO/TT 压缩 / 张量化Transformer,3,,
Verification of the area law of mutual information in a quantum field simulator,"M Tajik, I Kukuljan, S Sotiriadis, B Rauer, T Schweigler…",2023.0,71,"… the foundations for the overwhelming success of tensor network-based methods 2 . In … a logarithmic scaling instead of the area law 9 . In thermal states, although the mutual information …",2N5oRNBtcr0J,"M Tajik, I Kukuljan, S Sotiriadis, B Rauer, T Schweigler… - Nature Physics, 2023 - nature.com",['https://arxiv.org/pdf/2206.10563'],https://www.nature.com/articles/s41567-023-02027-1,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/2206.10563'],verification of the area law of mutual information in a quantum field simulator,互信息/标度,1,,
Tensor networks for unsupervised machine learning,"J Liu, S Li, J Zhang, P Zhang",2023.0,70,"… matrix product states (AMPS), a tensor network model … of our model using two applications, generative modeling on synthetic … For the MPS Born machine and the TTN Born machine, the …",8oysnt0KL8cJ,"J Liu, S Li, J Zhang, P Zhang - Physical Review E, 2023 - APS",['https://arxiv.org/pdf/2106.12974'],https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.L012103,unknown,unknown,MPS 生成/Born机,,['https://arxiv.org/pdf/2106.12974'],tensor networks for unsupervised machine learning,MPS 生成/Born机 / TTN/MERA/PEPS,3,,
Simulating quantum circuits using tree tensor networks,"P Seitz, I Medina, E Cruz, Q Huang, CB Mendl",2023.0,62,"… We say that a tree tensor network is of canonical form (ie, orthonormalized) if each node in … -orthonormalization of the tree tensor network. To ensure that the tree tensor network can be …",Wna7MDXLHegJ,"P Seitz, I Medina, E Cruz, Q Huang, CB Mendl - Quantum, 2023 - quantum-journal.org",['https://quantum-journal.org/papers/q-2023-03-30-964/pdf/'],https://quantum-journal.org/papers/q-2023-03-30-964/,unknown,unknown,TTN/MERA/PEPS,2206.01000,['https://quantum-journal.org/papers/q-2023-03-30-964/pdf/'],simulating quantum circuits using tree tensor networks,TTN/MERA/PEPS,1,"Quantum 7, 964 (2023)",
Tensor decomposition for model reduction in neural networks: A review [feature],"X Liu, KK Parhi",2023.0,61,"Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine translation. Most state-of-the-art neural networks are over-parameterized and require a high computational cost. One straightforward solution is to replace the layers of the networks with their low-rank tensor approximations using different tensor decomposition methods. This article reviews six tensor decomposition methods and illustrates their ability to compress model parameters of convolutional neural networks (CNNs), recurrent neural networks (RNNs) and Transformers. The accuracy of some compressed models can be higher than the original versions. Evaluations indicate that tensor decompositions can achieve significant reductions in model size, run-time and energy consumption, and are well suited for implementing neural networks on edge devices.",e6WFfGfAaCwJ,"X Liu, KK Parhi - IEEE Circuits and Systems Magazine, 2023 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2304.13539'],https://ieeexplore.ieee.org/abstract/document/10190238/,unknown,unknown,张量化Transformer,,['https://arxiv.org/pdf/2304.13539'],tensor decomposition for model reduction in neural networks a review feature,张量化Transformer,1,IEEE Circuits and Systems Magazine,
Tensor networks for interpretable and efficient quantum-inspired machine learning,"SJ Ran, G Su",2023.0,44,"It is a critical challenge to simultaneously achieve high interpretability and high efficiency with the current schemes of deep machine learning (ML). The tensor network (TN), a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages in developing efficient “white-box” ML schemes. Here, we provide a brief review of the inspiring progress in TN-based ML. On the one hand, the interpretability of TN ML can be accommodated by a solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be obtained from powerful TN representations and the advanced computational techniques developed in quantum many-body physics. Keeping pace with the rapid development of quantum computers, TNs are expected to produce novel schemes runnable on quantum hardware in the direction of “quantum artificial intelligence” in the near future.",cXTbCSZx6J8J,"SJ Ran, G Su - Intelligent Computing, 2023 - spj.science.org",['https://spj.science.org/doi/pdf/10.34133/icomputing.0061'],https://spj.science.org/doi/abs/10.34133/icomputing.0061,unknown,unknown,互信息/标度,,['https://spj.science.org/doi/pdf/10.34133/icomputing.0061'],tensor networks for interpretable and efficient quantum inspired machine learning,互信息/标度,1,Intelligent Computing,
Density Matrix Renormalization Group with Tensor Processing Units,"M Ganahl, J Beall, M Hauru, A G M Lewis, T Wojno, J H Yoo, Y Zou, G Vidal",2023.0,37,"A novel architecture is used to boost the density-matrix renormalization group, an important and widely used algorithm, impressively pushing the boundary of the current state of the art by at least an order of magnitude in complexity.",,"M Ganahl, J Beall, M Hauru, A G M Lewis, T Wojno, J H Yoo, Y Zou, G Vidal - PRX Quantum, 2023",[],https://doi.org/10.1103/prxquantum.4.010317,arxiv-completion,2026-09-26 (citations:OpenAlex),量子启发综述,,[],density matrix renormalization group with tensor processing units,量子启发综述,1,PRX Quantum,
An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation,"J Naumann, EL Weerda, M Rizzi, J Eisert…",2023.0,35,"Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results.",NOVV6uVQqTcJ,"J Naumann, EL Weerda, M Rizzi, J Eisert… - arXiv preprint arXiv …, 2023 - arxiv.org",['https://arxiv.org/pdf/2308.12358'],https://arxiv.org/abs/2308.12358,unknown,unknown,TTN/MERA/PEPS,2308.12358,['https://arxiv.org/pdf/2308.12358'],an introduction to infinite projected entangled pair state methods for variational ground state simulations using automatic differentiation,TTN/MERA/PEPS,1,SciPost Phys. Lect. Notes 86 (2024),
PROTES: probabilistic optimization with tensor sampling,"A Batsheva, A Chertkov…",2023.0,35,… “Tensor networks for dimensionality reduction and large-scale optimization: Part 2 applications … “Approximation and sampling of multivariate probability distributions in the tensor train …,3ktWtA4NhrMJ,"A Batsheva, A Chertkov… - Advances in Neural …, 2023 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2023/file/028957869e560af14243ac37663a471e-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2023/hash/028957869e560af14243ac37663a471e-Abstract-Conference.html,unknown,unknown,MPS/序列建模,2301.12162,['https://proceedings.neurips.cc/paper_files/paper/2023/file/028957869e560af14243ac37663a471e-Paper-Conference.pdf'],protes probabilistic optimization with tensor sampling,MPS/序列建模,1,,
Detecting genuine multipartite entanglement via machine learning,"YJ Luo, JM Liu, C Zhang",2023.0,29,"In recent years, supervised and semisupervised machine learning methods such as neural networks, support vector machines (SVMs), and semisupervised support vector machines (S4VMs) have been widely used in quantum entanglement and quantum steering verification problems. However, few studies have focused on detecting genuine multipartite entanglement based on machine learning. Here, we investigate supervised and semisupervised machine learning for detecting genuine multipartite entanglement of three-qubit states. We randomly generate three-qubit density matrices and train an SVM for the detection of genuine multipartite entangled states. Moreover, we improve the S4VM training method, which optimizes the grouping of prediction samples and then performs iterative predictions. Through numerical simulation, it is confirmed that this method can significantly improve the prediction accuracy.",QRsChV2I5doJ,"YJ Luo, JM Liu, C Zhang - Physical Review A, 2023 - APS",['https://arxiv.org/pdf/2311.17548'],https://journals.aps.org/pra/abstract/10.1103/PhysRevA.108.052424,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2311.17548'],detecting genuine multipartite entanglement via machine learning,TTN/MERA/PEPS,1,Physical Review A,
Typical correlation length of sequentially generated tensor network states,"D Haag, F Baccari, G Styliaris",2023.0,29,"… We extract the scaling behavior of the average correlations … For MPS, we also consider the Rényi-α mutual information. … the following scale invariance property, valid in the context of …",BQMgpod1y5oJ,"D Haag, F Baccari, G Styliaris - PRX Quantum, 2023 - APS",['https://link.aps.org/pdf/10.1103/PRXQuantum.4.030330'],https://link.aps.org/doi/10.1103/PRXQuantum.4.030330,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PRXQuantum.4.030330'],typical correlation length of sequentially generated tensor network states,互信息/标度,1,,
Renormalization group for measurement and entanglement phase transitions,"A Nahum, KJ Wiese",2023.0,28,"… , physical averages of entanglement entropies or correlation … a useful picture deep inside the entangled phases, where the … From now on we stick with the tensor network language. For …",w4Zt16dmFYEJ,"A Nahum, KJ Wiese - Physical Review B, 2023 - APS",['https://arxiv.org/pdf/2303.07848'],https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.104203,unknown,unknown,互信息/标度,,['https://arxiv.org/pdf/2303.07848'],renormalization group for measurement and entanglement phase transitions,互信息/标度,1,,
Symmetric tensor networks for generative modeling and constrained combinatorial optimization,"J Lopez-Piqueres, J Chen…",2023.0,27,… Using a binary search tree on top to match configurations of charges to the left and to the … Flowchart of all the steps entering in the tensor network generative algorithm for combinatorial …,60u9FlScSLcJ,"J Lopez-Piqueres, J Chen… - … Learning: Science and …, 2023 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/2632-2153/ace0f5/pdf'],https://iopscience.iop.org/article/10.1088/2632-2153/ace0f5/meta,unknown,unknown,TTN/MERA/PEPS,2211.09121,['https://iopscience.iop.org/article/10.1088/2632-2153/ace0f5/pdf'],symmetric tensor networks for generative modeling and constrained combinatorial optimization,TTN/MERA/PEPS,1,Mach. Learn.: Sci. Technol. 4 035009 (2023),
ETTE: Efficient tensor-train-based computing engine for deep neural networks,"Y Gong, M Yin, L Huang, J Xiao, Y Sui, C Deng…",2023.0,24,"… Tensor-train (TT) decomposition enables ultra-high compression ratio, making the deep neural network … speedups even the models are highly compressed. To unleash the full potential …",R2W60Sbw0xUJ,"Y Gong, M Yin, L Huang, J Xiao, Y Sui, C Deng… - Proceedings of the 50th …, 2023 - dl.acm.org",['https://dl.acm.org/doi/pdf/10.1145/3579371.3589103'],https://dl.acm.org/doi/abs/10.1145/3579371.3589103,unknown,unknown,MPO/TT 压缩,,['https://dl.acm.org/doi/pdf/10.1145/3579371.3589103'],ette efficient tensor train based computing engine for deep neural networks,MPO/TT 压缩,1,,
Introducing nonlinear activations into quantum generative models,"K Gili, M Sveistrys, C Ballance",2023.0,22,"… However, some of the most successful classical generative models, … in quantum generative modeling by introducing a model that … Born machine framework—the quantum neuron Born …",3xEHWCaJWOYJ,"K Gili, M Sveistrys, C Ballance - Physical Review A, 2023 - APS",['https://arxiv.org/pdf/2205.14506'],https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.012406,unknown,unknown,MPS 生成/Born机,,['https://arxiv.org/pdf/2205.14506'],introducing nonlinear activations into quantum generative models,MPS 生成/Born机,1,,
Generative learning of continuous data by tensor networks,"A Meiburg, J Chen, J Miller, R Tihon…",2023.0,16,"Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable features arising from their quantum-inspired nature, tensor network generative models have previously been largely restricted to binary or categorical data, limiting their utility in real-world modeling problems. We overcome this by introducing a new family of tensor network generative models for continuous data, which are capable of learning from distributions containing continuous random variables. We develop our method in the setting of matrix product states, first deriving a universal expressivity theorem proving the ability of this model family to approximate any reasonably smooth probability density function with arbitrary precision. We then benchmark the performance of this model on several synthetic and real-world datasets, finding that the model learns and generalizes well on distributions of continuous and discrete variables. We develop methods for modeling different data domains, and introduce a trainable compression layer which is found to increase model performance given limited memory or computational resources. Overall, our methods give important theoretical and empirical evidence of the efficacy of quantum-inspired methods for the rapidly growing field of generative learning.",wH3MxM4TMBYJ,"A Meiburg, J Chen, J Miller, R Tihon… - arXiv preprint arXiv …, 2023 - arxiv.org",['https://arxiv.org/pdf/2310.20498'],https://arxiv.org/abs/2310.20498,unknown,unknown,TTN/MERA/PEPS,2310.20498,['https://arxiv.org/pdf/2310.20498'],generative learning of continuous data by tensor networks,TTN/MERA/PEPS,1,,
TT-Net: Tensorized Transformer Network for 3D medical image segmentation,"J Wang, A Qu, Q Wang, Q Zhao, J Liu, Q Wu",2023.0,15,"… tensor with n matrices. Motivated by this, a lightweight self-attention mechanism based on Tucker decomposition … multi-head self-attention to construct a slight transformer with promising …",Ad6oL5Px3zwJ,"J Wang, A Qu, Q Wang, Q Zhao, J Liu, Q Wu - … Medical Imaging and …, 2023 - Elsevier",[],https://www.sciencedirect.com/science/article/pii/S0895611123000526,unknown,unknown,张量化Transformer,,[],tt net tensorized transformer network for 3d medical image segmentation,张量化Transformer,1,,
Generative modeling via tree tensor network states,"X Tang, YH Hur, Y Khoo, L Ying",2023.0,11,"… using a tree tensor network state as a generative model that enjoys … tensor network architectures for generative modeling. In Sect. 1.2, we discuss the connection between TTNS and tree…",qSwLJCTCm6oJ,"X Tang, YH Hur, Y Khoo, L Ying - Research in the Mathematical Sciences, 2023 - Springer",['https://par.nsf.gov/servlets/purl/10550346'],https://link.springer.com/article/10.1007/s40687-023-00381-3,unknown,unknown,TTN/MERA/PEPS,,"['https://par.nsf.gov/servlets/purl/10550346', 'https://arxiv.org/pdf/2209.01341']",generative modeling via tree tensor network states,TTN/MERA/PEPS,2,,
Tree-Invent: a novel multipurpose molecular generative model constrained with a topological tree,"M Xu, H Chen",2023.0,10,"De novo molecular design plays an important role in drug discovery. Here, a novel generative model, Tree-Invent, was proposed to integrate topological constraints in the generation of a molecular graph. In this model, a molecular graph is represented as a topological tree in which a ring system, a nonring atom, and a chemical bond are regarded as the ring node, single node, and edge, respectively. The molecule generation is driven by three independent submodels for carrying out operations of node addition, ring generation, and node connection. One unique feature of the generative model is that the topological tree structure can be specified as a constraint for structure generation, which provides more precise control of structure generation. Combined with reinforcement learning, the Tree-Invent model could efficiently explore targeted chemical space. Moreover, the Tree-Invent model is flexible enough to be used in versatile molecule design settings such as scaffold decoration, scaffold hopping, and linker generation.",8U0IxpFnm9QJ,"M Xu, H Chen - Journal of chemical information and modeling, 2023 - ACS Publications",[],https://pubs.acs.org/doi/abs/10.1021/acs.jcim.3c01626,unknown,unknown,TTN/MERA/PEPS,,[],tree invent a novel multipurpose molecular generative model constrained with a topological tree,TTN/MERA/PEPS,1,Journal of Chemical Information and Modeling,
Multi-layered projected entangled pair states for image classification,"L Li, H Lai",2023.0,9,"Tensor networks have been recognized as a powerful numerical tool; they are applied in various fields, including physics, computer science, and more. The idea of a tensor network originates from quantum physics as an efficient representation of quantum many-body states and their operations. Matrix product states (MPS) form one of the simplest tensor networks and have been applied to machine learning for image classification. However, MPS has certain limitations when processing two-dimensional images, meaning that it is preferable for an projected entangled pair states (PEPS) tensor network with a similar structure to the image to be introduced into machine learning. PEPS tensor networks are significantly superior to other tensor networks on the image classification task. Based on a PEPS tensor network, this paper constructs a multi-layered PEPS (MLPEPS) tensor network model for image classification. PEPS is used to extract features layer by layer from the image mapped to the Hilbert space, which fully utilizes the correlation between pixels while retaining the global structural information of the image. When performing classification tasks on the Fashion-MNIST dataset, MLPEPS achieves a classification accuracy of 90.44%, exceeding tensor network models such as the original PEPS. On the COVID-19 radiography dataset, MLPEPS has a test set accuracy of 91.63%, which is very close to the results of GoogLeNet. Under the same experimental conditions, the learning ability of MLPEPS is already close to that of existing neural networks while having fewer parameters. MLPEPS can be used to build different network models by modifying the structure, and as such it has great potential in machine learning.",PgrQ-KJ-mXMJ,"L Li, H Lai - Sustainability, 2023 - mdpi.com",[],https://www.mdpi.com/2071-1050/15/6/5120,unknown,unknown,TTN/MERA/PEPS,,[],multi layered projected entangled pair states for image classification,TTN/MERA/PEPS,1,Sustainability,
Sequence processing with quantum tensor networks,"C Harvey, R Yeung, K Meichanetzidis",2023.0,9,"We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network architecture, and is motivated by the correlation structure inherent in the data, as well as any relevant compositional structure, resulting in tree-like connectivity. Our models are specifically constructed using parameterised quantum circuits, widely used in quantum machine learning, effectively using Hilbert space as a feature space. Furthermore, they are efficiently trainable due to their tree-like structure. We demonstrate experimental results for the task of binary classification of sequences from real-world datasets relevant to natural language and bioinformatics, characterised by long-range correlations and often equipped with syntactic information. Since our models have a valid operational interpretation as quantum processes, we also demonstrate their implementation on Quantinuum's H2-1 trapped-ion quantum processor, demonstrating the possibility of efficient sequence processing on near-term quantum devices. This work constitutes the first scalable implementation of near-term quantum language processing, providing the tools for large-scale experimentation on the role of tensor structure and syntactic priors. Finally, this work lays the groundwork for generative sequence modelling in a hybrid pipeline where the training may be conducted efficiently in simulation, while sampling from learned probability distributions may be done with polynomial speed-up on quantum devices.",iRjs6hALOz4J,"C Harvey, R Yeung, K Meichanetzidis - arXiv preprint arXiv:2308.07865, 2023 - arxiv.org",['https://arxiv.org/pdf/2308.07865'],https://arxiv.org/abs/2308.07865,unknown,unknown,MPS/序列建模,2308.07865,['https://arxiv.org/pdf/2308.07865'],sequence processing with quantum tensor networks,MPS/序列建模,1,,
NeuKron: Constant-Size Lossy Compression of Sparse Reorderable Matrices and Tensors,"T Kwon, J Ko, J Jung, K Shin",2023.0,9,"Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an amount of space linear in the number of non-zeros, and lossy compression of sparse matrices (e.g., Truncated SVD) typically requires an amount of space linear in the number of rows and columns. In this work, we propose NeuKron for compressing a sparse reorderable matrix into a constant-size space. NeuKron generalizes Kronecker products using a recurrent neural network with a constant number of parameters. NeuKron updates the parameters so that a given matrix is approximated by the product and reorders the rows and columns of the matrix to facilitate the approximation. The updates take time linear in the number of non-zeros in the input matrix, and the approximation of each entry can be retrieved in logarithmic time. We also extend NeuKron to compress sparse reorderable tensors (e.g. multi-layer graphs), which generalize matrices. Through experiments on ten real-world datasets, we show that NeuKron is (a) Compact: requiring up to five orders of magnitude less space than its best competitor with similar approximation errors, (b) Accurate: giving up to 10 × smaller approximation error than its best competitors with similar size outputs, and (c) Scalable: successfully compressing a matrix with over 230 million non-zero entries.",,"T Kwon, J Ko, J Jung, K Shin - arXiv, 2023",[],https://doi.org/10.1145/3543507.3583226,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,,[],neukron constant size lossy compression of sparse reorderable matrices and tensors,MPO/TT 压缩 / MPS/序列建模,1,,
Undirected probabilistic model for tensor decomposition,"Z Tao, T Tanaka, Q Zhao",2023.0,8,"… model that captures the joint probability of the data and latent tensor factors through a deep energy-based model (… Recent research, known as tensor network structure search [TNSS, 22…",24IUkSUb1SsJ,"Z Tao, T Tanaka, Q Zhao - Advances in Neural Information …, 2023 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2023/file/51f9d542dea8bed1f66c8add6ec23c69-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2023/hash/51f9d542dea8bed1f66c8add6ec23c69-Abstract-Conference.html,unknown,unknown,MPS/序列建模,,['https://proceedings.neurips.cc/paper_files/paper/2023/file/51f9d542dea8bed1f66c8add6ec23c69-Paper-Conference.pdf'],undirected probabilistic model for tensor decomposition,MPS/序列建模,1,,
Distributive pre-training of generative modeling using matrix-product states,"SH Lin, O Kuijpers, S Peterhansl…",2023.0,7,"Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an alternative training scheme utilizing basic tensor network operations, e.g., summation and compression. The training algorithm is based on compressing the superposition state constructed from all the training data in product state representation. The algorithm could be parallelized easily and only iterates through the dataset once. Hence, it serves as a pre-training algorithm. We benchmark the algorithm on the MNIST dataset and show reasonable results for generating new images and classification tasks. Furthermore, we provide an interpretation of the algorithm as a compressed quantum kernel density estimation for the probability amplitude of input data.",mP_sXVhAv1AJ,"SH Lin, O Kuijpers, S Peterhansl… - arXiv preprint arXiv …, 2023 - arxiv.org",['https://arxiv.org/pdf/2306.14787'],https://arxiv.org/abs/2306.14787,unknown,unknown,MPS 生成/Born机,2306.14787,['https://arxiv.org/pdf/2306.14787'],distributive pre training of generative modeling using matrix product states,MPS 生成/Born机,1,arXiv (Cornell University),
A performance characterization of quantum generative models,"C A Riofrío, O Mitevski, C Jones, F Krellner, A Vučković, J Doetsch, J Klepsch, T Ehmer, A Luckow",2023.0,6,"Quantum generative modeling is a growing area of interest for industry-relevant applications. With the field still in its infancy, there are many competing techniques. This work is an attempt to systematically compare a broad range of these techniques to guide quantum computing practitioners when deciding which models and techniques to use in their applications. We compare fundamentally different architectural ansatzes of parametric quantum circuits used for quantum generative modeling: 1. A continuous architecture, which produces continuous-valued data samples, and 2. a discrete architecture, which samples on a discrete grid. We compare the performance of different data transformations: normalization by the min-max transform or by the probability integral transform. We learn the underlying probability distribution of the data sets via two popular training methods: 1. quantum circuit Born machines (QCBM), and 2. quantum generative adversarial networks (QGAN). We study their performance and trade-offs as the number of model parameters increases, with the baseline of similarly trained classical neural networks. The study is performed on six low-dimensional synthetic and two real financial data sets. Our two key findings are that: 1. For all data sets, our quantum models require similar or fewer parameters than their classical counterparts. In the extreme case, the quantum models require two of orders of magnitude less parameters. 2. We empirically find that a variant of the discrete architecture, which learns the copula of the probability distribution, outperforms all other methods.",,"C A Riofrío, O Mitevski, C Jones, F Krellner, A Vučković, J Doetsch, J Klepsch, T Ehmer, A Luckow - ACM Transactions on Quantum Computing, Volume 5, Issue 2 (2024)",[],https://arxiv.org/abs/2301.09363,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2301.09363,['https://arxiv.org/pdf/2301.09363'],a performance characterization of quantum generative models,MPS 生成/Born机,1,"ACM Transactions on Quantum Computing, Volume 5, Issue 2 (2024)",
Tetra-AML: Automatic Machine Learning via Tensor Networks,"A Naumov, A Melnikov, V Abronin, F Oxanichenko, K Izmailov, M Pflitsch, A Melnikov, M Perelshtein",2023.0,6,"Neural networks have revolutionized many aspects of society but in the era of huge models with billions of parameters, optimizing and deploying them for commercial applications can require significant computational and financial resources. To address these challenges, we introduce the Tetra-AML toolbox, which automates neural architecture search and hyperparameter optimization via a custom-developed black-box Tensor train Optimization algorithm, TetraOpt. The toolbox also provides model compression through quantization and pruning, augmented by compression using tensor networks. Here, we analyze a unified benchmark for optimizing neural networks in computer vision tasks and show the superior performance of our approach compared to Bayesian optimization on the CIFAR-10 dataset. We also demonstrate the compression of ResNet-18 neural networks, where we use 14.5 times less memory while losing just 3.2% of accuracy. The presented framework is generic, not limited by computer vision problems, supports hardware acceleration (such as with GPUs and TPUs) and can be further extended to quantum hardware and to hybrid quantum machine learning models.",,"A Naumov, A Melnikov, V Abronin, F Oxanichenko, K Izmailov, M Pflitsch, A Melnikov, M Perelshtein - Appl. Sci. 15(4), 1852 (2025)",[],https://arxiv.org/abs/2303.16214,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2303.16214,['https://arxiv.org/pdf/2303.16214'],tetra aml automatic machine learning via tensor networks,MPO/TT 压缩 / 量子/混合LLM,1,"Appl. Sci. 15(4), 1852 (2025)",
On Translation-Invariant Matrix Product States and advances in MPS representations of the -state,"P Klimov, R Sengupta, J Biamonte",2023.0,5,"This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS representations of a certain class of TI states and study their optimality in terms of their bond dimension. We pay particular attention to the $n$-party $W$-state and construct a TI MPS representation of bond dimension $\left \lfloor \dfrac{n}{2} \right \rfloor +1$ for it. We further study properties of this class and show that we can can always achieve a bond dimension of $n$ for TI MPS representation of states in this class. In the framework of studying optimality of TI MPS representations with PBC, we study the optimal bond dimension $d(ψ)$ for a given state $ψ$. In particular we introduce a deterministic algorithm for the search of $d(ψ)$ for an arbitary state. Using numerical methods, we verify the optimality of our previous construction for the $n$-party $W$-state for small $n$.",9uqC9YGxQPwJ,"P Klimov, R Sengupta, J Biamonte - arXiv preprint arXiv:2306.16456, 2023 - arxiv.org",['https://arxiv.org/pdf/2306.16456'],https://arxiv.org/abs/2306.16456,unknown,unknown,MPS 语言模型,2306.16456,['https://arxiv.org/pdf/2306.16456'],on translation invariant matrix product states and advances in mps representations of the state,MPS 语言模型,1,arXiv (Cornell University),
An efficient tensor-based transformer for industrial Internet of Things,"D Liu, LT Yang, R Zhao, J Cui…",2023.0,4,"… -play lightweight multi-head attention and lightweight position-wise … tensor-coupled transformers, lightweight tensorized trans… nents of transformer and the tensor decomposition …",ZZINRxNE1j8J,"D Liu, LT Yang, R Zhao, J Cui… - IEEE Transactions on …, 2023 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/10105902/,unknown,unknown,张量化Transformer,,[],an efficient tensor based transformer for industrial internet of things,张量化Transformer,1,,
Renormalized Von Neumann entropy with application to entanglement in genuine infinite dimensional systems: R. Gielerak,R Gielerak,2023.0,4,"Abstract A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) which obeys several of the natural physical demands (as expected for a “good” measure of entanglement in the case of general quantum states describing bipartite and infinite-dimensional systems) is proposed. The renormalized quantum entropy is defined by the explicit use of the Fredholm determinants theory. To prove the main results on continuity and finiteness of the introduced renormalization, the fundamental Grothendick approach, which is based on the infinite dimensional Grassmann algebra theory, is applied. Several features of majorization theory are preserved under the introduced renormalization as it is proved in this paper. This fact allows to extend most of the known (mainly, in the context of two-partite, finite-dimensional quantum systems) results of the LOCC comparison theory to the case of genuine infinite-dimensional, two-partite quantum systems.",-SlFzzo31xEJ,"R Gielerak - Quantum Information Processing, 2023 - Springer",['https://link.springer.com/content/pdf/10.1007/s11128-023-04059-1.pdf'],https://link.springer.com/article/10.1007/s11128-023-04059-1,unknown,unknown,互信息/标度,,['https://link.springer.com/content/pdf/10.1007/s11128-023-04059-1.pdf'],renormalized von neumann entropy with application to entanglement in genuine infinite dimensional systems r gielerak,互信息/标度,1,Quantum Information Processing,
Sequential learning on a tensor network Born machine with trainable token embedding,"W Hou, M Li, YZ You",2023.0,4,"Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum inspired generative models, such as Born machines based on the matrix product state framework, have demonstrated remarkable capabilities in unsupervised learning tasks. This study advances the Born machine paradigm by introducing trainable token embeddings through positive operator valued measurements, replacing the traditional approach of static tensor indices. Key technical innovations include encoding tokens as quantum measurement operators with trainable parameters and leveraging QR decomposition to adjust the physical dimensions of the MPS. This approach maximizes the utilization of operator space and enhances the model's expressiveness. Empirical results on RNA data demonstrate that the proposed method significantly reduces negative log likelihood compared to one hot embeddings, with higher physical dimensions further enhancing single site probabilities and multi site correlations. The model also outperforms GPT2 in single site estimation and achieves competitive correlation modeling, showcasing the potential of trainable POVM embeddings for complex data correlations in quantum inspired sequence modeling.",wSQahO8AYaMJ,"W Hou, M Li, YZ You - Mach. Learn.: Sci. Technol. 6, 025071 (2025)","['https://iopscience.iop.org/article/10.1088/2632-2153/adde29/pdf', 'https://arxiv.org/pdf/2311.05050v2']",https://arxiv.org/abs/2311.05050,unknown,2026-09-28 (发表版元数据:Crossref)；并入451行(Scholar:GejCS8uANrsJ),MPS 生成/Born机,2311.05050,"['https://iopscience.iop.org/article/10.1088/2632-2153/adde29/pdf', 'https://arxiv.org/pdf/2311.05050v2']",sequential learning on a tensor network born machine with trainable token embedding,MPS 生成/Born机 / MPS/序列建模,2,"Mach. Learn.: Sci. Technol. 6, 025071 (2025)",2025
Tensor networks for quantum machine learning,"H Rieser, F Köster, A P Raulf",2023.0,3,"Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems that classical computers are unable to solve efficiently. Their nature at the interface between physics and machine learning makes tensor networks easily deployable on quantum computers. In this review article, we shed light on one of the major architectures considered to be predestined for variational quantum machine learning. In particular, we discuss how layouts like MPS, PEPS, TTNs and MERA can be mapped to a quantum computer, how they can be used for machine learning and data encoding and which implementation techniques improve their performance.",,"H Rieser, F Köster, A P Raulf - arXiv preprint arXiv:2303.11735, 2023 - arxiv.org",[],https://arxiv.org/abs/2303.11735,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2303.11735,['https://arxiv.org/pdf/2303.11735'],tensor networks for quantum machine learning,量子/混合LLM / TTN/MERA/PEPS / 量子启发综述,1,,
Approximately Optimal Core Shapes for Tensor Decompositions,"M Ghadiri, M Fahrbach, G Fu, V Mirrokni",2023.0,2,"This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.",,"M Ghadiri, M Fahrbach, G Fu, V Mirrokni - Proceedings of the 40th International Conference on Machine Learning (ICML 2023) 11237-11254",[],https://arxiv.org/abs/2302.03886,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2302.03886,['https://arxiv.org/pdf/2302.03886'],approximately optimal core shapes for tensor decompositions,TTN/MERA/PEPS,1,Proceedings of the 40th International Conference on Machine Learning (ICML 2023) 11237-11254,
Quantum-inspired tensor network for Earth science,"S Otgonbaatar, D Kranzlmüller",2023.0,2,"Deep Learning (DL) is one of many successful methodologies to extract informative patterns and insights from ever increasing noisy large-scale datasets (in our case, satellite images). However, DL models consist of a few thousand to millions of training parameters, and these training parameters require tremendous amount of electrical power for extracting informative patterns from noisy large-scale datasets (e.g., computationally expensive). Hence, we employ a quantum-inspired tensor network for compressing trainable parameters of physics-informed neural networks (PINNs) in Earth science. PINNs are DL models penalized by enforcing the law of physics; in particular, the law of physics is embedded in DL models. In addition, we apply tensor decomposition to HyperSpectral Images (HSIs) to improve their spectral resolution. A quantum-inspired tensor network is also the native formulation to efficiently represent and train quantum machine learning models on big datasets on GPU tensor cores. Furthermore, the key contribution of this paper is twofold: (I) we reduced a number of trainable parameters of PINNs by using a quantum-inspired tensor network, and (II) we improved the spectral resolution of remotely-sensed images by employing tensor decomposition. As a benchmark PDE, we solved Burger's equation. As practical satellite data, we employed HSIs of Indian Pine, USA and of Pavia University, Italy.",,"S Otgonbaatar, D Kranzlmüller - IGARSS 2023",[],https://arxiv.org/abs/2301.07528,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2301.07528,['https://arxiv.org/pdf/2301.07528'],quantum inspired tensor network for earth science,MPO/TT 压缩 / 量子/混合LLM,1,IGARSS 2023,
Partial Tensorized Transformers for Natural Language Processing,"S Vadlamannati, R Solgi",2023.0,1,"The transformer architecture has revolutionized Natural Language Processing (NLP) and other machine-learning tasks, due to its unprecedented accuracy. However, their extensive memory and parameter requirements often hinder their practical applications. In this work, we study the effect of tensor-train decomposition to improve the accuracy and compress transformer vision-language neural networks, namely BERT and ViT. We focus both on embedding-layer compression and partial tensorization of neural networks (PTNN) through an algorithmic approach. Our novel PTNN approach significantly improves the accuracy of existing models by up to 5%, all without the need for post-training adjustments, breaking new ground in the field of tensor decomposition.",0Y8Vk2N58doJ,"S Vadlamannati, R Solgi - arXiv preprint arXiv:2310.20077, 2023 - arxiv.org",['https://arxiv.org/pdf/2310.20077'],https://arxiv.org/abs/2310.20077,unknown,unknown,张量化Transformer,2310.20077,['https://arxiv.org/pdf/2310.20077'],partial tensorized transformers for natural language processing,张量化Transformer,1,,
Implementing Quantum Generative Adversarial Network (qGAN) and QCBM in Finance,S Ganguly,2023.0,1,"Quantum machine learning (QML) is a cross-disciplinary subject made up of two of the most exciting research areas: quantum computing and classical machine learning (ML), with ML and artificial intelligence (AI) being projected as the first fields that will be impacted by the rise of quantum machines. Quantum computers are being used today in drug discovery, material & molecular modelling and finance. In this work, we discuss some upcoming active new research areas in application of quantum machine learning (QML) in finance. We discuss certain QML models that has become areas of active interest in the financial world for various applications. We use real world financial dataset and compare models such as qGAN (quantum generative adversarial networks) and QCBM (quantum circuit Born machine) among others, using simulated environments. For the qGAN, we define quantum circuits for discriminators and generators and show promises of future quantum advantage via QML in finance.",,"S Ganguly - arXiv preprint arXiv:2308.08448, 2023 - arxiv.org",[],https://arxiv.org/abs/2308.08448,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2308.08448,['https://arxiv.org/pdf/2308.08448'],implementing quantum generative adversarial network qgan and qcbm in finance,MPS 生成/Born机 / 量子/混合LLM,1,,
Density matrix representation of hybrid tensor networks for noisy quantum devices,"H Harada, Y Suzuki, B Yang, Y Tokunaga, S Endo",2023.0,1,"The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.",,"H Harada, Y Suzuki, B Yang, Y Tokunaga, S Endo - Quantum 9, 1823 (2025)",[],https://arxiv.org/abs/2309.15761,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2309.15761,['https://arxiv.org/pdf/2309.15761'],density matrix representation of hybrid tensor networks for noisy quantum devices,TTN/MERA/PEPS,1,"Quantum 9, 1823 (2025)",
Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms,"A M Ali, I P Delgado, M R Roura, A M F d Leceta",2023.0,1,"We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and positive lineal entrywise sums, depending on the type of tensor network involved. The core of this method is the use of the norm of subnetworks of the tensor network in an iterative way, so that we normalize by the finite values of the norms that led to the divergence or zero norm. In addition, the method benefits from the reuse of intermediate calculations. We have also applied it to the Matrix Product State/Tensor Train (MPS/TT) and Matrix Product Operator/Tensor Train Matrix (MPO/TT-M) layers and have seen its scaling versus the number of nodes, bond dimension, and physical dimension. All code is publicly available.",,"A M Ali, I P Delgado, M R Roura, A M F d Leceta - arXiv preprint arXiv:2309.06577, 2023 - arxiv.org",[],https://arxiv.org/abs/2309.06577,arxiv-completion,2026-09-26 (citations:OpenAlex),,2309.06577,['https://arxiv.org/pdf/2309.06577'],efficient finite initialization with partial norms for tensorized neural networks and tensor networks algorithms,,1,,
Efficient Quantum Mixed-State Tomography with Unsupervised Tensor Network Machine Learning,"W Li, K Xu, H Fan, S Ran, G Su",2023.0,1,"Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In this work, we propose an efficient and robust mixed-state tomography scheme based on the locally purified state ansatz. We demonstrate the efficiency and robustness of our scheme on various randomly initiated states with different purities. High tomography fidelity is achieved with much smaller numbers of positive-operator-valued measurement (POVM) bases than the conventional least-square (LS) method. On the superconducting quantum experimental circuit [Phys. Rev. Lett. 119, 180511 (2017)], our scheme accurately reconstructs the Greenberger-Horne-Zeilinger (GHZ) state and exhibits robustness to experimental noises. Specifically, we achieve the fidelity $F \simeq 0.92$ for the 10-qubit GHZ state with just $N_m = 500$ POVM bases, which far outperforms the fidelity $F \simeq 0.85$ by the LS method using the full $N_m = 3^{10} = 59049$ bases. Our work reveals the prospects of applying tensor network state ansatz and the machine learning approaches for efficient QST of many-body states.",,"W Li, K Xu, H Fan, S Ran, G Su - arXiv preprint arXiv:2308.06900, 2023 - arxiv.org",[],https://arxiv.org/abs/2308.06900,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2308.06900,['https://arxiv.org/pdf/2308.06900'],efficient quantum mixed state tomography with unsupervised tensor network machine learning,MPS 生成/Born机,1,,
Intelligent diagnostic scheme for lung cancer screening with Raman spectra data by tensor network machine learning,"Y An, S Bai, L Cheng, X Li, C Wang, X Han, G Su, S Ran, C Wang",2023.0,1,"Artificial intelligence (AI) has brought tremendous impacts on biomedical sciences from academic researches to clinical applications, such as in biomarkers' detection and diagnosis, optimization of treatment, and identification of new therapeutic targets in drug discovery. However, the contemporary AI technologies, particularly deep machine learning (ML), severely suffer from non-interpretability, which might uncontrollably lead to incorrect predictions. Interpretability is particularly crucial to ML for clinical diagnosis as the consumers must gain necessary sense of security and trust from firm grounds or convincing interpretations. In this work, we propose a tensor-network (TN)-ML method to reliably predict lung cancer patients and their stages via screening Raman spectra data of Volatile organic compounds (VOCs) in exhaled breath, which are generally suitable as biomarkers and are considered to be an ideal way for non-invasive lung cancer screening. The prediction of TN-ML is based on the mutual distances of the breath samples mapped to the quantum Hilbert space. Thanks to the quantum probabilistic interpretation, the certainty of the predictions can be quantitatively characterized. The accuracy of the samples with high certainty is almost 100$\%$. The incorrectly-classified samples exhibit obviously lower certainty, and thus can be decipherably identified as anomalies, which will be handled by human experts to guarantee high reliability. Our work sheds light on shifting the ``AI for biomedical sciences'' from the conventional non-interpretable ML schemes to the interpretable human-ML interactive approaches, for the purpose of high accuracy and reliability.",,"Y An, S Bai, L Cheng, X Li, C Wang, X Han, G Su, S Ran, C Wang - arXiv preprint arXiv:2303.06340, 2023 - arxiv.org",[],https://arxiv.org/abs/2303.06340,arxiv-completion,2026-09-26 (citations:OpenAlex),,2303.06340,['https://arxiv.org/pdf/2303.06340'],intelligent diagnostic scheme for lung cancer screening with raman spectra data by tensor network machine learning,,1,,
TensorKrowch: Smooth integration of tensor networks in machine learning,"J R P Monturiol, D Pérez-García, A Pozas-Kerstjens",2023.0,1,"Tensor networks are factorizations of high-dimensional tensors into networks of smaller tensors. They have applications in physics and mathematics, and recently have been proposed as promising machine learning architectures. To ease the integration of tensor networks in machine learning pipelines, we introduce TensorKrowch, an open source Python library built on top of PyTorch. Providing a user-friendly interface, TensorKrowch allows users to construct any tensor network, train it, and integrate it as a layer in more intricate deep learning models. In this paper, we describe the main functionality and basic usage of TensorKrowch, and provide technical details on its building blocks and the optimizations performed to achieve efficient operation.",,"J R P Monturiol, D Pérez-García, A Pozas-Kerstjens - Quantum 8, 1364 (2024)",[],https://arxiv.org/abs/2306.08595,arxiv-completion,2026-09-26 (citations:OpenAlex),,2306.08595,['https://arxiv.org/pdf/2306.08595'],tensorkrowch smooth integration of tensor networks in machine learning,,2,"Quantum 8, 1364 (2024)",
Generative machine learning with tensor networks,M Molnar,2023.0,0,,ed6hv9xzUKQJ,M Molnar - 2023,[],,unknown,unknown,MPS 生成/Born机,,[],generative machine learning with tensor networks,MPS 生成/Born机,1,,
A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models,"M Hibat-Allah, M Mauri, J Carrasquilla, A Perdomo-Ortiz",2023.0,0,"Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over a proposed framework for evaluating the generalization performance of generative models, and we establish the first quantitative comparative race towards practical quantum advantage (PQA) between classical and quantum generative models, namely Quantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent Neural Networks (RNNs), Variational Autoencoders (VAEs), and Wasserstein Generative Adversarial Networks (WGANs). After defining four types of PQAs scenarios, we focus on what we refer to as potential PQA, aiming to compare quantum models with the best-known classical algorithms for the task at hand. We let the models race on a well-defined and application-relevant competition setting, where we illustrate and demonstrate our framework on 20 variables (qubits) generative modeling task. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models. Such a feature is highly desirable in a wide range of real-world applications where the available data is scarce.",,"M Hibat-Allah, M Mauri, J Carrasquilla, A Perdomo-Ortiz - Communications Physics volume 7, Article number: 68 (2024)",[],https://arxiv.org/abs/2303.15626,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2303.15626,['https://arxiv.org/pdf/2303.15626'],a framework for demonstrating practical quantum advantage racing quantum against classical generative models,张量化Transformer / MPS 生成/Born机 / 量子/混合LLM / MPS/序列建模,1,"Communications Physics volume 7, Article number: 68 (2024)",
Fast gradient-free activation maximization for neurons in spiking neural networks,"N Pospelov, A Chertkov, M Beketov, I Oseledets, K Anokhin",2023.0,0,"Elements of neural networks, both biological and artificial, can be described by their selectivity for specific cognitive features. Understanding these features is important for understanding the inner workings of neural networks. For a living system, such as a neuron, whose response to a stimulus is unknown and not differentiable, the only way to reveal these features is through a feedback loop that exposes it to a large set of different stimuli. The properties of these stimuli should be varied iteratively in order to maximize the neuronal response. To utilize this feedback loop for a biological neural network, it is important to run it quickly and efficiently in order to reach the stimuli that maximizes certain neurons' activation with the least number of iterations possible. Here we present a framework with an efficient design for such a loop. We successfully tested it on an artificial spiking neural network (SNN), which is a model that simulates the asynchronous spiking activity of neurons in living brains. Our optimization method for activation maximization is based on the low-rank Tensor Train decomposition of the discrete activation function. The optimization space is the latent parameter space of images generated by SN-GAN or VQ-VAE generative models. To our knowledge, this is the first time that effective AM has been applied to SNNs. We track changes in the optimal stimuli for artificial neurons during training and show that highly selective neurons can form already in the early epochs of training and in the early layers of a convolutional spiking network. This formation of refined optimal stimuli is associated with an increase in classification accuracy. Some neurons, especially in the deeper layers, may gradually change the concepts they are selective for during learning, potentially explaining their importance for model performance.",,"N Pospelov, A Chertkov, M Beketov, I Oseledets, K Anokhin - arXiv preprint arXiv:2401.10748, 2023 - arxiv.org",[],https://arxiv.org/abs/2401.10748,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2401.10748,['https://arxiv.org/pdf/2401.10748'],fast gradient free activation maximization for neurons in spiking neural networks,MPO/TT 压缩 / MPS 生成/Born机,1,,
"On Model Compression for Neural Networks: Framework, Algorithm, and Convergence Guarantee","C Li, J Chung, M Du, H Wang, X Zhou, B Shen",2023.0,0,"Model compression is a crucial part of deploying neural networks (NNs), especially when the memory and storage of computing devices are limited in many applications. This paper focuses on two model compression techniques: low-rank approximation and weight pruning in neural networks, which are very popular nowadays. However, training NN with low-rank approximation and weight pruning always suffers significant accuracy loss and convergence issues. In this paper, a holistic framework is proposed for model compression from a novel perspective of nonconvex optimization by designing an appropriate objective function. Then, we introduce NN-BCD, a block coordinate descent (BCD) algorithm to solve the nonconvex optimization. One advantage of our algorithm is that an efficient iteration scheme can be derived with closed-form, which is gradient-free. Therefore, our algorithm will not suffer from vanishing/exploding gradient problems. Furthermore, with the Kurdyka-Łojasiewicz (KŁ) property of our objective function, we show that our algorithm globally converges to a critical point at the rate of O(1/k), where k denotes the number of iterations. Lastly, extensive experiments with tensor train decomposition and weight pruning demonstrate the efficiency and superior performance of the proposed framework. Our code implementation is available at https://github.com/ChenyangLi-97/NN-BCD",,"C Li, J Chung, M Du, H Wang, X Zhou, B Shen - arXiv preprint arXiv:2303.06815, 2023 - arxiv.org",[],https://arxiv.org/abs/2303.06815,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2303.06815,['https://arxiv.org/pdf/2303.06815'],on model compression for neural networks framework algorithm and convergence guarantee,MPO/TT 压缩 / 量子启发综述,1,,
Quantum Generative Modeling using Parameterized Quantum Circuits,S Sarkar,2023.0,0,"Quantum generative models use the intrinsic probabilistic nature of quantum mechanics to learn and reproduce complex probability distributions. In this paper, we present an implementation of a 3-qubit quantum circuit Born machine trained to model a 3-bit Gaussian distribution using a Kullback-Leibler (KL) divergence loss and parameter-shift gradient optimization. The variational quantum circuit consists of layers of parameterized rotations and entangling gates, and is optimized such that the Born rule output distribution closely matches the target distribution. We detail the mathematical formulation of the model distribution, the KL divergence cost function, and the parameter-shift rule for gradient evaluation. Training results on a statevector simulator show that the KL divergence is minimized to near zero, and the final generated distribution aligns quantitatively with the target probabilities. We analyze the convergence behavior and discuss the implications for scalability and quantum advantage. Our results demonstrate the feasibility of small-scale quantum generative learning and provide insight into the training dynamics of quantum circuit models.",,"S Sarkar - arXiv preprint arXiv:2303.16955, 2023 - arxiv.org",[],https://arxiv.org/abs/2303.16955,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2303.16955,['https://arxiv.org/pdf/2303.16955'],quantum generative modeling using parameterized quantum circuits,MPS 生成/Born机,1,,
Quantum-Inspired Machine Learning: a Survey,"L Huynh, J Hong, A Mian, H Suzuki, Y Wu, S Camtepe",2023.0,,"Quantum-inspired Machine Learning (QiML) is a burgeoning field, receiving global attention from researchers for its potential to leverage principles of quantum mechanics within classical computational frameworks. However, current review literature often presents a superficial exploration of QiML, focusing instead on the broader Quantum Machine Learning (QML) field. In response to this gap, this survey provides an integrated and comprehensive examination of QiML, exploring QiML's diverse research domains including tensor network simulations, dequantized algorithms, and others, showcasing recent advancements, practical applications, and illuminating potential future research avenues. Further, a concrete definition of QiML is established by analyzing various prior interpretations of the term and their inherent ambiguities. As QiML continues to evolve, we anticipate a wealth of future developments drawing from quantum mechanics, quantum computing, and classical machine learning, enriching the field further. This survey serves as a guide for researchers and practitioners alike, providing a holistic understanding of QiML's current landscape and future directions.",,"L Huynh, J Hong, A Mian, H Suzuki, Y Wu, S Camtepe - arXiv preprint arXiv:2308.11269, 2023 - arxiv.org",[],https://arxiv.org/abs/2308.11269,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2308.11269,['https://arxiv.org/pdf/2308.11269'],quantum inspired machine learning a survey,MPO/TT 压缩 / 量子/混合LLM / 量子启发综述,1,,
TensorCodec: Compact Lossy Compression of Tensors without Strong Data Assumptions,"T Kwon, J Ko, J Jung, K Shin",2023.0,0,"Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor compression algorithms are available, many of them rely on strong data assumptions regarding its order, sparsity, rank, and smoothness. In this work, we propose TENSORCODEC, a lossy compression algorithm for general tensors that do not necessarily adhere to strong input data assumptions. TENSORCODEC incorporates three key ideas. The first idea is Neural Tensor-Train Decomposition (NTTD) where we integrate a recurrent neural network into Tensor-Train Decomposition to enhance its expressive power and alleviate the limitations imposed by the low-rank assumption. Another idea is to fold the input tensor into a higher-order tensor to reduce the space required by NTTD. Finally, the mode indices of the input tensor are reordered to reveal patterns that can be exploited by NTTD for improved approximation. Our analysis and experiments on 8 real-world datasets demonstrate that TENSORCODEC is (a) Concise: it gives up to 7.38x more compact compression than the best competitor with similar reconstruction error, (b) Accurate: given the same budget for compressed size, it yields up to 3.33x more accurate reconstruction than the best competitor, (c) Scalable: its empirical compression time is linear in the number of tensor entries, and it reconstructs each entry in logarithmic time. Our code and datasets are available at https://github.com/kbrother/TensorCodec.",,"T Kwon, J Ko, J Jung, K Shin - arXiv preprint arXiv:2309.10310, 2023 - arxiv.org",[],https://arxiv.org/abs/2309.10310,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2309.10310,['https://arxiv.org/pdf/2309.10310'],tensorcodec compact lossy compression of tensors without strong data assumptions,MPO/TT 压缩 / MPS/序列建模,1,,
Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Quantum Data Loading,"C Li, H Cheng",2023.0,0,"Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups often predicated on access to an efficient data-loading oracle. In practice, constructing a circuit to prepare a generic $n$-qubit quantum state typically demands computational efforts scaling as $\mathcal{O}(2^n)$, posing a significant challenge for quantum algorithms to outperform their classical counterparts. To address this critical issue, various hybrid quantum-classical approaches have been proposed. However, many of these solutions favor simplistic circuit architectures, which are susceptible to substantial optimization challenges. In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we propose a framework called Adaptive Circuit Learning of Born Machine, which dynamically expands the ansatz circuit. Our algorithm is designed to selectively integrate two-qubit entangled gates that best capture the intricate entanglement present within the target state. Empirical experiments underscore the efficacy of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by prior research.",,"C Li, H Cheng - Quantum Science and Technology, 10(2):025019, 2025",[],https://arxiv.org/abs/2311.17798,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2311.17798,['https://arxiv.org/pdf/2311.17798'],adaptive circuit learning of born machine towards realization of amplitude embedding and quantum data loading,MPS 生成/Born机,1,"Quantum Science and Technology, 10(2):025019, 2025",
Deep Ising Born Machine,Z Cao,2023.0,0,"A quantum neural network (QNN) is a method to find patterns in quantum data and has a wide range of applications including quantum chemistry, quantum computation, quantum metrology, and quantum simulation. Efficiency and universality are two desirable properties of a QNN but are unfortunately contradictory. In this work, we examine a deep Ising Born machine (DIBoM), and show it has a good balance between efficiency and universality. More precisely, the DIBoM has a flexible number of parameters to be efficient, and achieves provable universality with sufficient parameters. The architecture of the DIBoM is based on generalized controlled-Z gates, conditional gates, and some other ingredients. To compare the universality of the DIBoM with other QNNs, we propose a fidelity-based expressivity measure, which may be of independent interest. Extensive empirical evaluations corroborate that the DIBoM is both efficient and expressive.",,"Z Cao - arXiv preprint arXiv:2304.03606, 2023 - arxiv.org",[],https://arxiv.org/abs/2304.03606,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2304.03606,['https://arxiv.org/pdf/2304.03606'],deep ising born machine,MPS 生成/Born机 / 量子/混合LLM,1,,
Deep Tensor Network,Y Zhang,2023.0,0,"The quadratic complexity of dot-product attention introduced in Transformer remains a fundamental bottleneck impeding the progress of foundation models toward unbounded context lengths. Addressing this challenge, we introduce the Deep Tensor Network, a new architectural framework that fundamentally reformulates attention by unifying the expressive power of tensor algebra with neural network design. Our approach moves beyond both conventional dot-product attention and subsequent linear-time approximations to capture higher-order statistical dependencies. We introduce two core operators derived from this framework: \emph{Tensor Attention}, which models complex token-mixing via data-dependent polynomial kernels, and Tensor Interaction, a novel mechanism for adaptive channel-mixing. We demonstrate that these operators are powered by second-order summaries that entirely bypass the formation of $n \times n$ matrices, enabling a causality-preserving streaming implementation with $O(d^2)$ per-token updates and $O(d^2)$ state. This efficiency rivals that of modern State Space Models while retaining an attention-like formulation. The Deep Tensor Network thus provides a principled and powerful new class of building blocks for next-generation sequence models, bridging the gap between scalable computation and rich, expressive interaction modeling.",,"Y Zhang - arXiv preprint arXiv:2311.11091, 2023 - arxiv.org",[],https://arxiv.org/abs/2311.11091,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2311.11091,['https://arxiv.org/pdf/2311.11091'],deep tensor network,MPS 语言模型 / 张量化Transformer / MPS/序列建模,1,,
Dequantizing quantum machine learning models using tensor networks,"S Shin, Y S Teo, H Jeong",2023.0,0,"Ascertaining whether a classical model can efficiently replace a given quantum model -- dequantization -- is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning~(VQML) models by employing the tensor network formalism, effectively identifying every VQML model as a subclass of matrix product state (MPS) model characterized by constrained coefficient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model's function class is dequantizable or not. Furthermore, we introduce an efficient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework.",,"S Shin, Y S Teo, H Jeong - Phys. Rev. Res. 6(2) 2024 023218",[],https://arxiv.org/abs/2307.06937,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2307.06937,['https://arxiv.org/pdf/2307.06937'],dequantizing quantum machine learning models using tensor networks,MPO/TT 压缩 / 量子/混合LLM,1,Phys. Rev. Res. 6(2) 2024 023218,
Derivation of Hamiltonians from time propagations using Born machines,"H Wakaura, A B Suksmono",2023.0,0,Recently there are more promising qubit technology such as Majorana fermions Rydberg atoms and Silicon quantum dot have yet to be developed for realizing a quantum computer than Superconductivity and Ion trap into the world The simulation of the quantum hardware of these qubits can only be done numerically However a classical numerical simulation is limited concerning available resources The method for simulation of quantum hardware by quantum hardware may be necessary In this paper we propose a novel method for optimizing time propagation from initial states to aimed given states of systems by the Born machine We call this method the Hamiltonian Engineering Born Machine HEBM We calculated the optimal Hamiltonians for propagation to Bars and Stripes distribution Gaussian distribution and Gibbs state for $H=-\Sum Z_j Z_{j+1}$ and revealed that they can be realized rapidly and accurately,,"H Wakaura, A B Suksmono - arXiv preprint arXiv:2312.16432, 2023 - arxiv.org",[],https://arxiv.org/abs/2312.16432,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2312.16432,['https://arxiv.org/pdf/2312.16432'],derivation of hamiltonians from time propagations using born machines,MPS 生成/Born机,1,,
Efficient tensor-network simulation for the few-atom multimode Dicke model via coupling-matrix transformation,"C J Ryu, D Na, W C Chew, E Kudeki",2023.0,0,"We present a novel generalization of the chain mapping technique that applies to multi-atom, multimode systems by making use of coupling matrix transformations. This is extremely useful for tensor network simulations of multimode Dicke model and multi-spin-boson model because their coupling structures are altered from the star form to the chain form with near-neighbor interactions. Our approach produces an equivalent Hamiltonian with the latter coupling form, which we call the band Hamiltonian, and we demonstrate its equivalence to the multimode Dicke Hamiltonian. In the single atom case, our approach reduces to the chain mapping technique. When considering several tens of field modes, we have found that tensor network simulation of two atoms in the ultrastrong coupling regime is possible with our approach. We demonstrate this by considering a pair of entangled atoms confined in a cavity, interacting with thirty electromagnetic modes.",,"C J Ryu, D Na, W C Chew, E Kudeki - Phys. Rev. A 108, 043707 (2023)",[],https://arxiv.org/abs/2305.03160,arxiv-completion,2026-09-26 (citations:OpenAlex),,2305.03160,['https://arxiv.org/pdf/2305.03160'],efficient tensor network simulation for the few atom multimode dicke model via coupling matrix transformation,,1,"Phys. Rev. A 108, 043707 (2023)",
Hardness of Low Rank Approximation of Entrywise Transformed Matrix Products,"T Sarlos, X Song, D Woodruff, Qiuyi, Zhang",2023.0,0,"Inspired by fast algorithms in natural language processing, we study low rank approximation in the entrywise transformed setting where we want to find a good rank $k$ approximation to $f(U \cdot V)$, where $U, V^\top \in \mathbb{R}^{n \times r}$ are given, $r = O(\log(n))$, and $f(x)$ is a general scalar function. Previous work in sublinear low rank approximation has shown that if both (1) $U = V^\top$ and (2) $f(x)$ is a PSD kernel function, then there is an $O(nk^{ω-1})$ time constant relative error approximation algorithm, where $ω\approx 2.376$ is the exponent of matrix multiplication. We give the first conditional time hardness results for this problem, demonstrating that both conditions (1) and (2) are in fact necessary for getting better than $n^{2-o(1)}$ time for a relative error low rank approximation for a wide class of functions. We give novel reductions from the Strong Exponential Time Hypothesis (SETH) that rely on lower bounding the leverage scores of flat sparse vectors and hold even when the rank of the transformed matrix $f(UV)$ and the target rank are $n^{o(1)}$, and when $U = V^\top$. Furthermore, even when $f(x) = x^p$ is a simple polynomial, we give runtime lower bounds in the case when $U \neq V^\top$ of the form $Ω(\min(n^{2-o(1)}, Ω(2^p)))$. Lastly, we demonstrate that our lower bounds are tight by giving an $O(n \cdot \text{poly}(k, 2^p, 1/ε))$ time relative error approximation algorithm and a fast $O(n \cdot \text{poly}(k, p, 1/ε))$ additive error approximation using fast tensor-based sketching. Additionally, since our low rank algorithms rely on matrix-vector product subroutines, our lower bounds extend to show that computing $f(UV)W$, for even a small matrix $W$, requires $Ω(n^{2-o(1)})$ time.",,"T Sarlos, X Song, D Woodruff, Qiuyi, Zhang - arXiv preprint arXiv:2311.01960, 2023 - arxiv.org",[],https://arxiv.org/abs/2311.01960,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2311.01960,['https://arxiv.org/pdf/2311.01960'],hardness of low rank approximation of entrywise transformed matrix products,MPS 语言模型,1,,
Identifying overparameterization in Quantum Circuit Born Machines,"A Delgado, F Rios, K E Hamilton",2023.0,0,"In machine learning, overparameterization is associated with qualitative changes in the empirical risk landscape, which can lead to more efficient training dynamics. For many parameterized models used in statistical learning, there exists a critical number of parameters, or model size, above which the model is constructed and trained in the overparameterized regime. There are many characteristics of overparameterized loss landscapes. The most significant is the convergence of standard gradient descent to global or local minima of low loss. In this work, we study the onset of overparameterization transitions for quantum circuit Born machines, generative models that are trained using non-adversarial gradient-based methods. We observe that bounds based on numerical analysis are in general good lower bounds on the overparameterization transition. However, bounds based on the quantum circuit's algebraic structure are very loose upper bounds. Our results indicate that fully understanding the trainability of these models remains an open question.",,"A Delgado, F Rios, K E Hamilton - arXiv preprint arXiv:2307.03292, 2023 - arxiv.org",[],https://arxiv.org/abs/2307.03292,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2307.03292,['https://arxiv.org/pdf/2307.03292'],identifying overparameterization in quantum circuit born machines,MPS 生成/Born机,1,,
Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits,"J Qi, C H Yang, P Chen, M Hsieh",2023.0,,"Data encoding remains a fundamental bottleneck in quantum machine learning, where amplitude encoding of high-dimensional classical vectors into quantum states incurs exponential cost. In this work, we propose a pre-trained tensor-train (TT) encoding network (Pre-TT-Encoder) that significantly reduces the computational complexity of amplitude encoding while preserving essential data structure. The Pre-TT-Encoder exploits low-rank TT decompositions learned from classical data, enabling polynomial-time state preparation in the number of qubits and TT-ranks. We provide a theoretical analysis of the encoding complexity and establish fidelity bounds that quantify the trade-off between TT-rank and approximation error. Empirical evaluations on classical (MNIST) and quantum-native (semiconductor quantum dot) datasets demonstrate that our approach achieves substantial gains in encoding efficiency over direct amplitude encoding and PCA-based dimensionality reduction, while maintaining competitive performance in downstream variational quantum circuit classification tasks. The proposed method highlights the role of tensor networks as scalable intermediaries between classical data and quantum processors.",,"J Qi, C H Yang, P Chen, M Hsieh - arXiv preprint arXiv:2306.03741, 2023 - arxiv.org",[],https://arxiv.org/abs/2306.03741,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2306.03741,['https://arxiv.org/pdf/2306.03741'],pre training tensor train networks facilitates machine learning with variational quantum circuits,MPO/TT 压缩 / 量子/混合LLM,1,,
"Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks","M Niedermeier, J L Lado, C Flindt",2023.0,0,"Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in practice, the available entanglement may be limited, leading to a reduced fidelity of the quantum algorithms. To simulate the execution of quantum algorithms with limited entanglement, tensor-network methods provide a useful framework, since they allow us to restrict the entanglement in a quantum circuit. Thus, we here use tensor-networks to analyze the fidelity of the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm as the entanglement is reduced, and we map out the entanglement that is generated during the execution of each algorithm. In all three cases, we find that the algorithms can be executed with high fidelity even if the entanglement is somewhat reduced. Our results are promising for the execution of these algorithms on future quantum computers, and our simulation method based on tensor networks may also be applied to other quantum algorithms.",,"M Niedermeier, J L Lado, C Flindt - Phys. Rev. Research 6, 033325 (2024)",[],https://arxiv.org/abs/2304.01751,arxiv-completion,2026-09-26 (citations:OpenAlex),,2304.01751,['https://arxiv.org/pdf/2304.01751'],simulating the quantum fourier transform grover s algorithm and the quantum counting algorithm with limited entanglement using tensor networks,,1,"Phys. Rev. Research 6, 033325 (2024)",
TT-SDF2PC: Registration of Point Cloud and Compressed SDF Directly in the Memory-Efficient Tensor Train Domain,"A I Boyko, A Kornilova, R Tariverdizadeh, M Musavian, L Markeeva, I Oseledets, G Ferrer",2023.0,0,"This paper addresses the following research question: ``can one compress a detailed 3D representation and use it directly for point cloud registration?''. Map compression of the scene can be achieved by the tensor train (TT) decomposition of the signed distance function (SDF) representation. It regulates the amount of data reduced by the so-called TT-ranks. Using this representation we have proposed an algorithm, the TT-SDF2PC, that is capable of directly registering a PC to the compressed SDF by making use of efficient calculations of its derivatives in the TT domain, saving computations and memory. We compare TT-SDF2PC with SOTA local and global registration methods in a synthetic dataset and a real dataset and show on par performance while requiring significantly less resources.",,"A I Boyko, A Kornilova, R Tariverdizadeh, M Musavian, L Markeeva, I Oseledets, G Ferrer - arXiv preprint arXiv:2304.05342, 2023 - arxiv.org",[],https://arxiv.org/abs/2304.05342,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2304.05342,['https://arxiv.org/pdf/2304.05342'],tt sdf2pc registration of point cloud and compressed sdf directly in the memory efficient tensor train domain,MPO/TT 压缩,1,,
Tensor Train Decomposition for Adversarial Attacks on Computer Vision Models,"A Chertkov, I Oseledets",2023.0,0,"Deep neural networks (DNNs) are widely used today, but they are vulnerable to adversarial attacks. To develop effective methods of defense, it is important to understand the potential weak spots of DNNs. Often attacks are organized taking into account the architecture of models (white-box approach) and based on gradient methods, but for real-world DNNs this approach in most cases is impossible. At the same time, several gradient-free optimization algorithms are used to attack black-box models. However, classical methods are often ineffective in the multidimensional case. To organize black-box attacks for computer vision models, in this work, we propose the use of an optimizer based on the low-rank tensor train (TT) format, which has gained popularity in various practical multidimensional applications in recent years. Combined with the attribution of the target image, which is built by the auxiliary (white-box) model, the TT-based optimization method makes it possible to organize an effective black-box attack by small perturbation of pixels in the target image. The superiority of the proposed approach over three popular baselines is demonstrated for seven modern DNNs on the ImageNet dataset.",,"A Chertkov, I Oseledets - arXiv preprint arXiv:2312.12556, 2023 - arxiv.org",[],https://arxiv.org/abs/2312.12556,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2312.12556,['https://arxiv.org/pdf/2312.12556'],tensor train decomposition for adversarial attacks on computer vision models,MPO/TT 压缩,1,,
Efficient GPT Model Pre-training using Tensor Train Matrix Representation,"V Chekalina, G Novikov, J Gusak, I Oseledets, A Panchenko",2023.0,,"Large-scale transformer models have shown remarkable performance in language modelling tasks. However, such models feature billions of parameters, leading to difficulties in their deployment and prohibitive training costs from scratch. To reduce the number of the parameters in the GPT-2 architecture, we replace the matrices of fully-connected layers with the corresponding Tensor Train Matrix~(TTM) structure. Finally, we customize forward and backward operations through the TTM-based layer for simplicity and the stableness of further training. % The resulting GPT-2-based model stores up to 40% fewer parameters, showing the perplexity comparable to the original model. On the downstream tasks, including language understanding and text summarization, the model performs similarly to the original GPT-2 model. The proposed tensorized layers could be used to efficiently pre-training other Transformer models.",,"V Chekalina, G Novikov, J Gusak, I Oseledets, A Panchenko - arXiv preprint arXiv:2306.02697, 2023 - arxiv.org",[],https://arxiv.org/abs/2306.02697,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2306.02697,['https://arxiv.org/pdf/2306.02697'],efficient gpt model pre training using tensor train matrix representation,MPS 语言模型 / 张量化Transformer,1,,
ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation,"Z Chen, L Newhouse, E Chen, D Luo, M Soljačić",2023.0,,"Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.",,"Z Chen, L Newhouse, E Chen, D Luo, M Soljačić - arXiv preprint arXiv:2304.01996, 2023 - arxiv.org",[],https://arxiv.org/abs/2304.01996,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2304.01996,['https://arxiv.org/pdf/2304.01996'],antn bridging autoregressive neural networks and tensor networks for quantum many body simulation,MPS 生成/Born机 / MPS/序列建模,1,,
Reusing Pretrained Models by Multi-linear Operators for Efficient Training,"Y Pan, Y Yuan, Y Yin, Z Xu, L Shang, X Jiang, Q Liu",2023.0,,"Training large models from scratch usually costs a substantial amount of resources. Towards this problem, recent studies such as bert2BERT and LiGO have reused small pretrained models to initialize a large model (termed the ``target model''), leading to a considerable acceleration in training. Despite the successes of these previous studies, they grew pretrained models by mapping partial weights only, ignoring potential correlations across the entire model. As we show in this paper, there are inter- and intra-interactions among the weights of both the pretrained and the target models. As a result, the partial mapping may not capture the complete information and lead to inadequate growth. In this paper, we propose a method that linearly correlates each weight of the target model to all the weights of the pretrained model to further enhance acceleration ability. We utilize multi-linear operators to reduce computational and spacial complexity, enabling acceptable resource requirements. Experiments demonstrate that our method can save 76\% computational costs on DeiT-base transferred from DeiT-small, which outperforms bert2BERT by +12.0\% and LiGO by +20.7\%, respectively.",,"Y Pan, Y Yuan, Y Yin, Z Xu, L Shang, X Jiang, Q Liu - arXiv preprint arXiv:2310.10699, 2023 - arxiv.org",[],https://arxiv.org/abs/2310.10699,arxiv-completion,2026-09-26 (citations:OpenAlex),,2310.10699,['https://arxiv.org/pdf/2310.10699'],reusing pretrained models by multi linear operators for efficient training,,1,,
A survey on model compression for large language models,"X Zhu, J Li, Y Liu, C Ma, W Wang",2024.0,844,"Abstract Large Language Models (LLMs) have transformed natural language processing tasks successfully. Yet, their large size and high computational needs pose challenges for practical use, especially in resource-limited settings. Model compression has emerged as a key research area to address these challenges. This paper presents a survey of model compression techniques for LLMs. We cover methods like quantization, pruning, and knowledge distillation, highlighting recent advancements. We also discuss benchmarking strategies and evaluation metrics crucial for assessing compressed LLMs. This survey offers valuable insights for researchers and practitioners, aiming to enhance efficiency and real-world applicability of LLMs while laying a foundation for future advancements.",hy-dUbcYbhoJ,"X Zhu, J Li, Y Liu, C Ma, W Wang - Transactions of the Association for …, 2024 - direct.mit.edu",['https://direct.mit.edu/tacl/article-pdf/doi/10.1162/tacl_a_00704/2482209/tacl_a_00704.pdf'],https://direct.mit.edu/tacl/article/doi/10.1162/tacl_a_00704/125482,unknown,unknown,MPO/TT 压缩,2308.07633,['https://direct.mit.edu/tacl/article-pdf/doi/10.1162/tacl_a_00704/2482209/tacl_a_00704.pdf'],a survey on model compression for large language models,MPO/TT 压缩,1,Transactions of the Association for Computational Linguistics,
Decomposition of matrix product states into shallow quantum circuits,"MS Rudolph, J Chen, J Miller, A Acharya…",2024.0,139,"Abstract Tensor networks (TNs) are a family of computational methods built on graph-structured factorizations of large tensors, which have long represented state-of-the-art methods for the approximate simulation of complex quantum systems on classical computers. The rapid pace of recent advancements in numerical computation, notably the rise of GPU and TPU hardware accelerators, have allowed TN algorithms to scale to even larger quantum simulation problems, and to be employed more broadly for solving machine learning tasks. The ‘quantum-inspired’ nature of TNs permits them to be mapped to parametrized quantum circuits (PQCs), a fact which has inspired recent proposals for enhancing the performance of TN algorithms using near-term quantum devices, as well as enabling joint quantum–classical training frameworks that benefit from the distinct strengths of TN and PQC models. However, the success of any such methods depends on efficient and accurate methods for approximating TN states using realistic quantum circuits, which remains an unresolved question. This work compares a range of novel and previously-developed algorithmic protocols for decomposing matrix product states (MPS) of arbitrary bond dimension into low-depth quantum circuits consisting of stacked linear layers of two-qubit unitaries. These protocols are formed from different combinations of a preexisting analytical decomposition method together with constrained optimization of circuit unitaries, with initialization by the former method helping to avoid poor-quality local minima in the latter optimization process. While all of these protocols have efficient classical runtimes, our experimental results reveal one particular protocol employing sequential growth and optimization of the quantum circuit to outperform all others, with even greater benefits in the setting of limited computational resources. Given these promising results, we expect our proposed decomposition protocol to form a useful ingredient within any joint application of TNs and PQCs, further unlocking the rich and complementary benefits of classical and quantum computation.",FbctYqK40LQJ,"MS Rudolph, J Chen, J Miller, A Acharya… - Quantum Science …, 2024 - iopscience.iop.org",['https://arxiv.org/pdf/2209.00595'],https://iopscience.iop.org/article/10.1088/2058-9565/ad04e6/meta,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/2209.00595'],decomposition of matrix product states into shallow quantum circuits,MPS 语言模型,1,Quantum Science and Technology,
Model compression and efficient inference for large language models: A survey,"W Wang, W Chen, Y Luo, Y Long, Z Lin…",2024.0,137,"Transformer based large language models have achieved tremendous success. However, the significant memory and computational costs incurred during the inference process make it challenging to deploy large models on resource-constrained devices. In this paper, we investigate compression and efficient inference methods for large language models from an algorithmic perspective. Regarding taxonomy, similar to smaller models, compression and acceleration algorithms for large language models can still be categorized into quantization, pruning, distillation, compact architecture design, dynamic networks. However, Large language models have two prominent characteristics compared to smaller models: (1) Most of compression algorithms require finetuning or even retraining the model after compression. The most notable aspect of large models is the very high cost associated with model finetuning or training. Therefore, many algorithms for large models, such as quantization and pruning, start to explore tuning-free algorithms. (2) Large models emphasize versatility and generalization rather than performance on a single task. Hence, many algorithms, such as knowledge distillation, focus on how to preserving their versatility and generalization after compression. Since these two characteristics were not very pronounced in early large models, we further distinguish large language models into medium models and ``real'' large models. Additionally, we also provide an introduction to some mature frameworks for efficient inference of large models, which can support basic compression or acceleration algorithms, greatly facilitating model deployment for users.",KdnkYWkKlUAJ,"W Wang, W Chen, Y Luo, Y Long, Z Lin… - arXiv preprint arXiv …, 2024 - arxiv.org",['https://arxiv.org/pdf/2402.09748'],https://arxiv.org/abs/2402.09748,unknown,unknown,MPO/TT 压缩,2402.09748,['https://arxiv.org/pdf/2402.09748'],model compression and efficient inference for large language models a survey,MPO/TT 压缩,1,,
Hydra: Bidirectional state space models through generalized matrix mixers,"S Hwang, A Lahoti, R Puduppully…",2024.0,68,"… In particular, we introduce Vandermonde and Cauchy matrix … matrix multiplication, hence are efficient as sequence models, … We pretrain our models on the masked language modeling …",J-nhuNaAhFwJ,"S Hwang, A Lahoti, R Puduppully… - Advances in Neural …, 2024 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2024/file/c7f795dc3b4eb6ae630695d90001a2f8-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2024/hash/c7f795dc3b4eb6ae630695d90001a2f8-Abstract-Conference.html,unknown,unknown,MPS 语言模型,2407.09941,['https://proceedings.neurips.cc/paper_files/paper/2024/file/c7f795dc3b4eb6ae630695d90001a2f8-Paper-Conference.pdf'],hydra bidirectional state space models through generalized matrix mixers,MPS 语言模型,1,,
Tensor attention training: Provably efficient learning of higher-order transformers,"Y Liang, Z Shi, Z Song, Y Zhou",2024.0,65,… Let X ∈ Rd×d×d be the tensorization of X ∈ Rd×d2 … Multiverse recommendation: n-dimensional tensor factorization for context-aware collaborative filtering. In Proceedings of the fourth …,Q2MBkD1PUK4J,"Y Liang, Z Shi, Z Song, Y Zhou - 2024 - openreview.net",['https://openreview.net/pdf?id=HtS2NUcqtD'],https://openreview.net/forum?id=HtS2NUcqtD,unknown,unknown,张量化Transformer,,['https://openreview.net/pdf?id=HtS2NUcqtD'],tensor attention training provably efficient learning of higher order transformers,张量化Transformer,1,,
Transition role of entangled data in quantum machine learning,"X Wang, Y Du, Z Tu, Y Luo, X Yuan, D Tao",2024.0,43,"Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.",HRk2VKHqN6cJ,"X Wang, Y Du, Z Tu, Y Luo, X Yuan, D Tao - Nature Communications, 2024 - nature.com",['https://www.nature.com/articles/s41467-024-47983-1.pdf'],https://www.nature.com/articles/s41467-024-47983-1,unknown,unknown,TTN/MERA/PEPS,2306.03481,['https://www.nature.com/articles/s41467-024-47983-1.pdf'],transition role of entangled data in quantum machine learning,TTN/MERA/PEPS,1,Nature Communications,
A neural matrix decomposition recommender system model based on the multimodal large language model,"A Xiang, B Huang, X Guo, H Yang…",2024.0,42,"Recommendation systems have become an important solution to information search problems. This article proposes a neural matrix factorization recommendation system model based on the multimodal large language model called BoNMF. This model combines BoBERTa's powerful capabilities in natural language processing, ViT in computer in vision, and neural matrix decomposition technology. By capturing the potential characteristics of users and items, and after interacting with a low-dimensional matrix composed of user and item IDs, the neural network outputs the results. recommend. Cold start and ablation experimental results show that the BoNMF model exhibits excellent performance on large public data sets and significantly improves the accuracy of recommendations.",WWFHotBs434J,"A Xiang, B Huang, X Guo, H Yang… - Proceedings of the 2024 …, 2024 - dl.acm.org",['https://dl.acm.org/doi/pdf/10.1145/3696271.3696295'],https://dl.acm.org/doi/abs/10.1145/3696271.3696295,unknown,unknown,MPS 语言模型,,['https://dl.acm.org/doi/pdf/10.1145/3696271.3696295'],a neural matrix decomposition recommender system model based on the multimodal large language model,MPS 语言模型,1,,
Temporal entanglement entropy as a probe of renormalization group flow,"S Grieninger, K Ikeda, DE Kharzeev",2024.0,41,"… of timelike entanglement entropy to Euclidean space (“temporal … entanglement entropy to Euclidean space, and interpret the resulting “temporal EE” in terms of the renormalization group …",Ls-cdP7ad3wJ,"S Grieninger, K Ikeda, DE Kharzeev - Journal of High Energy Physics, 2024 - Springer",['https://link.springer.com/content/pdf/10.1007/JHEP05%282024%29030.pdf'],https://link.springer.com/article/10.1007/JHEP05(2024)030,unknown,unknown,互信息/标度,2312.08534,['https://link.springer.com/content/pdf/10.1007/JHEP05%282024%29030.pdf'],temporal entanglement entropy as a probe of renormalization group flow,互信息/标度,1,JHEP 05 (2024) 030,
Compactifai: extreme compression of large language models using quantum-inspired tensor networks,"A Tomut, SS Jahromi, A Sarkar, U Kurt, S Singh…",2024.0,37,"Large Language Models (LLMs) such as ChatGPT and LlaMA are advancing rapidly in generative Artificial Intelligence (AI), but their immense size poses significant challenges, such as huge training and inference costs, substantial energy demands, and limitations for on-site deployment. Traditional compression methods such as pruning, distillation, and low-rank approximation focus on reducing the effective number of neurons in the network, while quantization focuses on reducing the numerical precision of individual weights to reduce the model size while keeping the number of neurons fixed. While these compression methods have been relatively successful in practice, there is no compelling reason to believe that truncating the number of neurons is an optimal strategy. In this context, this paper introduces CompactifAI, an innovative LLM compression approach using quantum-inspired Tensor Networks that focuses on the model's correlation space instead, allowing for a more controlled, refined and interpretable model compression. Our method is versatile and can be implemented with - or on top of - other compression techniques. As a benchmark, we demonstrate that a combination of CompactifAI with quantization allows to reduce a 93% the memory size of LlaMA 7B, reducing also 70% the number of parameters, accelerating 50% the training and 25% the inference times of the model, and just with a small accuracy drop of 2% - 3%, going much beyond of what is achievable today by other compression techniques. Our methods also allow to perform a refined layer sensitivity profiling, showing that deeper layers tend to be more suitable for tensor network compression, which is compatible with recent observations on the ineffectiveness of those layers for LLM performance. Our results imply that standard LLMs are, in fact, heavily overparametrized, and do not need to be large at all.",0UJQgHwyUosJ,"A Tomut, SS Jahromi, A Sarkar, U Kurt, S Singh… - arXiv preprint arXiv …, 2024 - arxiv.org",['https://arxiv.org/pdf/2401.14109'],https://arxiv.org/abs/2401.14109,unknown,unknown,MPO/TT 压缩,2401.14109,['https://arxiv.org/pdf/2401.14109'],compactifai extreme compression of large language models using quantum inspired tensor networks,MPO/TT 压缩,1,"Proceedings of the 33rd European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2025), Bruges, Belgium, pp. 531-537, April 2025. ISBN: 9782875870926",
"Machine learning with tree tensor networks, CP rank constraints, and tensor dropout","H Chen, T Barthel",2024.0,36,"… The main contribution of this work is to improve tensornetwork machine learning by introducing … , the same logic applies for generative modeling and clustering problems [24], [43]–[52]. …",uycJhakC0jwJ,"H Chen, T Barthel - IEEE Transactions on Pattern Analysis and …, 2024 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2305.19440'],https://ieeexplore.ieee.org/abstract/document/10517663/,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2305.19440'],machine learning with tree tensor networks cp rank constraints and tensor dropout,TTN/MERA/PEPS,1,,
Tensor decomposition based attention module for spiking neural networks,"H Deng, R Zhu, X Qiu, Y Duan, M Zhang…",2024.0,31,"… of the tensor decomposition process to combine the three tensors into the attention map … , surpassing the existing SNN models with Transformer-based and CNN-based backbones. …",dH-KrROwmf0J,"H Deng, R Zhu, X Qiu, Y Duan, M Zhang… - Knowledge-Based …, 2024 - Elsevier",['https://arxiv.org/pdf/2310.14576'],https://www.sciencedirect.com/science/article/pii/S0950705124004143,unknown,unknown,张量化Transformer,,['https://arxiv.org/pdf/2310.14576'],tensor decomposition based attention module for spiking neural networks,张量化Transformer,1,,
Enabling tensor language model to assist in generating {High-Performance} tensor programs for deep learning,"Y Zhai, S Yang, K Pan, R Zhang, S Liu, C Liu…",2024.0,28,"… to represent tensor programs, bridging the gap between tensor programs and language models. • We develop a tensor language model that combines knowledge from offline learning …",9xBA2o4AT4YJ,"Y Zhai, S Yang, K Pan, R Zhang, S Liu, C Liu… - … USENIX Symposium on …, 2024 - usenix.org",['https://www.usenix.org/system/files/osdi24-zhai.pdf'],https://www.usenix.org/conference/osdi24/presentation/zhai,unknown,unknown,MPO/TT 压缩,,['https://www.usenix.org/system/files/osdi24-zhai.pdf'],enabling tensor language model to assist in generating high performance tensor programs for deep learning,MPO/TT 压缩,1,,
Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry,"J Gray, G K Chan",2024.0,28,"Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyperoptimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both handcrafted contraction strategies in the literature as well as recently proposed general contraction algorithms on a variety of synthetic and physical problems on regular lattices and random regular graphs. We further showcase the power of the approach by demonstrating approximate contraction of tensor networks for frustrated three-dimensional lattice partition functions, dimer counting on random regular graphs, and to access the hardness transition of random tensor network models, in graphs with many thousands of tensors. Published by the American Physical Society 2024",,"J Gray, G K Chan - Physical Review X, 2024",[],https://doi.org/10.1103/physrevx.14.011009,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,,[],hyperoptimized approximate contraction of tensor networks with arbitrary geometry,MPO/TT 压缩,1,Physical Review X,
Nuclear norm regularized loop optimization for tensor network,"K Homma, T Okubo, N Kawashima",2024.0,26,"… find that our method further improves the scale-invariance of the … Among them, we tried local entropy, or mutual information, … In the main text, we choose to penalize the nuclear norm of S[…",Ms17LbFk674J,"K Homma, T Okubo, N Kawashima - Physical Review Research, 2024 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.043102'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043102,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.043102'],nuclear norm regularized loop optimization for tensor network,互信息/标度,1,,
Quantum large language models via tensor network disentanglers,"B Aizpurua, SS Jahromi, S Singh, R Orus",2024.0,22,"We introduce a framework for seamlessly integrating quantum computing into pretrained large language models (LLMs). The key idea is to construct a hybrid quantum-classical representation that exactly reproduces the original model, providing a principled starting point from which quantum resources can only improve performance. Our approach replaces the weight matrices in self-attention and multilayer perceptron layers with two variational quantum circuits coupled to a matrix product operator (MPO). Tensor network disentanglers transfer much of each layer's information into the quantum circuits, enabling the remaining tensor network to be compressed to a bond-dimension-one MPO with over three orders of magnitude fewer classical parameters (in our experiments, from 110,592 to approximately 36 for the replaced layer) and less than a 0.3\% increase in perplexity. Training an added unitary adapter on top of this representation then surpasses the original model, reducing perplexity by up to 1.6\%. Finally, we validate the hybrid architecture on a real quantum processor, demonstrating a practical route towards quantum-enhanced language models.",v3CCFISlAd0J,"B Aizpurua, SS Jahromi, S Singh, R Orus - arXiv preprint arXiv …, 2024 - arxiv.org",['https://arxiv.org/pdf/2410.17397'],https://arxiv.org/abs/2410.17397,unknown,unknown,MPO/TT 压缩,2410.17397,['https://arxiv.org/pdf/2410.17397'],quantum large language models via tensor network disentanglers,MPO/TT 压缩 / 量子/混合LLM,2,arXiv (Cornell University),
Neural network compression based on tensor ring decomposition,"K Xie, C Liu, X Wang, X Li, G Xie…",2024.0,19,"… tensor ring (TR) factorization to compress the neural network. We investigate the impact of both parameter tensor … However, the tensor train (TT) model highly depends on permutations …",kUinIgKaLD0J,"K Xie, C Liu, X Wang, X Li, G Xie… - … on Neural Networks …, 2024 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/10510501/,unknown,unknown,MPO/TT 压缩,,[],neural network compression based on tensor ring decomposition,MPO/TT 压缩,1,,
Compressing multivariate functions with tree tensor networks,"J Tindall, EM Stoudenmire, R Levy",2024.0,17,"Tensor networks are a compressed format for multi-dimensional data. One dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum functions by ``quantizing'' the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks (TTNs) for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient ansatz than the commonly used tensor train. Finally, we demonstrate how the methods introduced in this work can be used to realize a TTN-based solver for multi-dimensional, non-linear Fredholm equations.",eGzvuYKM_hwJ,"J Tindall, EM Stoudenmire, R Levy - arXiv preprint arXiv:2410.03572, 2024 - arxiv.org",['https://arxiv.org/pdf/2410.03572'],https://arxiv.org/abs/2410.03572,unknown,unknown,互信息/标度,2410.03572,['https://arxiv.org/pdf/2410.03572'],compressing multivariate functions with tree tensor networks,互信息/标度,1,,
TNGPS: Discovering unknown tensor network structure search algorithms via large language models (LLMs),"J Zeng, C Li, Z Sun, Q Zhao, G Zhou",2024.0,17,"Tensor networks are efficient for extremely high-dimensional representation, but their model selection, known as tensor network structure search (TN-SS), is a challenging problem. Although several works have targeted TN-SS, most existing algorithms are manually crafted heuristics with poor performance, suffering from the curse of dimensionality and local convergence. In this work, we jump out of the box, studying how to harness large language models (LLMs) to automatically discover new TN-SS algorithms, replacing the involvement of human experts. By observing how human experts innovate in research, we model their common workflow and propose an automatic algorithm discovery framework called tnGPS. The proposed framework is an elaborate prompting pipeline that instruct LLMs to generate new TN-SS algorithms through iterative refinement and enhancement. The experimental results demonstrate that the algorithms discovered by tnGPS exhibit superior performance in benchmarks compared to the current state-of-the-art methods.",RsTFXL4ASiEJ,"J Zeng, C Li, Z Sun, Q Zhao, G Zhou - arXiv preprint arXiv:2402.02456, 2024 - arxiv.org",['https://arxiv.org/pdf/2402.02456'],https://arxiv.org/abs/2402.02456,unknown,unknown,MPO/TT 压缩,2402.02456,['https://arxiv.org/pdf/2402.02456'],tngps discovering unknown tensor network structure search algorithms via large language models llms,MPO/TT 压缩,1,,
Dual-isometric projected entangled pair states,"XH Yu, JI Cirac, P Kos, G Styliaris",2024.0,16,"Efficient characterization of higher dimensional many-body physical states presents significant challenges. In this Letter, we propose a new class of projected entangled pair states (…",BXTqx-VFQfoJ,"XH Yu, JI Cirac, P Kos, G Styliaris - Physical Review Letters, 2024 - APS",['https://link.aps.org/pdf/10.1103/PhysRevLett.133.190401'],https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.190401,unknown,unknown,TTN/MERA/PEPS,,['https://link.aps.org/pdf/10.1103/PhysRevLett.133.190401'],dual isometric projected entangled pair states,TTN/MERA/PEPS,1,,
Identification of quantum entanglement with Siamese convolutional neural networks and semisupervised learning,"J Pawłowski, M Krawczyk",2024.0,15,"… In this study, we use deep convolutional NNs, a type of supervised machine learning, to … Trebst, Machine learning quantum phases of matter beyond the fermion sign problem, Sci. …",cgOD700wpSEJ,"J Pawłowski, M Krawczyk - Physical Review Applied, 2024 - APS",['https://arxiv.org/pdf/2210.07410'],https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.22.014068,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2210.07410'],identification of quantum entanglement with siamese convolutional neural networks and semisupervised learning,TTN/MERA/PEPS,1,,
Probabilistic inference in the era of tensor networks and differential programming,"M Roa-Villescas, X Gao, S Stuijk, H Corporaal…",2024.0,12,"… probabilistic modeling in terms of tensor networks, thereby allowing the field of probabilistic modeling to leverage the remarkable developments achieved in tensor network modeling in …",DexCEa1h4vgJ,"M Roa-Villescas, X Gao, S Stuijk, H Corporaal… - Physical Review …, 2024 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.033261'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033261,unknown,unknown,MPS/序列建模,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.033261'],probabilistic inference in the era of tensor networks and differential programming,MPS/序列建模 / TTN/MERA/PEPS,2,,
"Rényi mutual information in quantum field theory, tensor networks, and gravity","J Kudler-Flam, L Nie, A Vijay",2024.0,12,"A bstract We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z , the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.",r9LLFMk4sSIJ,"J Kudler-Flam, L Nie, A Vijay - Journal of High Energy Physics, 2024 - Springer",['https://link.springer.com/content/pdf/10.1007/JHEP06(2024)195.pdf'],https://link.springer.com/article/10.1007/JHEP06(2024)195,unknown,unknown,互信息/标度,2308.08600,['https://link.springer.com/content/pdf/10.1007/JHEP06(2024)195.pdf'],r nyi mutual information in quantum field theory tensor networks and gravity,互信息/标度,1,Journal of High Energy Physics,
Accelerating large language model training with hybrid gpu-based compression,"L Xu, Q Anthony, Q Zhou, N Alnaasan…",2024.0,10,"… We selected the largest language model checkpointed in the GPT-NeoX library - GPT-NeoX-20B. Due to a lack of resources to train the original foundation model, it was necessary to …",IgwYgPjyZGIJ,"L Xu, Q Anthony, Q Zhou, N Alnaasan… - … , Cloud and Internet …, 2024 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2409.02423?'],https://ieeexplore.ieee.org/abstract/document/10701315/,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/2409.02423?'],accelerating large language model training with hybrid gpu based compression,MPO/TT 压缩,1,,
Higher order transformers: Efficient attention mechanism for tensor structured data,"S Omranpour, G Rabusseau, R Rabbany",2024.0,10,"… tensor attention, we introduce a novel Kronecker factorized attention mechanism that reduces the attention … of the input tensor. To further enhance efficiency, HOT leverages kernelized …",VVumLQ4J3KAJ,"S Omranpour, G Rabusseau, R Rabbany - 2024 - openreview.net",['https://openreview.net/pdf?id=MxGGdhDmv5'],https://openreview.net/forum?id=MxGGdhDmv5,unknown,unknown,张量化Transformer,,['https://openreview.net/pdf?id=MxGGdhDmv5'],higher order transformers efficient attention mechanism for tensor structured data,张量化Transformer,1,,
Long sequence modeling with attention tensorization: From sequence to tensor learning,"A Feng, R Ying, L Tassiulas",2024.0,8,"As the demand for processing extended textual data grows, the ability to handle long-range dependencies and maintain computational efficiency is more critical than ever.One of the key issues for long-sequence modeling using attention-based model is the mismatch between the limited-range modeling power of full attention and the long-range token dependency in the input sequence.In this work, we propose to scale up the attention receptive field by tensorizing long input sequences into compact tensor representations followed by attention on each transformed dimension.The resulting Tensorized Attention can be adopted as efficient transformer backbones to extend input context length with improved memory and time efficiency.We show that the proposed attention tensorization encodes token dependencies as a multi-hop attention process, and is equivalent to Kronecker decomposition of full attention.Extensive experiments show that tensorized attention can be used to adapt pretrained LLMs with improved efficiency.Notably, using customized Triton kernels, tensorization enables Llama-8B training under 32,768 context length and can steadily extrapolate to 128k length during inference with 11× speedup (compared to full attention with FlashAttention-2).",Sum2XMxMlFEJ,"A Feng, R Ying, L Tassiulas - Findings of the Association for …, 2024 - aclanthology.org",['https://aclanthology.org/2024.findings-emnlp.858.pdf'],https://aclanthology.org/2024.findings-emnlp.858/,unknown,unknown,张量化Transformer,2410.20926,['https://aclanthology.org/2024.findings-emnlp.858.pdf'],long sequence modeling with attention tensorization from sequence to tensor learning,张量化Transformer,1,,
Teaformers: Tensor-augmented transformers for multi-dimensional time series forecasting,"L Kong, E Chen, Y Chen, Y Han",2024.0,8,"Multi-dimensional time series data, such as matrix and tensor-variate time series, are increasingly prevalent in fields such as economics, finance, and climate science. Traditional Transformer models, though adept with sequential data, do not effectively preserve these multi-dimensional structures, as their internal operations in effect flatten multi-dimensional observations into vectors, thereby losing critical multi-dimensional relationships and patterns. To address this, we introduce the Tensor-Augmented Transformer (TEAFormer), a novel method that incorporates tensor expansion and compression within the Transformer framework to maintain and leverage the inherent multi-dimensional structures, thus reducing computational costs and improving prediction accuracy. The core feature of the TEAFormer, the Tensor-Augmentation (TEA) module, utilizes tensor expansion to enhance multi-view feature learning and tensor compression for efficient information aggregation and reduced computational load. The TEA module is not just a specific model architecture but a versatile component that is highly compatible with the attention mechanism and the encoder-decoder structure of Transformers, making it adaptable to existing Transformer architectures. Our comprehensive experiments, which integrate the TEA module into three popular time series Transformer models across three real-world benchmarks, show significant performance enhancements, highlighting the potential of TEAFormers for cutting-edge time series forecasting.",gZ-ntC2o4y8J,"L Kong, E Chen, Y Chen, Y Han - arXiv preprint arXiv:2410.20439, 2024 - arxiv.org",['https://arxiv.org/pdf/2410.20439?'],https://arxiv.org/abs/2410.20439,unknown,unknown,张量化Transformer,2410.20439,['https://arxiv.org/pdf/2410.20439?'],teaformers tensor augmented transformers for multi dimensional time series forecasting,张量化Transformer,1,,
Quantum topic model: Topic modeling using variational quantum circuits,"W Qiao, P Zhang, J Zhao, C Yang",2024.0,6,… The topic model is a statistical language model capable of modeling and clustering words in massive text data. It is one of the most important techniques in text mining and finds ex…,FB7dTMgE7woJ,"W Qiao, P Zhang, J Zhao, C Yang - ICASSP 2024-2024 IEEE …, 2024 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/10447349/,unknown,unknown,量子/混合LLM,,[],quantum topic model topic modeling using variational quantum circuits,量子/混合LLM,1,,
QuanTA: Efficient High-Rank Fine-Tuning of LLMs with Quantum-Informed Tensor Adaptation,"Z Chen, R Dangovski, C Loh, O Dugan, D Luo, M Soljačić",2024.0,6,"We propose Quantum-informed Tensor Adaptation (QuanTA), a novel, easy-to-implement, fine-tuning method with no inference overhead for large-scale pre-trained language models. By leveraging quantum-inspired methods derived from quantum circuit structures, QuanTA enables efficient high-rank fine-tuning, surpassing the limitations of Low-Rank Adaptation (LoRA)--low-rank approximation may fail for complicated downstream tasks. Our approach is theoretically supported by the universality theorem and the rank representation theorem to achieve efficient high-rank adaptations. Experiments demonstrate that QuanTA significantly enhances commonsense reasoning, arithmetic reasoning, and scalability compared to traditional methods. Furthermore, QuanTA shows superior performance with fewer trainable parameters compared to other approaches and can be designed to integrate with existing fine-tuning algorithms for further improvement, providing a scalable and efficient solution for fine-tuning large language models and advancing state-of-the-art in natural language processing.",,"Z Chen, R Dangovski, C Loh, O Dugan, D Luo, M Soljačić - arXiv preprint arXiv:2406.00132, 2024 - arxiv.org",[],https://arxiv.org/abs/2406.00132,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2406.00132,['https://arxiv.org/pdf/2406.00132'],quanta efficient high rank fine tuning of llms with quantum informed tensor adaptation,MPS 语言模型 / MPO/TT 压缩,1,,
Tensor-networks-based learning of probabilistic cellular automata dynamics,"HP Casagrande, B Xing, WJ Munro, C Guo…",2024.0,4,… IV we explain how we prepare the data and train our model. In Secs. V and VI we describe … model. We provide analytical insights on the tensor network’s ability to represent probabilistic …,tSeM6gyksB4J,"HP Casagrande, B Xing, WJ Munro, C Guo… - Physical Review …, 2024 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.043202'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043202,unknown,unknown,MPS/序列建模,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.043202'],tensor networks based learning of probabilistic cellular automata dynamics,MPS/序列建模,1,,
Leveraging pre-trained neural networks to enhance machine learning with variational quantum circuits,"J Qi, CH Yang, SYC Chen, PY Chen, H Zenil…",2024.0,3,"Quantum Machine Learning (QML) offers tremendous potential but is currently limited by the availability of qubits. We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC). This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions, making QML more viable for real-world applications. Our method significantly improves parameter optimization for VQC while delivering notable gains in representation and generalization capabilities, as evidenced by rigorous theoretical analysis and extensive empirical testing on quantum dot classification tasks. Moreover, our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach. By addressing the constraints of current quantum hardware, our work paves the way for a new era of advanced QML applications, unlocking the full potential of quantum computing in fields such as machine learning, materials science, medicine, mimetics, and various interdisciplinary areas.",l3QpOxLzPlYJ,"J Qi, CH Yang, SYC Chen, PY Chen, H Zenil… - arXiv preprint arXiv …, 2024 - arxiv.org",['https://arxiv.org/pdf/2411.08552'],https://arxiv.org/abs/2411.08552,unknown,unknown,量子/混合LLM,2411.08552,['https://arxiv.org/pdf/2411.08552'],leveraging pre trained neural networks to enhance machine learning with variational quantum circuits,量子/混合LLM,1,,
Markov chain Monte Carlo in tensor network representation,S Todo,2024.0,3,"Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the convergence of statistical error. We propose a novel MCMC formulation based on tensor network representations to reduce the population variance and mitigate these issues systematically. By introducing stochastic projectors into the tensor network framework and employing Markov chain sampling, our method eliminates the systematic error associated with low-rank approximation in tensor contraction while maintaining the high accuracy of the tensor network method. We demonstrate the effectiveness of the proposed method on the two-dimensional Ising model, achieving an exponential reduction in statistical error with increasing bond dimension cutoff. Furthermore, we address the sign problem in systems with negative weights, showing significant improvements in average signs as bond dimension cutoff increases. The proposed framework provides a robust solution for accurate statistical estimation in complex systems, paving the way for broader applications in computational physics and beyond.",1rkND5PqISoJ,"S Todo - arXiv preprint arXiv:2412.02974, 2024 - arxiv.org",['https://arxiv.org/pdf/2412.02974'],https://arxiv.org/abs/2412.02974,unknown,unknown,MPS/序列建模,2412.02974,['https://arxiv.org/pdf/2412.02974'],markov chain monte carlo in tensor network representation,MPS/序列建模,1,,
An adaptive tensor-train decomposition approach for efficient deep neural network compression,"S Luo, M Liu, Y Yu, S Ren, Y Bai",2024.0,2,"In the field of model compression, choosing an appropriate rank for tensor decomposition is pivotal for balancing model compression rate and efficiency. However, this selection, whether done manually or through optimization-based automatic methods, often increases computational complexity. Manual rank selection lacks efficiency and scalability, often requiring extensive trial-and-error, while optimization-based automatic methods significantly increase the computational burden. To address this, we introduce a novel, automatic, and budget-aware rank selection method for efficient model compression, which employs Layer-Wise Imprinting Quantitation (LWIQ). LWIQ quantifies each layer's significance within a neural network by integrating a proxy classifier. This classifier assesses the layer's impact on overall model performance, allowing for a more informed adjustment of tensor rank. Furthermore, our approach includes a scaling factor to cater to varying computational budget constraints. This budget awareness eliminates the need for repetitive rank recalculations for different budget scenarios. Experimental results on the CIFAR-10 dataset show that our LWIQ improved by 63.2% in rank search efficiency, and the accuracy only dropped by 0.86% with 3.2x less model size on the ResNet-56 model as compared to the state-of-the-art proxy-based automatic tensor rank selection method.",BeGsGOhQnkQJ,"S Luo, M Liu, Y Yu, S Ren, Y Bai - arXiv preprint arXiv:2408.01534, 2024 - arxiv.org",['https://arxiv.org/pdf/2408.01534'],https://arxiv.org/abs/2408.01534,unknown,unknown,MPO/TT 压缩,2408.01534,['https://arxiv.org/pdf/2408.01534'],an adaptive tensor train decomposition approach for efficient deep neural network compression,MPO/TT 压缩,1,,
Many-body localized hidden generative models,"W Zhong, X Gao, SF Yelin, K Najafi",2024.0,2,"… with tensor network state ansätze. The elements of these matrix product states or tree tensor … In this paper, we introduce the new quantum generative model, the hidden Born machine in …",0Q8jP7xSQtAJ,"W Zhong, X Gao, SF Yelin, K Najafi - Physical Review Research, 2024 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.043041'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043041,unknown,unknown,MPS 生成/Born机,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.6.043041'],many body localized hidden generative models,MPS 生成/Born机,1,,
Direct interpolative construction of the discrete Fourier transform as a matrix product operator,"J Chen, M Lindsey",2024.0,2,"The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.",,"J Chen, M Lindsey - Applied and Computational Harmonic Analysis 81, 101817 (2026)",[],https://arxiv.org/abs/2404.03182,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2404.03182,['https://arxiv.org/pdf/2404.03182'],direct interpolative construction of the discrete fourier transform as a matrix product operator,MPO/TT 压缩,1,"Applied and Computational Harmonic Analysis 81, 101817 (2026)",
Low-rank Tree Tensor Network Operators for Long-Range Pairwise Interactions,"G Ceruti, D Kressner, D Sulz",2024.0,2,"Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we study such representations for tree tensor networks, the so called tree tensor network operators (TTNOs), paying particular attention to Hamiltonian operators that involve long-range pairwise interactions between particles. Generalizing the work by Lin, Tong, and others on matrix product operators, we establish a direct connection between the hierarchical low-rank structure of the interaction matrix and the TTNO property. This connection allows us to arrive at very compact TTNO representations by compressing the interaction matrix into a hierarchically semi-separable matrix. Numerical experiments for different quantum spin systems validate our results and highlight the potential advantages of TTNOs over matrix product operators.",,"G Ceruti, D Kressner, D Sulz - arXiv preprint arXiv:2405.09952, 2024 - arxiv.org",[],https://arxiv.org/abs/2405.09952,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2405.09952,['https://arxiv.org/pdf/2405.09952'],low rank tree tensor network operators for long range pairwise interactions,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
PyTreeNet: A Python Library for easy Utilisation of Tree Tensor Networks,"R M Milbradt, Q Huang, C B Mendl",2024.0,2,"In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library PyTreeNet. It includes code examples and exercises to introduce the library's functions and familiarise the reader with the concepts and methods surrounding tree tensor networks. PyTreeNet implements all the tools required to implement general tree tensor network methods, such as tensor decompositions and arbitrary tree structures. The main focus is on the time evolution of quantum systems. This includes an introduction to tree tensor network states and operators and the time-evolving block decimation and time-dependent variational principle. The library's capabilities are showcased with the example of a modified transverse field Ising model on tree structures that go far beyond the ability of common state vector methods.",,"R M Milbradt, Q Huang, C B Mendl - arXiv preprint arXiv:2407.13249, 2024 - arxiv.org",[],https://arxiv.org/abs/2407.13249,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2407.13249,['https://arxiv.org/pdf/2407.13249'],pytreenet a python library for easy utilisation of tree tensor networks,TTN/MERA/PEPS,1,,
Beyond Boundaries: efficient Projected Entangled Pair States methods for periodic quantum systems,"S Dong, C Wang, H Zhang, M Zhang, L He",2024.0,1,"Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic boundary conditions (PBC), attributed to the prohibitive computational scaling with the bond dimension. This has notably restricted the study of systems with complex boundary conditions. To address this challenge, we have developed a strategy that involves the superposition of PEPS with open boundary conditions (OBC) to treat systems with PBC. This approach significantly reduces the computational complexity of such systems while maintaining their translational invariance and the PBC. We benchmark this method against the Heisenberg model and the $J_1$-$J_2$ model, demonstrating its capability to yield highly accurate results at low computational costs, even for large system sizes. The techniques are adaptable to other boundary conditions, including cylindrical and twisted boundary conditions, and therefore significantly expands the application scope of the PEPS approach, shining new light on numerous applications.",9Vm0jbU8TSwJ,"S Dong, C Wang, H Zhang, M Zhang, L He - arXiv preprint arXiv …, 2024 - arxiv.org",['https://arxiv.org/pdf/2407.15333'],https://arxiv.org/abs/2407.15333,unknown,unknown,TTN/MERA/PEPS,2407.15333,['https://arxiv.org/pdf/2407.15333'],beyond boundaries efficient projected entangled pair states methods for periodic quantum systems,TTN/MERA/PEPS,1,,
Enhancing Neural Language Models: A Comprehensive Approach With Tensorized Transformer and Over-Parameterization,"P Taneja, K Chandra, D Batra, A Gupta, R Kumar…",2024.0,1,"… linear attention with Block-Term Tensor Decomposition (BTD), a self-attention model leveraging tensor decomposition … Comparative evaluations against traditional Transformer models …",9yI0DfQjE_4J,"P Taneja, K Chandra, D Batra, A Gupta, R Kumar… - 2024 - researchgate.net",['https://www.researchgate.net/profile/Bhaumik-Tyagi/publication/378157352_Enhancing_Neural_Language_Models_A_Comprehensive_Approach_with_Tensorized_Transformer_and_Over-Parameterization/links/65cb32bf790074549781841f/Enhancing-Neural-Language-Models-A-Comprehensive-Approach-with-Tensorized-Transformer-and-Over-Parameterization.pdf'],https://www.researchgate.net/profile/Bhaumik-Tyagi/publication/378157352_Enhancing_Neural_Language_Models_A_Comprehensive_Approach_with_Tensorized_Transformer_and_Over-Parameterization/links/65cb32bf790074549781841f/Enhancing-Neural-Language-Models-A-Comprehensive-Approach-with-Tensorized-Transformer-and-Over-Parameterization.pdf,unknown,unknown,张量化Transformer,,['https://www.researchgate.net/profile/Bhaumik-Tyagi/publication/378157352_Enhancing_Neural_Language_Models_A_Comprehensive_Approach_with_Tensorized_Transformer_and_Over-Parameterization/links/65cb32bf790074549781841f/Enhancing-Neural-Language-Models-A-Comprehensive-Approach-with-Tensorized-Transformer-and-Over-Parameterization.pdf'],enhancing neural language models a comprehensive approach with tensorized transformer and over parameterization,张量化Transformer,1,,
Training Tensor Attention Efficiently: From Cubic to Almost Linear Time,"Y Cao, Y Liang, Z Shi, Z Song",2024.0,1,"Tensor Attention, a multi-view attention that is able to capture high-order correlations among multiple modalities, can overcome the representational limitations of classical matrix attention. However, the $O(n^3)$ time complexity of tensor attention poses a significant obstacle to its utilization in transformers, where $n$ is the input sequence length. In this work, we prove that the backward gradient of tensor attention training can be computed in almost linear time $n^{1+o(1)}$, the same complexity as its forward computation under the bounded entries assumption. We provide a closed-form solution for the gradient and propose a fast computation method utilizing polynomial approximation methods and tensor algebraic techniques. Furthermore, we prove the necessity and tightness of our assumption through hardness analysis, showing that slightly weakening it renders the gradient problem unsolvable in truly subcubic time. Our theoretical results establish the feasibility of efficient higher-order transformer training and may facilitate practical applications of tensor attention architectures.",Yrlj3-iT2UoJ,"Y Cao, Y Liang, Z Shi, Z Song - arXiv preprint arXiv:2405.16411, 2024 - arxiv.org",['https://arxiv.org/pdf/2405.16411'],https://arxiv.org/abs/2405.16411,unknown,unknown,张量化Transformer,2405.16411,['https://arxiv.org/pdf/2405.16411'],training tensor attention efficiently from cubic to almost linear time,张量化Transformer,1,arXiv (Cornell University),
A parallel Basis Update and Galerkin Integrator for Tree Tensor Networks,"G Ceruti, J Kusch, C Lubich, D Sulz",2024.0,1,"Computing the numerical solution to high-dimensional tensor differential equations can lead to prohibitive computational costs and memory requirements. To reduce the memory and computational footprint, dynamical low-rank approximation (DLRA) has proven to be a promising approach. DLRA represents the solution as a low-rank tensor factorization and evolves the resulting low-rank factors in time. A central challenge in DLRA is to find time integration schemes that are robust to the arising small singular values. A robust parallel basis update & Galerkin integrator, which simultaneously evolves all low-rank factors, has recently been derived for matrix differential equations. This work extends the parallel low-rank matrix integrator to Tucker tensors and general tree tensor networks, yielding an algorithm in which all bases and connecting tensors are evolved in parallel over a time step. We formulate the algorithm, provide a robust error bound, and demonstrate the efficiency of the new integrators for problems in quantum many-body physics, uncertainty quantification, and radiative transfer.",,"G Ceruti, J Kusch, C Lubich, D Sulz - arXiv preprint arXiv:2412.00858, 2024 - arxiv.org",[],https://arxiv.org/abs/2412.00858,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2412.00858,['https://arxiv.org/pdf/2412.00858'],a parallel basis update and galerkin integrator for tree tensor networks,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
Error-mitigated photonic quantum circuit Born machine,"A Salavrakos, T Sedrakyan, J Mills, S Mansfield, R Mezher",2024.0,1,"In this article, we study quantum circuit Born machines (QCBMs) in the context of photonic quantum computing. QCBMs are a popular choice of quantum generative machine learning models, and we present a QCBM designed for linear optics. We show that a recently developed error mitigation technique called recycling mitigation greatly improves the training of QCBMs in realistic scenarios with photon loss, which is the primary source of noise in photonic systems. We demonstrate this through numerical simulations and through an experiment on a quantum photonic integrated processor. We expect our work to pave the way towards more demonstrations of error mitigation techniques tailored to photonic devices which can enhance the performance of a quantum algorithm.",,"A Salavrakos, T Sedrakyan, J Mills, S Mansfield, R Mezher - Phys. Rev. A 111, L030401 (2025)",[],https://arxiv.org/abs/2405.02277,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2405.02277,['https://arxiv.org/pdf/2405.02277'],error mitigated photonic quantum circuit born machine,MPS 生成/Born机 / 量子/混合LLM,1,"Phys. Rev. A 111, L030401 (2025)",
Tensor-Train WENO Scheme for Compressible Flows,"M E Danis, D Truong, I Boureima, O Korobkin, K Rasmussen, B Alexandrov",2024.0,1,"In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce \emph{LF-cross} and \emph{WENO-cross} methods to compute numerical fluxes and the WENO reconstruction using the cross interpolation technique. A tensor-train approach is developed for boundary condition types commonly encountered in Computational Fluid Dynamics (CFD). The performance of the proposed WENO-TT solver is investigated in a rich set of numerical experiments. We demonstrate that the WENO-TT method achieves the theoretical $\text{5}^{\text{th}}$-order accuracy of the classical WENO scheme in smooth problems while successfully capturing complicated shock structures. In an effort to avoid the growth of TT ranks, we propose a dynamic method to estimate the TT approximation error that governs the ranks and overall truncation error of the WENO-TT scheme. Finally, we show that the traditional WENO scheme can be accelerated up to 1000 times in the TT format, and the memory requirements can be significantly decreased for low-rank problems, demonstrating the potential of tensor-train approach for future CFD application. This paper is the first study that develops a finite difference WENO scheme using the tensor-train approach for compressible flows. It is also the first comprehensive work that provides a detailed perspective into the relationship between rank, truncation error, and the TT approximation error for compressible WENO solvers.",,"M E Danis, D Truong, I Boureima, O Korobkin, K Rasmussen, B Alexandrov - arXiv preprint arXiv:2405.12301, 2024 - arxiv.org",[],https://arxiv.org/abs/2405.12301,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2405.12301,['https://arxiv.org/pdf/2405.12301'],tensor train weno scheme for compressible flows,MPO/TT 压缩 / 量子启发综述,1,,
Validating Large-Scale Quantum Machine Learning: Efficient Simulation of Quantum Support Vector Machines Using Tensor Networks,"K Chen, T Li, Y Wang, S See, C Wang, R Wille, N Chen, A Yang, C Lin",2024.0,1,"We present an efficient tensor-network-based approach for simulating large-scale quantum circuits, demonstrated using Quantum Support Vector Machines (QSVMs). Our method effectively reduces exponential runtime growth to near-quadratic scaling with respect to the number of qubits in practical scenarios. Traditional state-vector simulations become computationally infeasible beyond approximately 50 qubits; in contrast, our simulator successfully handles QSVMs with up to 784 qubits, completing simulations within seconds on a single high-performance GPU. Furthermore, by employing the Message Passing Interface (MPI) in multi-GPU environments, the approach shows strong linear scalability, reducing computation time as dataset size increases. We validate the framework on the MNIST and Fashion MNIST datasets, achieving successful multiclass classification and emphasizing the potential of QSVMs for high-dimensional data analysis. By integrating tensor-network techniques with high-performance computing resources, this work demonstrates both the feasibility and scalability of large-qubit quantum machine learning models, providing a valuable validation tool in the emerging Quantum-HPC ecosystem.",,"K Chen, T Li, Y Wang, S See, C Wang, R Wille, N Chen, A Yang, C Lin - arXiv preprint arXiv:2405.02630, 2024 - arxiv.org",[],https://arxiv.org/abs/2405.02630,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2405.02630,['https://arxiv.org/pdf/2405.02630'],validating large scale quantum machine learning efficient simulation of quantum support vector machines using tensor networks,量子/混合LLM,1,,
Deep Learning and Tensor-Based Multiple Clustering Approaches for Cyber-Physical-Social Applications,"H Zhang, H Zhang, Y Lei, H Ye, P Li, D Shi",2024.0,0,"… , complex relationships, large scale, and rapid generation of … Finally, the paper summarizes the entire text and discusses … attribute clustering network based on tensor network physics …",Ra_0Rt5UaUYJ,"H Zhang, H Zhang, Y Lei, H Ye, P Li, D Shi - Computers, Materials and …, 2024 - Elsevier",[],https://www.sciencedirect.com/org/science/article/pii/S1546221824003588,unknown,unknown,互信息/标度,,[],deep learning and tensor based multiple clustering approaches for cyber physical social applications,互信息/标度,1,,
Enhancing Generation Stability with Generative Matrix Product States in Adversarial Networks,"W Sun, Z Gao",2024.0,0,"… As machine learning and artificial intelligence rapidly progress, generative modeling has … interpretation of quantum probabilities and serves as the foundation for the Born machine. For …",6cPLYt36OlUJ,"W Sun, Z Gao - 2024 IEEE 6th International Conference on …, 2024 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/10797185/,unknown,unknown,MPS 生成/Born机,,[],enhancing generation stability with generative matrix product states in adversarial networks,MPS 生成/Born机,1,,
Generating Quantum Circuits with Finetuned Pretrained Large Language Models,M Choi,2024.0,0,"… Thus, quantum algorithms such as the Variational Quantum Eigensolver (VQE) [14] and the … of large language models on quantum problems; thus, eliminating the number of models to …",Wv6KvDTyn6wJ,M Choi - 2024 - matthew9655.github.io,['https://matthew9655.github.io/files/thesis.pdf'],https://matthew9655.github.io/files/thesis.pdf,unknown,unknown,量子/混合LLM,,['https://matthew9655.github.io/files/thesis.pdf'],generating quantum circuits with finetuned pretrained large language models,量子/混合LLM,1,,
Tensor Mutual Information for Similarity Measurement of High-Dimensional Data: An Image Classification Perspective,"J Kamruzzaman, S Pang, L Lu, J Liu",2024.0,0,"… Amidst the profound surge in the scale of image and video data… Mutual information, rooted in Shannon entropy, stands as a … Notably, extracting mutual information between tensors while …",L3nEV5IAJ9sJ,"J Kamruzzaman, S Pang, L Lu, J Liu - … Conference on Neural Information …, 2024 - Springer",[],https://link.springer.com/chapter/10.1007/978-981-96-6606-5_19,unknown,unknown,互信息/标度,,[],tensor mutual information for similarity measurement of high dimensional data an image classification perspective,互信息/标度,1,,
Extraction of nonlinearity in neural networks with Koopman operator,"N Sugishita, K Kinjo, J Ohkubo",2024.0,0,"Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode decomposition, and the tensor-train format. The Koopman operator approach has been recently developed in physics and nonlinear sciences; the Koopman operator deals with the time evolution in the observable space instead of the state space. Since we can replace the nonlinearity in the state space with the linearity in the observable space, it is a hopeful candidate for understanding complex behavior in nonlinear systems. Here, we analyze learned neural networks for the classification problems. As a result, the replacement of the nonlinear middle layers with the Koopman matrix yields enough accuracy in numerical experiments. In addition, we confirm that the pruning of the Koopman matrix gives sufficient accuracy even at high compression ratios. These results indicate the possibility of extracting some features in the neural networks with the Koopman operator approach.",,"N Sugishita, K Kinjo, J Ohkubo - J. Stat. Mech. Vol. 2024, Article No. 073401, pp. 1-22 (2024)",[],https://arxiv.org/abs/2402.11740,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2402.11740,['https://arxiv.org/pdf/2402.11740'],extraction of nonlinearity in neural networks with koopman operator,MPO/TT 压缩,1,"J. Stat. Mech. Vol. 2024, Article No. 073401, pp. 1-22 (2024)",
Problem-informed Graphical Quantum Generative Learning,"B Bakó, D T R Nagy, P Hága, Z Kallus, Z Zimborás",2024.0,,"Leveraging the intrinsic probabilistic nature of quantum systems, generative quantum machine learning (QML) offers the potential to outperform classical learning models. Current generative QML algorithms mostly rely on general-purpose models that, while being very expressive, face several training challenges. One potential way to address these setbacks is by constructing problem-informed models that are capable of more efficient training on structured problems. In particular, probabilistic graphical models provide a flexible framework for representing structure in generative learning problems and can thus be exploited to incorporate inductive bias into QML algorithms. In this work, we propose a problem-informed quantum circuit Born machine Ansatz for learning the joint probability distribution of random variables, with independence relations efficiently represented by a Markov network (MN). We further demonstrate the applicability of the MN framework in constructing generative learning benchmarks and compare our model's performance to previous designs, showing that it outperforms problem-agnostic circuits. Based on a preliminary analysis of trainability, we narrow down the class of MNs to those exhibiting favourable trainability properties. Finally, we discuss the potential of our model to offer quantum advantage in the context of generative learning.",,"B Bakó, D T R Nagy, P Hága, Z Kallus, Z Zimborás - Quantum Science and Technology 11 (3), 035012 (2026)",[],https://arxiv.org/abs/2405.14072,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2405.14072,['https://arxiv.org/pdf/2405.14072'],problem informed graphical quantum generative learning,MPS 生成/Born机 / 量子/混合LLM,1,"Quantum Science and Technology 11 (3), 035012 (2026)",
Scalable quantum dynamics compilation via quantum machine learning,"Y Zhang, R Wiersema, J Carrasquilla, L Cincio, Y B Kim",2024.0,,"Quantum dynamics compilation is an important task for improving quantum simulation efficiency: It aims to synthesize multi-qubit target dynamics into a circuit consisting of as few elementary gates as possible. Compared to deterministic methods such as Trotterization, variational quantum compilation (VQC) methods employ variational optimization to reduce gate costs while maintaining high accuracy. In this work, we explore the potential of a VQC scheme by making use of out-of-distribution generalization results in quantum machine learning (QML): By learning the action of a given many-body dynamics on a small data set of product states, we can obtain a unitary circuit that generalizes to highly entangled states such as the Haar random states. The efficiency in training allows us to use tensor network methods to compress such time-evolved product states by exploiting their low entanglement features. Our approach exceeds state-of-the-art compilation results in both system size and accuracy in one dimension ($1$D). For the first time, we extend VQC to systems on two-dimensional (2D) strips with a quasi-1D treatment, demonstrating a significant resource advantage over standard Trotterization methods, highlighting the method's promise for advancing quantum simulation tasks on near-term quantum processors.",,"Y Zhang, R Wiersema, J Carrasquilla, L Cincio, Y B Kim - arXiv preprint arXiv:2409.16346, 2024 - arxiv.org",[],https://arxiv.org/abs/2409.16346,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2409.16346,['https://arxiv.org/pdf/2409.16346'],scalable quantum dynamics compilation via quantum machine learning,MPO/TT 压缩 / 量子/混合LLM,1,,
VeriQR: A Robustness Verification Tool for Quantum Machine Learning Models,"Y Lin, J Guan, W Fang, M Ying, Z Su",2024.0,0,"Adversarial noise attacks present a significant threat to quantum machine learning (QML) models, similar to their classical counterparts. This is especially true in the current Noisy Intermediate-Scale Quantum era, where noise is unavoidable. Therefore, it is essential to ensure the robustness of QML models before their deployment. To address this challenge, we introduce \textit{VeriQR}, the first tool designed specifically for formally verifying and improving the robustness of QML models, to the best of our knowledge. This tool mimics real-world quantum hardware's noisy impacts by incorporating random noise to formally validate a QML model's robustness. \textit{VeriQR} supports exact (sound and complete) algorithms for both local and global robustness verification. For enhanced efficiency, it implements an under-approximate (complete) algorithm and a tensor network-based algorithm to verify local and global robustness, respectively. As a formal verification tool, \textit{VeriQR} can detect adversarial examples and utilize them for further analysis and to enhance the local robustness through adversarial training, as demonstrated by experiments on real-world quantum machine learning models. Moreover, it permits users to incorporate customized noise. Based on this feature, we assess \textit{VeriQR} using various real-world examples, and experimental outcomes confirm that the addition of specific quantum noise can enhance the global robustness of QML models. These processes are made accessible through a user-friendly graphical interface provided by \textit{VeriQR}, catering to general users without requiring a deep understanding of the counter-intuitive probabilistic nature of quantum computing.",,"Y Lin, J Guan, W Fang, M Ying, Z Su - arXiv preprint arXiv:2407.13533, 2024 - arxiv.org",[],https://arxiv.org/abs/2407.13533,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2407.13533,['https://arxiv.org/pdf/2407.13533'],veriqr a robustness verification tool for quantum machine learning models,量子/混合LLM,1,,
An Efficient Two-Sided Sketching Method for Large-Scale Tensor Decomposition Based on Transformed Domains,"Z Cheng, G Yu, X Cai, L Qi",2024.0,0,"Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage. Fortunately, they typically exhibit a low-rank structure that can be leveraged through tensor decomposition. However, performing large-scale tensor decomposition can be time-consuming. Sketching is a useful technique to reduce the dimensionality of the data. In this paper, we propose a novel two-sided sketching method based on the $\star_{L}$-product decomposition and transformed domains like the discrete cosine transformation. A rigorous theoretical analysis is also conducted to assess the approximation error of the proposed method. Specifically, we improve our method with power iteration to achieve more precise approximate solutions. Extensive numerical experiments and comparisons on low-rank approximation of synthetic large tensors and real-world data like color images and grayscale videos illustrate the efficiency and effectiveness of the proposed approach in terms of both CPU time and approximation accuracy.",,"Z Cheng, G Yu, X Cai, L Qi - arXiv preprint arXiv:2404.16580, 2024 - arxiv.org",[],https://arxiv.org/abs/2404.16580,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2404.16580,['https://arxiv.org/pdf/2404.16580'],an efficient two sided sketching method for large scale tensor decomposition based on transformed domains,MPO/TT 压缩,1,,
Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm,"L Ma, M Fishman, M Stoudenmire, E Solomonik",2024.0,0,"Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate tensor generated during the contractions is approximated as a low-rank binary tree tensor network. The proposed algorithm has the flexibility to incorporate a large portion of the environment when performing low-rank approximations, which can lead to high accuracy for a given rank. Here, the environment refers to the remaining set of tensors in the network, and low-rank approximations with larger environments can generally provide higher accuracy. For contracting tensor networks defined on lattices, the proposed algorithm can be viewed as a generalization of the standard boundary-based algorithms. In addition, the algorithm includes a cost-efficient density matrix algorithm for approximating a tensor network with a general graph structure into a tree structure, whose computational cost is asymptotically upper-bounded by that of the standard algorithm that uses canonicalization. Experimental results indicate that the proposed technique outperforms previously proposed approximate tensor network contraction algorithms for multiple problems in terms of both accuracy and efficiency.",,"L Ma, M Fishman, M Stoudenmire, E Solomonik - Quantum 8, 1580 (2024)",[],https://arxiv.org/abs/2406.09769,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2406.09769,['https://arxiv.org/pdf/2406.09769'],approximate contraction of arbitrary tensor networks with a flexible and efficient density matrix algorithm,MPO/TT 压缩 / TTN/MERA/PEPS,1,"Quantum 8, 1580 (2024)",
Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms,D S M Alves,2024.0,0,"We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the \emph{Multiscale Entanglement Renormalization Ansatz} (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.",,"D S M Alves - arXiv preprint arXiv:2404.11715, 2024 - arxiv.org",[],https://arxiv.org/abs/2404.11715,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2404.11715,['https://arxiv.org/pdf/2404.11715'],entanglement renormalization for quantum field theories with discrete wavelet transforms,TTN/MERA/PEPS,1,,
Entangling Machine Learning with Quantum Tensor Networks,"C v d Poel, D Zhao",2024.0,0,"This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will abstract the problem down to modeling Motzkin spin chains, which exhibit long-range correlations reminiscent of those found in language. The Matrix Product State (MPS), also known as the tensor train, has a bond dimension which scales as the length of the sequence it models. To combat this, we use the factored core MPS, whose bond dimension scales sub-linearly. We find that the tensor models reach near perfect classifying ability, and maintain a stable level of performance as the number of valid training examples is decreased.",,"C v d Poel, D Zhao - arXiv preprint arXiv:2403.12969, 2024 - arxiv.org",[],https://arxiv.org/abs/2403.12969,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2403.12969,['https://arxiv.org/pdf/2403.12969'],entangling machine learning with quantum tensor networks,MPS 语言模型 / 量子/混合LLM / MPS/序列建模,1,,
Fractal decompositions and tensor network representations of Bethe wavefunctions,"S Sahu, G Vidal",2024.0,,"We investigate the entanglement structure of a generic $M$-particle Bethe wavefunction (not necessarily an eigenstate of an integrable model) on a 1d lattice by dividing the lattice into $L$ parts and decomposing the wavefunction into a sum of products of $L$ local wavefunctions. Using the fact that a Bethe wavefunction accepts a \textit{fractal} multipartite decomposition -- it can always be written as a linear combination of $L^M$ products of $L$ local wavefunctions, where each local wavefunction is in turn also a Bethe wavefunction -- we then build \textit{exact, analytical} tensor network representations with finite bond dimension $χ=2^M$, for a generic planar tree tensor network (TTN), which includes a matrix product states (MPS) and a regular binary TTN as prominent particular cases. For a regular binary tree, the network has depth $\log_{2}(N/M)$ and can be transformed into an adaptive quantum circuit of the same depth, composed of unitary gates acting on $2^M$-dimensional qudits and mid-circuit measurements, that deterministically prepares the Bethe wavefunction. Finally, we put forward a much larger class of \textit{generalized} Bethe wavefunctions, for which the above decompositions, tensor network and quantum circuit representations are also possible.",,"S Sahu, G Vidal - SciPost Phys. Core 8, 067 (2025)",[],https://arxiv.org/abs/2412.00923,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2412.00923,['https://arxiv.org/pdf/2412.00923'],fractal decompositions and tensor network representations of bethe wavefunctions,TTN/MERA/PEPS,1,"SciPost Phys. Core 8, 067 (2025)",
Functional Tensor Decompositions for Physics-Informed Neural Networks,"S K Vemuri, T Büchner, J Niebling, J Denzler",2024.0,0,"Physics-Informed Neural Networks (PINNs) have shown continuous and increasing promise in approximating partial differential equations (PDEs), although they remain constrained by the curse of dimensionality. In this paper, we propose a generalized PINN version of the classical variable separable method. To do this, we first show that, using the universal approximation theorem, a multivariate function can be approximated by the outer product of neural networks, whose inputs are separated variables. We leverage tensor decomposition forms to separate the variables in a PINN setting. By employing Canonic Polyadic (CP), Tensor-Train (TT), and Tucker decomposition forms within the PINN framework, we create robust architectures for learning multivariate functions from separate neural networks connected by outer products. Our methodology significantly enhances the performance of PINNs, as evidenced by improved results on complex high-dimensional PDEs, including the 3d Helmholtz and 5d Poisson equations, among others. This research underscores the potential of tensor decomposition-based variably separated PINNs to surpass the state-of-the-art, offering a compelling solution to the dimensionality challenge in PDE approximation.",,"S K Vemuri, T Büchner, J Niebling, J Denzler - arXiv preprint arXiv:2408.13101, 2024 - arxiv.org",[],https://arxiv.org/abs/2408.13101,arxiv-completion,2026-09-26 (citations:OpenAlex),,2408.13101,['https://arxiv.org/pdf/2408.13101'],functional tensor decompositions for physics informed neural networks,,1,,
Hybrid Tree Tensor Networks for quantum simulation,"J Schuhmacher, M Ballarin, A Baiardi, G Magnifico, F Tacchino, S Montangero, I Tavernelli",2024.0,0,"Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many operational aspects of hTN-based algorithms, like the optimization of hTNs, the generalization of standard contraction rules to an hybrid setting, and the design of application-oriented architectures have not been thoroughly investigated yet. In this work, we introduce a novel algorithm to perform ground state optimizations with hybrid Tree Tensor Networks (hTTNs), discussing its advantages and roadblocks, and identifying a set of promising applications. We benchmark our approach on two paradigmatic models, namely the Ising model at the critical point and the Toric code Hamiltonian. In both cases, we successfully demonstrate that hTTNs can improve upon classical equivalents with equal bond dimension in the classical part.",,"J Schuhmacher, M Ballarin, A Baiardi, G Magnifico, F Tacchino, S Montangero, I Tavernelli - PRX Quantum 6.1 (2025): 010320",[],https://arxiv.org/abs/2404.05784,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2404.05784,['https://arxiv.org/pdf/2404.05784'],hybrid tree tensor networks for quantum simulation,TTN/MERA/PEPS,1,PRX Quantum 6.1 (2025): 010320,
Nearly tight bounds for testing tree tensor network states,"B Lovitz, A Lowe",2024.0,0,"Tree tensor network states (TTNS) generalize the notion of having low Schmidt-rank to multipartite quantum states, through a parameter known as the bond dimension. This leads to succinct representations of quantum many-body systems with a tree-like entanglement structure. In this work, we study the task of testing whether an unknown pure state is a TTNS on $n$ qudits with bond dimension at most $r$, or is far in trace distance from any such state. We first establish that, independent of the dimension of the state, $O(nr^2)$ copies suffice to accomplish this task with one-sided error. We then prove that $Ω(n r^2/\log n)$ copies are necessary for any test with one-sided error whenever $r\geq 2 + \log n$. In particular, this closes a roughly quadratic gap in the previous bounds for testing matrix product states in this setting. On the other hand, when $r=2$ we show that $Θ(\sqrt{n})$ copies are both necessary and sufficient for the related task of testing whether a state is a product of $n$ bipartite states having Schmidt-rank at most $r$, for some choice of the qudit dimensions. We also study the performance of tests using measurements performed on a small number of copies at a time. Here, we obtain new bounds for testing rank, Schmidt-rank, and TTNS when the tester is restricted to making measurements on $r+1$ copies of the state.",,"B Lovitz, A Lowe - arXiv preprint arXiv:2410.21417, 2024 - arxiv.org",[],https://arxiv.org/abs/2410.21417,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2410.21417,['https://arxiv.org/pdf/2410.21417'],nearly tight bounds for testing tree tensor network states,TTN/MERA/PEPS,1,,
No-Free-Lunch Theories for Tensor-Network Machine Learning Models,"J Wu, Q Ye, D Deng, L Yu",2024.0,0,"Tensor network machine learning models have shown remarkable versatility in tackling complex data-driven tasks, ranging from quantum many-body problems to classical pattern recognitions. Despite their promising performance, a comprehensive understanding of the underlying assumptions and limitations of these models is still lacking. In this work, we focus on the rigorous formulation of their no-free-lunch theorem -- essential yet notoriously challenging to formalize for specific tensor network machine learning models. In particular, we rigorously analyze the generalization risks of learning target output functions from input data encoded in tensor network states. We first prove a no-free-lunch theorem for machine learning models based on matrix product states, i.e., the one-dimensional tensor network states. Furthermore, we circumvent the challenging issue of calculating the partition function for two-dimensional Ising model, and prove the no-free-lunch theorem for the case of two-dimensional projected entangled-pair state, by introducing the combinatorial method associated to the ""puzzle of polyominoes"". Our findings reveal the intrinsic limitations of tensor network-based learning models in a rigorous fashion, and open up an avenue for future analytical exploration of both the strengths and limitations of quantum-inspired machine learning frameworks.",,"J Wu, Q Ye, D Deng, L Yu - arXiv preprint arXiv:2412.05674, 2024 - arxiv.org",[],https://arxiv.org/abs/2412.05674,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2412.05674,['https://arxiv.org/pdf/2412.05674'],no free lunch theories for tensor network machine learning models,TTN/MERA/PEPS,2,,
On the learning abilities of photonic continuous-variable Born machines,"Z Kolarovszki, D T R Nagy, Z Zimborás",2024.0,0,"This paper investigates photonic continuous-variable Born machines (CVBMs), which utilize photonic quantum states as resources for continuous probability distributions. Implementing exact gradient descent in the CVBM training process is often infeasible, bringing forward the need to approximate the gradients using an estimator obtained from a smaller number of samples, obtaining a quantum stochastic gradient descent (SGD) method. In this work, the ability to train CVBMs is analyzed using stochastic gradients obtained using relatively few samples from the probability distribution corresponding to homodyne measurement. The main obstacle to this analysis is that classically simulating CVBMs and obtaining samples is a demanding task, while a large number of iterations are needed to achieve convergence. The present research is enabled by a novel strategy to simulate homodyne detections of generic multimode photonic states using a classical computer. With this approach, a more comprehensive study of CVBMs is made possible, and the training of multimode CVBMs is demonstrated with parametric quantum circuits considerably larger than in previous articles. More specifically, we use the proposed algorithm to demonstrate learning of multimode quantum distributions using CVBMs. Moreover, successful CVBM trainings were demonstrated with the use of stochastic gradients.",,"Z Kolarovszki, D T R Nagy, Z Zimborás - 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), 2024, pp. 750-756",[],https://arxiv.org/abs/2410.11785,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2410.11785,['https://arxiv.org/pdf/2410.11785'],on the learning abilities of photonic continuous variable born machines,MPS 生成/Born机,1,"2024 IEEE International Conference on Quantum Computing and Engineering (QCE), 2024, pp. 750-756",
Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval,"A Wulff, B Chen, M Steinberg, Y Tang, M Möller, S Feld",2024.0,0,"As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters. To adapt this problem for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.",,"A Wulff, B Chen, M Steinberg, Y Tang, M Möller, S Feld - Comput. Methods Appl. Mech. Eng. 432 (2024) 117380",[],https://arxiv.org/abs/2402.06455,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,2402.06455,['https://arxiv.org/pdf/2402.06455'],quantum computing and tensor networks for laminate design a novel approach to stacking sequence retrieval,MPS/序列建模,1,Comput. Methods Appl. Mech. Eng. 432 (2024) 117380,
Randomized algorithms for streaming low-rank approximation in tree tensor network format,"A Bucci, G Verzella",2024.0,,"In this work, we present the tree tensor network Nyström (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nyström approximation for matrices, that is randomized, single-pass, streamable, and cost-effective. Additionally, the structure of the sketching allows for parallel implementation. We provide a deterministic error bound for the algorithm and, in the specific case of Gaussian dimension reduction maps, also a probabilistic one. We also introduce a sequential variant of the algorithm, referred to as sequential tree tensor network Nyström (STTNN), which offers better performance for dense tensors. Furthermore, both algorithms are well-suited for the recompression or rounding of tensors in the tree tensor network format. Numerical experiments highlight the efficiency and effectiveness of the proposed methods.",,"A Bucci, G Verzella - arXiv preprint arXiv:2412.06111, 2024 - arxiv.org",[],https://arxiv.org/abs/2412.06111,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2412.06111,['https://arxiv.org/pdf/2412.06111'],randomized algorithms for streaming low rank approximation in tree tensor network format,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
TT-SNN: Tensor Train Decomposition for Efficient Spiking Neural Network Training,"D Lee, R Yin, Y Kim, A Moitra, Y Li, P Panda",2024.0,0,"Spiking Neural Networks (SNNs) have gained significant attention as a potentially energy-efficient alternative for standard neural networks with their sparse binary activation. However, SNNs suffer from memory and computation overhead due to spatio-temporal dynamics and multiple backpropagation computations across timesteps during training. To address this issue, we introduce Tensor Train Decomposition for Spiking Neural Networks (TT-SNN), a method that reduces model size through trainable weight decomposition, resulting in reduced storage, FLOPs, and latency. In addition, we propose a parallel computation pipeline as an alternative to the typical sequential tensor computation, which can be flexibly integrated into various existing SNN architectures. To the best of our knowledge, this is the first of its kind application of tensor decomposition in SNNs. We validate our method using both static and dynamic datasets, CIFAR10/100 and N-Caltech101, respectively. We also propose a TT-SNN-tailored training accelerator to fully harness the parallelism in TT-SNN. Our results demonstrate substantial reductions in parameter size (7.98X), FLOPs (9.25X), training time (17.7%), and training energy (28.3%) during training for the N-Caltech101 dataset, with negligible accuracy degradation.",,"D Lee, R Yin, Y Kim, A Moitra, Y Li, P Panda - arXiv preprint arXiv:2401.08001, 2024 - arxiv.org",[],https://arxiv.org/abs/2401.08001,arxiv-completion,2026-09-26 (citations:OpenAlex),,2401.08001,['https://arxiv.org/pdf/2401.08001'],tt snn tensor train decomposition for efficient spiking neural network training,,1,,
Tensor Star Tensor Decomposition and Its Applications to Higher-order Compression and Completion,"W Zhou, Y Zheng, Q Zhao, D Mandic",2024.0,0,"A novel tensor decomposition framework, termed Tensor Star (TS) decomposition, is proposed which represents a new type of tensor network decomposition based on tensor contractions. This is achieved by connecting the core tensors in a ring shape, whereby the core tensors act as skip connections between the factor tensors and allow for direct correlation characterisation between any two arbitrary dimensions. Uniquely, this makes it possible to decompose an order-$N$ tensor into $N$ order-$3$ factor tensors $\{\mathcal{G}_{k}\}_{k=1}^{N}$ and $N$ order-$4$ core tensors $\{\mathcal{C}_{k}\}_{k=1}^{N}$, which are arranged in a star shape. Unlike the class of Tensor Train (TT) decompositions, these factor tensors are not directly connected to one another. The so obtained core tensors also enable consecutive factor tensors to have different latent ranks. In this way, the TS decomposition alleviates the ""curse of dimensionality"" and controls the ""curse of ranks"", exhibiting a storage complexity which scales linearly with the number of dimensions and as the fourth power of the ranks.",,"W Zhou, Y Zheng, Q Zhao, D Mandic - arXiv preprint arXiv:2403.10481, 2024 - arxiv.org",[],https://arxiv.org/abs/2403.10481,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2403.10481,['https://arxiv.org/pdf/2403.10481'],tensor star tensor decomposition and its applications to higher order compression and completion,MPO/TT 压缩,1,,
Tensor network approximation of Koopman operators,"D Giannakis, M J L Jebelli, M Montgomery, P Pfeffer, J Schumacher, J Slawinska",2024.0,0,"We propose a tensor network framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approximation of the skew-adjoint Koopman generator by a diagonalizable, skew-adjoint operator $W_τ$ that acts on a reproducing kernel Hilbert space $\mathcal H_τ$ with coalgebra structure and Banach algebra structure under the pointwise product of functions. Leveraging this structure, we lift the unitary evolution operators $e^{t W_τ}$ (which can be thought of as regularized Koopman operators) to a unitary evolution group on the Fock space $F(\mathcal H_τ)$ generated by $\mathcal H_τ$ that acts multiplicatively with respect to the tensor product. Our scheme also employs a representation of classical observables ($L^\infty$ functions of the state) by quantum observables (self-adjoint operators) acting on the Fock space, and a representation of probability densities in $L^1$ by quantum states. Combining these constructions leads to an approximation of the Koopman evolution of observables that is representable as evaluation of a tree tensor network built on a tensor product subspace $\mathcal H_τ^{\otimes n} \subset F(\mathcal H_τ)$ of arbitrarily high grading $n \in \mathbb N$. A key feature of this quantum-inspired approximation is that it captures information from a tensor product space of dimension $(2d+1)^n$, generated from a collection of $2d + 1$ eigenfunctions of $W_τ$. Furthermore, the approximation is positivity preserving. The paper contains a theoretical convergence analysis of the method and numerical applications to two dynamical systems on the 2-torus: an ergodic torus rotation as an example with pure point Koopman spectrum and a Stepanoff flow as an example with topological weak mixing.",,"D Giannakis, M J L Jebelli, M Montgomery, P Pfeffer, J Schumacher, J Slawinska - arXiv preprint arXiv:2407.07242, 2024 - arxiv.org",[],https://arxiv.org/abs/2407.07242,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2407.07242,['https://arxiv.org/pdf/2407.07242'],tensor network approximation of koopman operators,TTN/MERA/PEPS,1,,
Tensor-Train Point Cloud Compression and Efficient Approximate Nearest-Neighbor Search,"G Novikov, A Gneushev, A Kadeishvili, I Oseledets",2024.0,0,"Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and enable fast approximate nearest-neighbor searches. We propose a probabilistic interpretation and utilize density estimation losses like Sliced Wasserstein to train TT decompositions, resulting in robust point cloud compression. We reveal an inherent hierarchical structure within TT point clouds, facilitating efficient approximate nearest-neighbor searches. In our paper, we provide detailed insights into the methodology and conduct comprehensive comparisons with existing methods. We demonstrate its effectiveness in various scenarios, including out-of-distribution (OOD) detection problems and approximate nearest-neighbor (ANN) search tasks.",,"G Novikov, A Gneushev, A Kadeishvili, I Oseledets - arXiv preprint arXiv:2410.04462, 2024 - arxiv.org",[],https://arxiv.org/abs/2410.04462,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2410.04462,['https://arxiv.org/pdf/2410.04462'],tensor train point cloud compression and efficient approximate nearest neighbor search,MPO/TT 压缩,1,,
The State Preparation of Multivariate Normal Distributions using Tree Tensor Network,"H Manabe, Y Sano",2024.0,,"The quantum state preparation of probability distributions is an important subroutine for many quantum algorithms. When embedding $D$-dimensional multivariate probability distributions by discretizing each dimension into $2^n$ points, we need a state preparation circuit comprising a total of $nD$ qubits, which is often difficult to compile. In this study, we propose a scalable method to generate state preparation circuits for $D$-dimensional multivariate normal distributions, utilizing tree tensor networks (TTN). We establish theoretical guarantees that multivariate normal distributions with 1D correlation structures can be efficiently represented using TTN. Based on these analyses, we propose a compilation method that uses automatic structural optimization to find the most efficient network structure and compact circuit. We apply our method to state preparation circuits for various high-dimensional random multivariate normal distributions. The numerical results suggest that our method can dramatically reduce the circuit depth and CNOT count while maintaining fidelity compared to existing approaches.",,"H Manabe, Y Sano - Quantum 9, 1755 (2025)",[],https://arxiv.org/abs/2412.12067,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2412.12067,['https://arxiv.org/pdf/2412.12067'],the state preparation of multivariate normal distributions using tree tensor network,TTN/MERA/PEPS,1,"Quantum 9, 1755 (2025)",
Towards LLM-guided Efficient and Interpretable Multi-linear Tensor Network Rank Selection,"G Iacovides, W Zhou, D Mandic",2024.0,0,"We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs, our approach offers enhanced interpretability of the rank choices and can effectively optimise the objective function. This framework enables users without specialised domain expertise to utilise tensor network decompositions and understand the underlying rationale within the rank selection process. Experimental results validate our method on financial higher-order datasets, demonstrating interpretable reasoning, strong generalisation to unseen test data, and its potential for self-enhancement over successive iterations. This work is placed at the intersection of large language models and higher-order data analysis.",,"G Iacovides, W Zhou, D Mandic - arXiv preprint arXiv:2410.10728, 2024 - arxiv.org",[],https://arxiv.org/abs/2410.10728,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2410.10728,['https://arxiv.org/pdf/2410.10728'],towards llm guided efficient and interpretable multi linear tensor network rank selection,MPS 语言模型,1,,
Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers,"S Bai, S Ran",2024.0,0,"Interpreting the representation and generalization powers has been a long-standing issue in the field of machine learning (ML) and artificial intelligence. This work contributes to uncovering the emergence of universal scaling laws in quantum-probabilistic ML. We take the generative tensor network (GTN) in the form of a matrix product state as an example and show that with an untrained GTN (such as a random TN state), the negative logarithmic likelihood (NLL) $L$ generally increases linearly with the number of features $M$, i.e., $L \simeq k M + const$. This is a consequence of the so-called ``catastrophe of orthogonality,'' which states that quantum many-body states tend to become exponentially orthogonal to each other as $M$ increases. We reveal that while gaining information through training, the linear scaling law is suppressed by a negative quadratic correction, leading to $L \simeq βM - αM^2 + const$. The scaling coefficients exhibit logarithmic relationships with the number of training samples and the number of quantum channels $χ$. The emergence of the quadratic correction term in NLL for the testing (training) set can be regarded as evidence of the generalization (representation) power of GTN. Over-parameterization can be identified by the deviation in the values of $α$ between training and testing sets while increasing $χ$. We further investigate how orthogonality in the quantum feature map relates to the satisfaction of quantum probabilistic interpretation, as well as to the representation and generalization powers of GTN. The unveiling of universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum probabilistic framework.",,"S Bai, S Ran - Chinese Physics Letters 41, 120701 (2024)",[],https://arxiv.org/abs/2410.09703,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2410.09703,['https://arxiv.org/pdf/2410.09703'],universal scaling laws in quantum probabilistic machine learning by tensor network towards interpreting representation and generalization powers,MPS 生成/Born机 / 互信息/标度 / MPS/序列建模,1,"Chinese Physics Letters 41, 120701 (2024)",
CoMERA: Computing- and Memory-Efficient Training via Rank-Adaptive Tensor Optimization,"Z Yang, Z Liu, S Choudhary, X Xie, C Gao, S Kunzmann, Z Zhang",2024.0,,"Training large AI models such as LLMs and DLRMs costs massive GPUs and computing time. The high training cost has become only affordable to big tech companies, meanwhile also causing increasing concerns about the environmental impact. This paper presents CoMERA, a Computing- and Memory-Efficient training method via Rank-Adaptive tensor optimization. CoMERA achieves rank-adaptive tensor-compressed (pre)-training via a multi-objective optimization formulation and improves the training to provide both a high compression ratio and excellent accuracy in the training process. Our optimized numerical computation (e.g., optimized tensorized embedding and tensor-network contractions) and GPU implementation eliminate part of the run-time overhead in the tensorized training on GPU. This leads to, for the first time, $2-3\times$ speedup per training epoch compared with standard training. CoMERA also outperforms the recent GaLore in terms of both memory and computing efficiency. Specifically, CoMERA is $2\times$ faster per training epoch and $9\times$ more memory-efficient than GaLore on a tested six-encoder transformer with single-batch training. Our method also shows $\sim 2\times$ speedup than standard pre-training on a BERT-like code-generation LLM while achieving $4.23\times$ compression ratio in pre-training. With further HPC optimization, CoMERA may reduce the pre-training cost of many other LLMs. An implementation of CoMERA is available at https://github.com/ziyangjoy/CoMERA.",,"Z Yang, Z Liu, S Choudhary, X Xie, C Gao, S Kunzmann, Z Zhang - arXiv preprint arXiv:2405.14377, 2024 - arxiv.org",[],https://arxiv.org/abs/2405.14377,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2405.14377,['https://arxiv.org/pdf/2405.14377'],comera computing and memory efficient training via rank adaptive tensor optimization,张量化Transformer / MPO/TT 压缩,1,,
DoTA: Weight-Decomposed Tensor Adaptation for Large Language Models,"X Hu, X Cheng, P Liu, W Liu, J Luan, B Wang, Y Liu",2024.0,,"Low-rank adaptation (LoRA) reduces the computational and memory demands of fine-tuning large language models (LLMs) by approximating updates with low-rank matrices. However, low-rank approximation in two-dimensional space fails to capture high-dimensional structures within the target matrix. Recently, tensor decomposition methods have been explored for fine-tuning LLMs, leveraging their ability to extract structured information. Yet, these approaches primarily rely on random initialization, and the impact of initialization on tensor adaptation remains underexplored. In this paper, we reveal that random initialization significantly diverges from the validation loss achieved by full fine-tuning. To address this, we propose Weight-Decomposed Tensor Adaptation (DoTA), which leverages the Matrix Product Operator (MPO) decomposition of pre-trained weights for effective initialization in fine-tuning LLMs. Additionally, we introduce QDoTA, a quantized version of DoTA designed for 4-bit quantization. Experiments on commonsense and arithmetic reasoning tasks show that DoTA outperforms random initialization methods with fewer parameters. QDoTA further reduces memory consumption and achieves comparable performance to DoTA on commonsense reasoning tasks. We will release our code to support future research.",,"X Hu, X Cheng, P Liu, W Liu, J Luan, B Wang, Y Liu - arXiv preprint arXiv:2412.20891, 2024 - arxiv.org",[],https://arxiv.org/abs/2412.20891,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2412.20891,['https://arxiv.org/pdf/2412.20891'],dota weight decomposed tensor adaptation for large language models,MPS 语言模型 / MPO/TT 压缩,1,,
Tensor Train Low-rank Approximation (TT-LoRA): Democratizing AI with Accelerated LLMs,"A Anjum, M E Eren, I Boureima, B Alexandrov, M Bhattarai",2024.0,,"In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing (NLP) tasks, such as question-answering, sentiment analysis, text summarization, and machine translation. However, the ever-growing complexity of LLMs demands immense computational resources, hindering the broader research and application of these models. To address this, various parameter-efficient fine-tuning strategies, such as Low-Rank Approximation (LoRA) and Adapters, have been developed. Despite their potential, these methods often face limitations in compressibility. Specifically, LoRA struggles to scale effectively with the increasing number of trainable parameters in modern large scale LLMs. Additionally, Low-Rank Economic Tensor-Train Adaptation (LoRETTA), which utilizes tensor train decomposition, has not yet achieved the level of compression necessary for fine-tuning very large scale models with limited resources. This paper introduces Tensor Train Low-Rank Approximation (TT-LoRA), a novel parameter-efficient fine-tuning (PEFT) approach that extends LoRETTA with optimized tensor train (TT) decomposition integration. By eliminating Adapters and traditional LoRA-based structures, TT-LoRA achieves greater model compression without compromising downstream task performance, along with reduced inference latency and computational overhead. We conduct an exhaustive parameter search to establish benchmarks that highlight the trade-off between model compression and performance. Our results demonstrate significant compression of LLMs while maintaining comparable performance to larger models, facilitating their deployment on resource-constraint platforms.",,"A Anjum, M E Eren, I Boureima, B Alexandrov, M Bhattarai - arXiv preprint arXiv:2408.01008, 2024 - arxiv.org",[],https://arxiv.org/abs/2408.01008,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2408.01008,['https://arxiv.org/pdf/2408.01008'],tensor train low rank approximation tt lora democratizing ai with accelerated llms,MPS 语言模型 / MPO/TT 压缩,1,,
LoRETTA: Low-Rank Economic Tensor-Train Adaptation for Ultra-Low-Parameter Fine-Tuning of Large Language Models,"Y Yang, J Zhou, N Wong, Z Zhang",2024.0,,"Various parameter-efficient fine-tuning (PEFT) techniques have been proposed to enable computationally efficient fine-tuning while maintaining model performance. However, existing PEFT methods are still limited by the growing number of trainable parameters with the rapid deployment of Large Language Models (LLMs). To address this challenge, we present LoRETTA, an ultra-parameter-efficient framework that significantly reduces trainable parameters through tensor-train decomposition. Specifically, we propose two methods, named {LoRETTA}$_{adp}$ and {LoRETTA}$_{rep}$. The former employs tensorized adapters, offering a high-performance yet lightweight approach for the fine-tuning of LLMs. The latter emphasizes fine-tuning via weight parameterization with a set of small tensor factors. LoRETTA achieves comparable or better performance than most widely used PEFT methods with up to $100\times$ fewer parameters on the LLaMA-2-7B models. Furthermore, empirical results demonstrate that the proposed method effectively improves training efficiency, enjoys better multi-task learning performance, and enhances the anti-overfitting capability. Plug-and-play codes built upon the Huggingface framework and PEFT library will be released.",,"Y Yang, J Zhou, N Wong, Z Zhang - arXiv preprint arXiv:2402.11417, 2024 - arxiv.org",[],https://arxiv.org/abs/2402.11417,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2402.11417,['https://arxiv.org/pdf/2402.11417'],loretta low rank economic tensor train adaptation for ultra low parameter fine tuning of large language models,MPS 语言模型 / MPO/TT 压缩,1,,
LoRTA: Low Rank Tensor Adaptation of Large Language Models,"I Hounie, C Kanatsoulis, A Tandon, A Ribeiro",2024.0,,"Low Rank Adaptation (LoRA) is a popular Parameter Efficient Fine Tuning (PEFT) method that effectively adapts large pre-trained models for downstream tasks. LoRA parameterizes model updates using low-rank matrices at each layer, significantly reducing the number of trainable parameters and, consequently, resource requirements during fine-tuning. However, the lower bound on the number of trainable parameters remains high due to the use of the low-rank matrix model. Recent works have addressed this limitation by proposing low rank tensor parameterizations for model updates. However, they only exploit redundancy across layers, or tensorize individual matrices using ad-hoc schemes that introduce additional hyperparameters. In this work, we propose a higher-order Candecomp/Parafac (CP) decomposition, enabling a more compact and flexible representation compared to existing matrix and tensor based PEFT methods. Our experiments on Natural Language Understanding, Instruction Tuning, Preference Optimization and Protein Folding benchmarks demonstrate that our method can achieve a reduction in the number of parameters while maintaining comparable performance.",,"I Hounie, C Kanatsoulis, A Tandon, A Ribeiro - arXiv preprint arXiv:2410.04060, 2024 - arxiv.org",[],https://arxiv.org/abs/2410.04060,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2410.04060,['https://arxiv.org/pdf/2410.04060'],lorta low rank tensor adaptation of large language models,MPS 语言模型 / MPO/TT 压缩,1,,
LoTR: Low Tensor Rank Weight Adaptation,"D Bershatsky, D Cherniuk, T Daulbaev, A Mikhalev, I Oseledets",2024.0,,"In this paper we generalize and extend an idea of low-rank adaptation (LoRA) of large language models (LLMs) based on Transformer architecture. Widely used LoRA-like methods of fine-tuning LLMs are based on matrix factorization of gradient update. We introduce LoTR, a novel approach for parameter-efficient fine-tuning of LLMs which represents a gradient update to parameters in a form of tensor decomposition. Low-rank adapter for each layer is constructed as a product of three matrices, and tensor structure arises from sharing left and right multipliers of this product among layers. Simultaneous compression of a sequence of layers with low-rank tensor representation allows LoTR to archive even better parameter efficiency then LoRA especially for deep models. Moreover, the core tensor does not depend on original weight dimension and can be made arbitrary small, which allows for extremely cheap and fast downstream fine-tuning.",,"D Bershatsky, D Cherniuk, T Daulbaev, A Mikhalev, I Oseledets - arXiv preprint arXiv:2402.01376, 2024 - arxiv.org",[],https://arxiv.org/abs/2402.01376,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2402.01376,['https://arxiv.org/pdf/2402.01376'],lotr low tensor rank weight adaptation,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩 / MPS/序列建模,1,,
TQCompressor: improving tensor decomposition methods in neural networks via permutations,"V Abronin, A Naumov, D Mazur, D Bystrov, K Tsarova, A Melnikov, I Oseledets, S Dolgov, R Brasher, M Perelshtein",2024.0,,"We introduce TQCompressor, a novel method for neural network model compression with improved tensor decompositions. We explore the challenges posed by the computational and storage demands of pre-trained language models in NLP tasks and propose a permutation-based enhancement to Kronecker decomposition. This enhancement makes it possible to reduce loss in model expressivity which is usually associated with factorization. We demonstrate this method applied to the GPT-2$_{small}$. The result of the compression is TQCompressedGPT-2 model, featuring 81 mln. parameters compared to 124 mln. in the GPT-2$_{small}$. We make TQCompressedGPT-2 publicly available. We further enhance the performance of the TQCompressedGPT-2 through a training strategy involving multi-step knowledge distillation, using only a 3.1% of the OpenWebText. TQCompressedGPT-2 surpasses DistilGPT-2 and KnGPT-2 in comparative evaluations, marking an advancement in the efficient and effective deployment of models in resource-constrained environments.",,"V Abronin, A Naumov, D Mazur, D Bystrov, K Tsarova, A Melnikov, I Oseledets, S Dolgov, R Brasher, M Perelshtein - arXiv preprint arXiv:2401.16367, 2024 - arxiv.org",[],https://arxiv.org/abs/2401.16367,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2401.16367,['https://arxiv.org/pdf/2401.16367'],tqcompressor improving tensor decomposition methods in neural networks via permutations,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩,1,,
Unlocking Data-free Low-bit Quantization with Matrix Decomposition for KV Cache Compression,"P Liu, Z Gao, W X Zhao, Y Ma, T Wang, J Wen",2024.0,,"Key-value~(KV) caching is an important technique to accelerate the inference of large language models~(LLMs), but incurs significant memory overhead. To compress the size of KV cache, existing methods often compromise precision or require extra data for calibration, limiting their practicality in LLM deployment. In this paper, we introduce \textbf{DecoQuant}, a novel data-free low-bit quantization technique based on tensor decomposition methods, to effectively compress KV cache. Our core idea is to adjust the outlier distribution of the original matrix by performing tensor decomposition, so that the quantization difficulties are migrated from the matrix to decomposed local tensors. Specially, we find that outliers mainly concentrate on small local tensors, while large tensors tend to have a narrower value range. Based on this finding, we propose to apply low-bit quantization to the large tensor, while maintaining high-precision representation for the small tensor. Furthermore, we utilize the proposed quantization method to compress the KV cache of LLMs to accelerate the inference and develop an efficient dequantization kernel tailored specifically for DecoQuant. Through extensive experiments, DecoQuant demonstrates remarkable efficiency gains, showcasing up to a $\sim$75\% reduction in memory footprint while maintaining comparable generation quality.",,"P Liu, Z Gao, W X Zhao, Y Ma, T Wang, J Wen - arXiv preprint arXiv:2405.12591, 2024 - arxiv.org",[],https://arxiv.org/abs/2405.12591,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2405.12591,['https://arxiv.org/pdf/2405.12591'],unlocking data free low bit quantization with matrix decomposition for kv cache compression,MPS 语言模型 / MPO/TT 压缩,1,,
Bilinear MLPs enable weight-based mechanistic interpretability,"M T Pearce, T Dooms, A Rigg, J M Oramas, L Sharkey",2024.0,,"A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.",,"M T Pearce, T Dooms, A Rigg, J M Oramas, L Sharkey - arXiv preprint arXiv:2410.08417, 2024 - arxiv.org",[],https://arxiv.org/abs/2410.08417,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2410.08417,['https://arxiv.org/pdf/2410.08417'],bilinear mlps enable weight based mechanistic interpretability,MPS 语言模型 / MPO/TT 压缩,1,,
An introduction to graphical tensor notation for mechanistic interpretability,J K Taylor,2024.0,,"Graphical tensor notation is a simple way of denoting linear operations on tensors, originating from physics. Modern deep learning consists almost entirely of operations on or between tensors, so easily understanding tensor operations is quite important for understanding these systems. This is especially true when attempting to reverse-engineer the algorithms learned by a neural network in order to understand its behavior: a field known as mechanistic interpretability. It's often easy to get confused about which operations are happening between tensors and lose sight of the overall structure, but graphical tensor notation makes it easier to parse things at a glance and see interesting equivalences. The first half of this document introduces the notation and applies it to some decompositions (SVD, CP, Tucker, and tensor network decompositions), while the second half applies it to some existing some foundational approaches for mechanistically understanding language models, loosely following ``A Mathematical Framework for Transformer Circuits'', then constructing an example ``induction head'' circuit in graphical tensor notation.",,"J K Taylor - arXiv preprint arXiv:2402.01790, 2024 - arxiv.org",[],https://arxiv.org/abs/2402.01790,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2402.01790,['https://arxiv.org/pdf/2402.01790'],an introduction to graphical tensor notation for mechanistic interpretability,MPS 语言模型 / 张量化Transformer,1,,
What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?,"L Loconte, A Mari, G Gala, R Peharz, C d Campos, E Quaeghebeur, G Vessio, A Vergari",2024.0,,"This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can benefit both communities. Our work generalizes popular tensor factorizations within the circuit language, and unifies various circuit learning algorithms under a single, generalized hierarchical factorization framework. Specifically, we introduce a modular ""Lego block"" approach to build tensorized circuit architectures. This, in turn, allows us to systematically construct and explore various circuit and tensor factorization models while maintaining tractability. This connection not only clarifies similarities and differences in existing models, but also enables the development of a comprehensive pipeline for building and optimizing new circuit/tensor factorization architectures. We show the effectiveness of our framework through extensive empirical evaluations, and highlight new research opportunities for tensor factorizations in probabilistic modeling.",,"L Loconte, A Mari, G Gala, R Peharz, C d Campos, E Quaeghebeur, G Vessio, A Vergari - Transactions on Machine Learning Research, 2025",[],https://arxiv.org/abs/2409.07953,arxiv-completion,2026-09-26 (citations:OpenAlex),,2409.07953,['https://arxiv.org/pdf/2409.07953'],what is the relationship between tensor factorizations and circuits and how can we exploit it,,1,"Transactions on Machine Learning Research, 2025",
Interpretable Tensor Fusion,"S Varshneya, A Ledent, P Liznerski, A Balinskyy, P Mehta, W Mustafa, M Kloft",2024.0,,"Conventional machine learning methods are predominantly designed to predict outcomes based on a single data type. However, practical applications may encompass data of diverse types, such as text, images, and audio. We introduce interpretable tensor fusion (InTense), a multimodal learning method for training neural networks to simultaneously learn multimodal data representations and their interpretable fusion. InTense can separately capture both linear combinations and multiplicative interactions of diverse data types, thereby disentangling higher-order interactions from the individual effects of each modality. InTense provides interpretability out of the box by assigning relevance scores to modalities and their associations. The approach is theoretically grounded and yields meaningful relevance scores on multiple synthetic and real-world datasets. Experiments on six real-world datasets show that InTense outperforms existing state-of-the-art multimodal interpretable approaches in terms of accuracy and interpretability.",,"S Varshneya, A Ledent, P Liznerski, A Balinskyy, P Mehta, W Mustafa, M Kloft - arXiv preprint arXiv:2405.04671, 2024 - arxiv.org",[],https://arxiv.org/abs/2405.04671,arxiv-completion,2026-09-26 (citations:OpenAlex),,2405.04671,['https://arxiv.org/pdf/2405.04671'],interpretable tensor fusion,,1,,
A Tensor Decomposition Perspective on Second-order RNNs,"M Lizaire, M Rizvi-Martel, M G A Hameed, G Rabusseau",2024.0,,"Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied models from formal language theory. However, their large parameter tensor makes computations intractable. To circumvent this issue, one approach known as MIRNN consists in limiting the type of interactions used by the model. Another is to leverage tensor decomposition to diminish the parameter count. In this work, we study the model resulting from parameterizing 2RNNs using the CP decomposition, which we call CPRNN. Intuitively, the rank of the decomposition should reduce expressivity. We analyze how rank and hidden size affect model capacity and show the relationships between RNNs, 2RNNs, MIRNNs, and CPRNNs based on these parameters. We support these results empirically with experiments on the Penn Treebank dataset which demonstrate that, with a fixed parameter budget, CPRNNs outperforms RNNs, 2RNNs, and MIRNNs with the right choice of rank and hidden size.",,"M Lizaire, M Rizvi-Martel, M G A Hameed, G Rabusseau - arXiv preprint arXiv:2406.05045, 2024 - arxiv.org",[],https://arxiv.org/abs/2406.05045,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,2406.05045,['https://arxiv.org/pdf/2406.05045'],a tensor decomposition perspective on second order rnns,MPS/序列建模 / 量子启发综述,1,,
Quantum generative adversarial network based on the quantum Born machine,"Y Ding, Z Li, N Zhou",2025.0,54,"… Quantum Born machines are regarded as implicit generative models that can directly sample and efficiently generate new data [52]. As illustrated in Fig. 1, the QBMs perform the …",381qPTvCOQ8J,"Y Ding, Z Li, N Zhou - Advanced Engineering Informatics, 2025 - Elsevier",[],https://www.sciencedirect.com/science/article/pii/S1474034625005154,unknown,unknown,MPS 生成/Born机,,[],quantum generative adversarial network based on the quantum born machine,MPS 生成/Born机,1,,
Tensor networks and efficient descriptions of classical data,"S Lu, M Kanász-Nagy, I Kukuljan, JI Cirac",2025.0,43,"… IV and V, we analyze the mutual information scaling in images and text numerically and introduce toy models to interpret the power-law scaling of both MI and correlations in text. Finally…",oVAH7Mh9uzoJ,"S Lu, M Kanász-Nagy, I Kukuljan, JI Cirac - Physical Review A, 2025 - APS",['https://link.aps.org/pdf/10.1103/PhysRevA.111.032409'],https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.032409,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PhysRevA.111.032409'],tensor networks and efficient descriptions of classical data,互信息/标度,1,,
Spin- Kagome Heisenberg Antiferromagnet: Machine Learning Discovery of the Spinon Pair-Density-Wave Ground State,"T Đurić, JH Chung, B Yang, P Sengupta",2025.0,28,"… a novel machine learning technique … predicted Z2 or U(1) Dirac spin-liquid states, our results strongly indicate that the ground state of the kagome lattice antiferromagnet is a spinon pair …",iXcB1HNuB_YJ,"T Đurić, JH Chung, B Yang, P Sengupta - Physical Review X, 2025 - APS",['https://link.aps.org/pdf/10.1103/PhysRevX.15.011047'],https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011047,unknown,unknown,TTN/MERA/PEPS,,['https://link.aps.org/pdf/10.1103/PhysRevX.15.011047'],spin kagome heisenberg antiferromagnet machine learning discovery of the spinon pair density wave ground state,TTN/MERA/PEPS,1,,
Agent-q: fine-tuning large language models for quantum circuit generation and optimization,"L Jern, V Uotila, C Yu, B Zhao",2025.0,25,"… , the method aims to circumvent specific problems that the current variational methods … large language models and our approach to building a pipeline for generating quantum circuits. …",iQ9nYN1KTuoJ,"L Jern, V Uotila, C Yu, B Zhao - … Conference on Quantum …, 2025 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2504.11109'],https://ieeexplore.ieee.org/abstract/document/11250264/,unknown,unknown,量子/混合LLM,,['https://arxiv.org/pdf/2504.11109'],agent q fine tuning large language models for quantum circuit generation and optimization,量子/混合LLM,1,,
Entanglement and the density matrix renormalization group in the generalized Landau paradigm,"L Lootens, C Delcamp, F Verstraete",2025.0,24,"The fields of entanglement theory and tensor networks have recently emerged as central tools for characterizing quantum phases of matter. Here we determine the entanglement structure of ground states of gapped symmetric quantum lattice models and use this to obtain the most efficient tensor network representation of those ground states. We do this by showing that degeneracies in the entanglement spectrum arise through a duality transformation of the original model to the unique dual model where the entire dual symmetry is spontaneously broken. Physically, this duality transformation amounts to a-potentially twisted-gauging of the unbroken symmetry in the original ground state. In general, the dual symmetries of the resulting models are generalized non-invertible symmetries that cannot be described by groups. This result has strong implications for the complexity of simulating many-body systems using variational tensor network methods. For every phase in the phase diagram, the dual representation of the ground state that completely breaks the symmetry minimizes both the entanglement entropy and the required number of variational parameters. We demonstrate the applicability of this idea by developing a generalized density matrix renormalization group algorithm that works on constrained Hilbert spaces and quantify the computational gains obtained over traditional tensor network methods in a perturbed Heisenberg model. Our work testifies to the usefulness of generalized non-invertible symmetries and their formal category theoretic description for the practical simulation of strongly correlated systems.",dtXp0FyPdjoJ,"L Lootens, C Delcamp, F Verstraete - Nature Physics, 2025 - nature.com",['https://www.nature.com/articles/s41567-025-02961-2.pdf'],https://www.nature.com/articles/s41567-025-02961-2,unknown,unknown,互信息/标度,,['https://www.nature.com/articles/s41567-025-02961-2.pdf'],entanglement and the density matrix renormalization group in the generalized landau paradigm,互信息/标度,1,Nature Physics,
Thermalization from quantum entanglement: Jet simulations in the massive Schwinger model,"A Florio, D Frenklakh, S Grieninger, DE Kharzeev…",2025.0,24,"We investigate the emergence of thermalization in a quantum-field-theoretic model mimicking the production of jets in QCD: the massive lattice Schwinger model coupled to external sources. Specifically, we compute the expectation values of local operators as functions of time and compare them to their thermal counterparts, quantify the overlap between the evolving density matrix and the thermal one, and compare the dynamics of the energy-momentum tensor to predictions from relativistic hydrodynamics. Through these studies, we find that the system approaches thermalization at late times and elucidate the mechanisms by which quantum entanglement drives thermalization in closed field-theoretic systems. Our results show how thermodynamic behavior emerges in real time from unitary quantum dynamics.",3lcLyf6Q-osJ,"A Florio, D Frenklakh, S Grieninger, DE Kharzeev… - Physical Review D, 2025 - APS",['https://link.aps.org/pdf/10.1103/sgrx-jpp9'],https://link.aps.org/doi/10.1103/sgrx-jpp9,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/sgrx-jpp9'],thermalization from quantum entanglement jet simulations in the massive schwinger model,互信息/标度,1,Physical review. D/Physical review. D.,
Direct entanglement detection of quantum systems using machine learning,"Y Huang, L Che, C Wei, F Xu, X Nie, J Li, D Lu…",2025.0,23,"… predicted entanglement by the machine learning model falls below a threshold, say 5 × 10 −3 , we consider the state … designed to detect entanglement in states prepared in our own …",q14zU2kIQYQJ,"Y Huang, L Che, C Wei, F Xu, X Nie, J Li, D Lu… - npj Quantum …, 2025 - nature.com",['https://www.nature.com/articles/s41534-025-00970-w.pdf'],https://www.nature.com/articles/s41534-025-00970-w,unknown,unknown,TTN/MERA/PEPS,,['https://www.nature.com/articles/s41534-025-00970-w.pdf'],direct entanglement detection of quantum systems using machine learning,TTN/MERA/PEPS,1,,
Tensor networks for explainable machine learning in cybersecurity,"B Aizpurua, S Palmer, R Orús",2025.0,21,"… Last but not least, our MPS model can be scaled easily to datasets with a huge number of … The incorporation of mutual information into our MPS framework allows to understand the …",r-vs79p1higJ,"B Aizpurua, S Palmer, R Orús - Neurocomputing, 2025 - Elsevier",[],https://www.sciencedirect.com/science/article/pii/S0925231225008835,unknown,unknown,互信息/标度,2401.00867,['https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=4899212'],tensor networks for explainable machine learning in cybersecurity,互信息/标度,2,Neurocomputing,
A review of state-of-the-art techniques for large language model compression,"PV Dantas, LC Cordeiro, WSS Junior",2025.0,19,"… of large language models (LLMs) has driven significant progress in natural language processing … This work presents a comprehensive review of state-of-the-art compression techniques, …",0arLmTK1_vAJ,"PV Dantas, LC Cordeiro, WSS Junior - Complex & Intelligent Systems, 2025 - Springer",['https://link.springer.com/content/pdf/10.1007/s40747-025-02019-z.pdf'],https://link.springer.com/article/10.1007/s40747-025-02019-z,unknown,unknown,MPO/TT 压缩,,['https://link.springer.com/content/pdf/10.1007/s40747-025-02019-z.pdf'],a review of state of the art techniques for large language model compression,MPO/TT 压缩,1,,
Compressing neural networks using tensor networks with exponentially fewer variational parameters,"Y Qing, K Li, PF Zhou, SJ Ran",2025.0,17,"… Denoting the parameters to be compressed as tensor T, our idea is to represent T as the contraction of an ADTN with multiple layers. The structure of the ADTN is flexible. Here, we …",zaC_0qi33JIJ,"Y Qing, K Li, PF Zhou, SJ Ran - Intelligent Computing, 2025 - spj.science.org",['https://spj.science.org/doi/pdf/10.34133/icomputing.0123'],https://spj.science.org/doi/abs/10.34133/icomputing.0123,unknown,unknown,MPO/TT 压缩,,['https://spj.science.org/doi/pdf/10.34133/icomputing.0123'],compressing neural networks using tensor networks with exponentially fewer variational parameters,MPO/TT 压缩,1,,
Fermionic born machines: Classical training of quantum generative models based on fermion sampling,"B Bakó, Z Kolarovszki, Z Zimborás",2025.0,14,"Quantum generative learning is a promising application of quantum computers, but faces several trainability challenges, including the difficulty in experimental gradient estimations. For certain structured quantum generative models, however, expectation values of local observables can be efficiently computed on a classical computer, enabling fully classical training without quantum gradient evaluations. Although training is classically efficient, sampling from these circuits is still believed to be classically hard, so inference must be carried out on a quantum device, potentially yielding a computational advantage. In this work, we introduce Fermionic Born Machines as an example of such classically trainable quantum generative models. The model employs parameterized magic states and fermionic linear optical (FLO) transformations with learnable parameters. The training exploits a decomposition of the magic states into Gaussian operators, which permits efficient estimation of expectation values. Furthermore, the specific structure of the ansatz induces a loss landscape that exhibits favorable characteristics for optimization. The FLO circuits can be implemented, via fermion-to-qubit mappings, on qubit architectures to sample from the learned distribution during inference. Numerical experiments on systems up to 160 qubits demonstrate the effectiveness of our model and training framework.",R8Gf6AV3SMgJ,"B Bakó, Z Kolarovszki, Z Zimborás - arXiv preprint arXiv:2511.13844, 2025 - arxiv.org",['https://arxiv.org/pdf/2511.13844'],https://arxiv.org/abs/2511.13844,unknown,unknown,MPS 生成/Born机,2511.13844,['https://arxiv.org/pdf/2511.13844'],fermionic born machines classical training of quantum generative models based on fermion sampling,MPS 生成/Born机,1,,
Quantum large language model fine-tuning,"SH Kim, J Mei, C Girotto, M Yamada…",2025.0,14,"We introduce a hybrid quantum-classical deep learning architecture for large language model fine-tuning. The classical portion of the architecture is a sentence transformer that is powerful enough to display significant accuracy for complex tasks such as sentiment prediction. The quantum portion of the architecture consists of parameterized quantum circuits that utilize long-range connections between qubits. We analyze the performance of the hybrid models for various settings of hyperparameters, including the number of qubits, the depth of the quantum circuits, learning rate, number of reuploading steps, etc. Based on a screening study of main effects, we show an overall improvement in prediction accuracy over a comparable classical baseline, with a trend of increasing accuracy with number of qubits. We observe up to 3.14% improvements in accuracy over classical architectures of comparable model size, within the set of hyperparameters probed in this study. We demonstrate the contribution of each module in our architecture through ablation studies. Our studies are based on finite shot-counts and include simulations based on noisy quantum gates.",szSRgBHG2B0J,"SH Kim, J Mei, C Girotto, M Yamada… - … on Quantum …, 2025 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2504.08732'],https://ieeexplore.ieee.org/abstract/document/11250157/,unknown,unknown,量子/混合LLM,,['https://arxiv.org/pdf/2504.08732'],quantum large language model fine tuning,量子/混合LLM,1,,
A matrix product state model for simultaneous classification and generation,"A Mossi, B Žunkovič, K Flouris",2025.0,12,"… quantum methods, specifically the Matrix Product States (MPS), … model, in which the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model …",4MpCQerNL8AJ,"A Mossi, B Žunkovič, K Flouris - Quantum Machine Intelligence, 2025 - Springer",['https://link.springer.com/content/pdf/10.1007/s42484-025-00272-6.pdf'],https://link.springer.com/article/10.1007/s42484-025-00272-6,unknown,unknown,MPS 语言模型,,['https://link.springer.com/content/pdf/10.1007/s42484-025-00272-6.pdf'],a matrix product state model for simultaneous classification and generation,MPS 生成/Born机 / MPS 语言模型,2,,
Application of large language models to quantum state simulation,"S Zhou, R Chen, Z An, C Zhang, SY Hou",2025.0,12,"… Large Language Models (LLMs) to simulate quantum circuits. This paper details the process of constructing 1-qubit and 2-qubit quantum simulator models, … a variational quantum circuit …",go7-l3F4VXcJ,"S Zhou, R Chen, Z An, C Zhang, SY Hou - Science China Physics …, 2025 - Springer",['https://www.sciengine.com/doi/pdf/549C67C1B1794F26BC1F34DF5796D4BE'],https://link.springer.com/article/10.1007/s11433-024-2598-y,unknown,unknown,量子/混合LLM,2410.06629,['https://www.sciengine.com/doi/pdf/549C67C1B1794F26BC1F34DF5796D4BE'],application of large language models to quantum state simulation,量子/混合LLM,1,,
Simulating quantum circuits using the multi-scale entanglement renormalization ansatz,"AV Berezutskii, IA Luchnikov, AK Fedorov",2025.0,12,"… system size, MERA supports logarithmic entanglement entropy scaling with length of a 1D … of the entanglement entropy perfectly matches the scaling of the entanglement entropy of …",dr2u-aU8vhkJ,"AV Berezutskii, IA Luchnikov, AK Fedorov - Physical Review Research, 2025 - APS",['https://link.aps.org/pdf/10.1103/PhysRevResearch.7.013063'],https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013063,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/PhysRevResearch.7.013063'],simulating quantum circuits using the multi scale entanglement renormalization ansatz,互信息/标度,1,,
Steps: sequential probability tensor estimation for text-to-image hard prompt search,"Y Qiu, A Wang, C Li, H Huang, G Zhou…",2025.0,11,"Recent text-to-image (T2I) diffusion models have demonstrated remarkable capabilities in visual synthesis, yet their performance heavily relies on the quality of input prompts. However, optimizing discrete prompts remains challenging because the discrete nature of tokens prevents the direct application of the gradient descent method and the vast search space of possible token combinations. As a result, existing approaches either suffer from quantization errors when employing continuous optimization techniques or be- come trapped in local optima due to coordinate-wise greedy search. In this paper, we propose STEPS, a novel Sequential probability Tensor Estimation approach for hard Prompt Search. Our method reformulates discrete prompt optimization as a sequential probability tensor estimation problem, leveraging the inherent low-rank characteristics to address the curse of dimensionality. To further improve the computational efficiency, we develop a memory-bounded sampling approach that shrinks the prompt space without the iteration step dependency while preserving sequential optimization dynamics. Extensive experiments on various public datasets demonstrate that our method consistently outperforms existing approaches in T2I generation, cross-model prompt transferability, and harmful prompt optimization, validating the effectiveness of the proposed framework.",yF5sOrFqG9sJ,"Y Qiu, A Wang, C Li, H Huang, G Zhou… - 2025 IEEE/CVF …, 2025 - ieeexplore.ieee.org",['https://openaccess.thecvf.com/content/CVPR2025/papers/Qiu_STEPS_Sequential_Probability_Tensor_Estimation_for_Text-to-Image_Hard_Prompt_Search_CVPR_2025_paper.pdf'],https://ieeexplore.ieee.org/abstract/document/11092817/,unknown,unknown,MPS/序列建模,,['https://openaccess.thecvf.com/content/CVPR2025/papers/Qiu_STEPS_Sequential_Probability_Tensor_Estimation_for_Text-to-Image_Hard_Prompt_Search_CVPR_2025_paper.pdf'],steps sequential probability tensor estimation for text to image hard prompt search,MPS/序列建模,1,,
Matrix product states as observations of entangled hidden Markov models: A. Souissi,A Souissi,2025.0,10,… This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a …,jK7ZahwOlAYJ,"A Souissi - Journal of Statistical Physics, 2025 - Springer",['https://arxiv.org/pdf/2502.12641'],https://link.springer.com/article/10.1007/s10955-025-03472-3,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/2502.12641'],matrix product states as observations of entangled hidden markov models a souissi,MPS 语言模型,1,,
Sequence processing with quantum-inspired tensor networks,"C Harvey, R Yeung, K Meichanetzidis",2025.0,10,"… tensor network models for sequence processing motivated by correspondence to probabilistic graphical models… -dimensional tensor networks for probabilistic sequence modelling25,48,…",EtgcpB2Pt2gJ,"C Harvey, R Yeung, K Meichanetzidis - Scientific Reports, 2025 - nature.com",['https://www.nature.com/articles/s41598-024-84295-2.pdf'],https://www.nature.com/articles/s41598-024-84295-2,unknown,unknown,MPS/序列建模,,['https://www.nature.com/articles/s41598-024-84295-2.pdf'],sequence processing with quantum inspired tensor networks,MPS/序列建模,1,,
Tensor tree learns hidden relational structures in data to construct generative models,"K Harada, T Okubo, N Kawashima",2025.0,10,"… tensor tree network with the Born machine framework, we propose a general method for constructing a generative model … a tensor network with no loop, which we call tensor tree. Each …",RP7OqdTaAPsJ,"K Harada, T Okubo, N Kawashima - Machine Learning: Science …, 2025 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/2632-2153/adc2c7/pdf'],https://iopscience.iop.org/article/10.1088/2632-2153/adc2c7/meta,unknown,unknown,TTN/MERA/PEPS,2408.10669,['https://iopscience.iop.org/article/10.1088/2632-2153/adc2c7/pdf'],tensor tree learns hidden relational structures in data to construct generative models,TTN/MERA/PEPS,1,Mach. Learn.: Sci. Technol. 6 025002 (2025),
Trawl: Tensor reduced and approximated weights for large language models,"Y Luo, H Patel, Y Fu, D Ahn, J Chen, Y Dong…",2025.0,10,"… We propose a post-training compression approach that uses tensor decomposition … language models and three benchmark datasets, the extent to which they generalize to other models …",o8BbZzgcWpQJ,"Y Luo, H Patel, Y Fu, D Ahn, J Chen, Y Dong… - Pacific-Asia Conference …, 2025 - Springer",['https://arxiv.org/pdf/2406.17261?'],https://link.springer.com/chapter/10.1007/978-981-96-8298-0_32,unknown,unknown,MPO/TT 压缩,,['https://arxiv.org/pdf/2406.17261?'],trawl tensor reduced and approximated weights for large language models,MPO/TT 压缩,1,,
Embedding of tree tensor networks into shallow quantum circuits,"S Sugawara, K Inomata, T Okubo, S Todo",2025.0,9,"Variational Quantum Algorithms (VQAs) are being highlighted as key quantum algorithms for demonstrating quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices, which are limited to executing shallow quantum circuits because of noise. However, the barren plateau problem, where the gradient of the loss function becomes exponentially small with system size, hinders this goal. Recent studies suggest that embedding tensor networks into quantum circuits and initializing the parameters can avoid the barren plateau. Yet, embedding tensor networks into quantum circuits is generally difficult, and methods have been limited to the simplest structure, Matrix Product States (MPSs). This study proposes a method to embed Tree Tensor Networks (TTNs), characterized by their hierarchical structure, into shallow quantum circuits. TTNs are suitable for representing two-dimensional systems and systems with long-range correlations, which MPSs are inadequate for representing. Our numerical results show that embedding TTNs provides better initial quantum circuits than MPS. Additionally, our method has a practical computational complexity, making it applicable to a wide range of TTNs. This study is expected to extend the application of VQAs to two-dimensional systems and those with long-range correlations, which have been challenging to utilize.",QEk12HsB5wQJ,"S Sugawara, K Inomata, T Okubo, S Todo - arXiv preprint arXiv …, 2025 - arxiv.org",['https://arxiv.org/pdf/2501.18856'],https://arxiv.org/abs/2501.18856,unknown,unknown,TTN/MERA/PEPS,2501.18856,['https://arxiv.org/pdf/2501.18856'],embedding of tree tensor networks into shallow quantum circuits,TTN/MERA/PEPS,1,,
Optimizing ansatz design in quantum generative adversarial networks using large language models,"K Ueda, A Matsuo",2025.0,9,"We present a novel approach for improving the design of ansatzes in Quantum Generative Adversarial Networks (qGANs) by leveraging Large Language Models (LLMs). By combining the strengths of LLMs with qGANs, our approach iteratively refines ansatz structures to improve accuracy while reducing circuit depth and the number of parameters. This study paves the way for further exploration in AI-driven quantum algorithm design. The flexibility of our proposed workflow extends to other quantum variational algorithms, providing a general framework for optimizing quantum circuits in a variety of quantum computing tasks.",O4bZXbU4IBcJ,"K Ueda, A Matsuo - arXiv preprint arXiv:2503.12884, 2025 - arxiv.org",['https://arxiv.org/pdf/2503.12884'],https://arxiv.org/abs/2503.12884,unknown,unknown,量子/混合LLM,2503.12884,['https://arxiv.org/pdf/2503.12884'],optimizing ansatz design in quantum generative adversarial networks using large language models,量子/混合LLM,1,,
Bridging classical and quantum computing for next-generation language models,"Y Pan, H Jiang, J Chen, Y Li, H Zhao, L Zhao…",2025.0,8,… • We propose an entropy-driven adaptive quantum circuit architecture that bridges classical and … The variational quantum circuit with depth L as a unitary transformation U(θ) defined by: …,ePCxtIABi24J,"Y Pan, H Jiang, J Chen, Y Li, H Zhao, L Zhao… - Proceedings of the …, 2025 - ojs.aaai.org",['https://ojs.aaai.org/index.php/AAAI-SS/article/download/36909/39047'],https://ojs.aaai.org/index.php/AAAI-SS/article/view/36909,unknown,unknown,量子/混合LLM,,['https://ojs.aaai.org/index.php/AAAI-SS/article/download/36909/39047'],bridging classical and quantum computing for next generation language models,量子/混合LLM,1,,
Coupled Tensor Decomposition for Compact Network Representation,"V T Pham, Y Zniyed, T P Nguyễn",2025.0,8,"In this article, we introduce an approach called coupled filters decomposition, which builds on the key observation that redundancy exists among filters in a convolutional layer, meaning that similar filters can produce partially overlapping outputs. Leveraging this insight, we propose a joint decomposition of filters using coupled tensor decompositions, specifically coupled canonical polyadic decomposition (CPD), which enables the sharing of a common factor matrix across similar filters. This joint factorization not only reduces the number of parameters but also lowers computational complexity by eliminating redundant computations. To further improve efficiency, we first cluster the filters before decomposition. The grouping relies on a custom metric based on the subspace spanned by the shared-mode factor. Within each group, the coupling constraint is less restrictive. Extensive experiments across various architectures, datasets, and tasks validate the effectiveness of our method, demonstrating its competitive performance compared to state-of-the-art model compression techniques. Our code is available for research purposes at https://codec-ai.github.io/.",,"V T Pham, Y Zniyed, T P Nguyễn - IEEE Transactions on Neural Networks and Learning Systems, 2025",[],https://doi.org/10.1109/tnnls.2025.3609797,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,,[],coupled tensor decomposition for compact network representation,MPO/TT 压缩,1,IEEE Transactions on Neural Networks and Learning Systems,
Compact lossy compression of tensors via neural tensor-train decomposition: T. Kwon et al.,"T Kwon, J Ko, J Jung, JG Jang, K Shin",2025.0,7,"… compression algorithm for general tensors that do not depend on strict input data assumptions. To achieve this, we first introduce neural tensor-train … TensorCodec to compress tensors …",nr2lK5vxWigJ,"T Kwon, J Ko, J Jung, JG Jang, K Shin - Knowledge and Information …, 2025 - Springer",['https://link.springer.com/content/pdf/10.1007/s10115-024-02252-x.pdf'],https://link.springer.com/article/10.1007/s10115-024-02252-x,unknown,unknown,MPO/TT 压缩,,['https://link.springer.com/content/pdf/10.1007/s10115-024-02252-x.pdf'],compact lossy compression of tensors via neural tensor train decomposition t kwon et al,MPO/TT 压缩,1,,
Deep tree tensor networks,C Nie,2025.0,7,"Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parametric decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful application in natural image recognition. When employed, they primarily serve to compress parameters within pre-existing networks, thereby losing their distinctive capability to capture exponential-order feature interactions. This paper introduces a novel architecture named \textit{\textbf{D}eep \textbf{T}ree \textbf{T}ensor \textbf{N}etwork} (DTTN), which captures $2^L$-order multiplicative interactions across features through multilinear operations, while essentially unfolding into a \emph{tree}-like TN topology with the parameter-sharing property. DTTN is stacked with multiple antisymmetric interaction modules (AIMs), and this design facilitates efficient implementation. Furthermore, our theoretical analysis demonstrates the equivalence between quantum-inspired TN models and polynomial/multilinear networks under specific conditions. We posit that the DTTN could catalyze more interpretable research within this field. The proposed model is evaluated across multiple benchmarks and domains, demonstrating superior performance compared to both peer methods and state-of-the-art architectures. Our code is publicly available at https://github.com/NieCha/deep_tree_tensor_network.",GZcaDJjXD1AJ,"C Nie - arXiv preprint arXiv:2502.09928, 2025 - arxiv.org",['https://arxiv.org/pdf/2502.09928'],https://arxiv.org/abs/2502.09928,unknown,unknown,TTN/MERA/PEPS,2502.09928,"['https://arxiv.org/pdf/2502.09928', 'https://proceedings.neurips.cc/paper_files/paper/2025/file/42d6cda0d721d41ea5751b4bf4d53616-Paper-Conference.pdf']",deep tree tensor networks,TTN/MERA/PEPS,2,,
Discrete generative diffusion models without stochastic differential equations: A tensor network approach,"L Causer, GM Rotskoff, JP Garrahan",2025.0,7,"… Note that while there exist other tensor network Ansätze that might be more appropiate for … dimensions on thin cylinders), other TN topologies, such as tree tensor networks (TTNs) [80…",e0D1tSSLt0oJ,"L Causer, GM Rotskoff, JP Garrahan - Physical Review E, 2025 - APS",['https://link.aps.org/pdf/10.1103/PhysRevE.111.025302'],https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.025302,unknown,unknown,TTN/MERA/PEPS,,['https://link.aps.org/pdf/10.1103/PhysRevE.111.025302'],discrete generative diffusion models without stochastic differential equations a tensor network approach,TTN/MERA/PEPS,1,,
Efficient projected entangled pair states methods for periodic quantum systems,"S Dong, C Wang, H Zhang, M Zhang, L He",2025.0,6,"… Projected entangled pair states (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when …",rFEp65DVe4oJ,"S Dong, C Wang, H Zhang, M Zhang, L He - Physical Review Letters, 2025 - APS",[],https://link.aps.org/doi/10.1103/fvq2-msr4,unknown,unknown,TTN/MERA/PEPS,,[],efficient projected entangled pair states methods for periodic quantum systems,TTN/MERA/PEPS,1,,
Fieldformer: Self-supervised reconstruction of physical fields via tensor attention prior,"P Chen, S Li, L Cheng, X Fu, YC Wu…",2025.0,6,"… , grounded in the Tucker decomposition, is obtained that can … , similar to the attention map in transformers (see the second … We first tensorize each row of S ∈ RN×N into a subtensor (…",dmsRlqKZsNUJ,"P Chen, S Li, L Cheng, X Fu, YC Wu… - IEEE Transactions on …, 2025 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2506.11629'],https://ieeexplore.ieee.org/abstract/document/11053683/,unknown,unknown,张量化Transformer,,['https://arxiv.org/pdf/2506.11629'],fieldformer self supervised reconstruction of physical fields via tensor attention prior,张量化Transformer,1,,
Improving the accuracy of the tree-tensor network approach by optimization of network structure,"T Hikihara, H Ueda, K Okunishi, K Harada, T Nishino",2025.0,6,"… based on the tree-tensor networks (TTNs), which are tensor networks without loops. We … on binary trees, ie, TTNs composed of three-leg tensors, although the extension to m-ary trees is …",8r3NE3TrjpUJ,"T Hikihara, H Ueda, K Okunishi, K Harada, T Nishino - Physical Review B, 2025 - APS",['https://arxiv.org/pdf/2501.15514'],https://link.aps.org/doi/10.1103/ljj8-tkpc,unknown,unknown,TTN/MERA/PEPS,,['https://arxiv.org/pdf/2501.15514'],improving the accuracy of the tree tensor network approach by optimization of network structure,TTN/MERA/PEPS,1,,
Programming quantum computers with large language models,"ER Henderson, JM Henderson, J Ange…",2025.0,6,"… little investigation into the same for quantum programming.Consequently, this work is a … quantum circuits. We examine how well OpenAI’s ChatGPT (GPT-4) can write quantum circuits …",4-c0opfdAiMJ,"ER Henderson, JM Henderson, J Ange… - Quantum Information …, 2025 - spiedigitallibrary.org",['https://arxiv.org/pdf/2506.18125'],https://www.spiedigitallibrary.org/conference-proceedings-of-spie/13451/3049666/Programming-quantum-computers-with-large-language-models/10.1117/12.3049666.short,unknown,unknown,量子/混合LLM,,['https://arxiv.org/pdf/2506.18125'],programming quantum computers with large language models,量子/混合LLM,1,,
Entanglement across scales: Quantics tensor trains as a natural framework for renormalization,"S Rohshap, JW Li, A Lorenz, S Hasil, K Held…",2025.0,5,"Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length- or energy-scale entanglement—quantifying the information exchange between different length scales—has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations, as a renormalization group method by analytically expressing an exact cyclic reduction-based real-space renormalization scheme in QTT language, which serves as a natural formalism for the method. In doing so, we precisely match the QTT bond dimension—a measure of length-scale entanglement—to the number of rescaled couplings generated in each coarse-graining renormalization step. While QTTs have so far been applied almost exclusively to numerical problems in physics, our analytical calculations demonstrate that they are also powerful tools for mitigating computational costs in semianalytical treatments. We present our results for the one-dimensional tight-binding model with n th -nearest-neighbor hopping, where the 2 n rescaled couplings generated in the renormalization procedure precisely match the QTT bond dimension of the one-particle Green's function.",PdkwsouTr0cJ,"S Rohshap, JW Li, A Lorenz, S Hasil, K Held… - Physical Review …, 2025 - APS",['https://link.aps.org/pdf/10.1103/qlrs-6f8t'],https://link.aps.org/doi/10.1103/qlrs-6f8t,unknown,unknown,互信息/标度,,['https://link.aps.org/pdf/10.1103/qlrs-6f8t'],entanglement across scales quantics tensor trains as a natural framework for renormalization,互信息/标度,1,Physical Review Research,
Deep tensor decomposition: A survey,"M Zhao, J Hu, Z Li, Z Wang, L Sun",2025.0,4,"… ) layer followed by a deep tensorized MLP. This hybrid design … current embeddings; (2) an attention-based module that encodes … , combining TD with transformers, diffusion models, and …",5wZvP-PDDtUJ,"M Zhao, J Hu, Z Li, Z Wang, L Sun - Neurocomputing, 2025 - Elsevier",['https://engineering.lehigh.edu/sites/engineering.lehigh.edu/files/_DEPARTMENTS/ise/pdf/tech-papers/25/25T_022.pdf'],https://www.sciencedirect.com/science/article/pii/S0925231225027468,unknown,unknown,张量化Transformer,,['https://engineering.lehigh.edu/sites/engineering.lehigh.edu/files/_DEPARTMENTS/ise/pdf/tech-papers/25/25T_022.pdf'],deep tensor decomposition a survey,张量化Transformer,1,,
Scalable quantum state preparation via large-language-model-driven discovery,"QH Cao, ZY Hou, YY Li, X Liu, ZY Song…",2025.0,4,"Efficient quantum state preparation remains a central challenge in first-principles quantum simulations of dynamics in quantum field theories, where the Hilbert space is intrinsically infinite-dimensional. Here, we introduce a large language model (LLM)-assisted framework for quantum-circuit design that systematically scales state-preparation circuits to large lattice volumes. Applied to a 1+1d XY spin chain, the LLM autonomously discovers a compact 4-parameter circuit that captures boundary-induced symmetry breaking with sub-percent energy deviation, enabling successful validation on the \texttt{Zuchongzhi} quantum processor. Guided by this insight, we extend the framework to 2+1d quantum field theories, where scalable variational ansätze have remained elusive. For a scalar field theory, the search yields a symmetry-preserving, 3-parameter shallow-depth ansatz whose optimized parameters converge to size-independent constants for lattices $n \ge 4$, providing, to our knowledge, the first scalable ansatz for this class of 2+1d models. Our results establish a practical route toward AI-assisted, human-guided discovery in quantum simulation.",gp4goekwV_YJ,"QH Cao, ZY Hou, YY Li, X Liu, ZY Song… - arXiv preprint arXiv …, 2025 - arxiv.org",['https://arxiv.org/pdf/2505.06347'],https://arxiv.org/abs/2505.06347,unknown,unknown,量子/混合LLM,2505.06347,['https://arxiv.org/pdf/2505.06347'],scalable quantum state preparation via large language model driven discovery,量子/混合LLM,1,,
Regularized second-order optimization of tensor-network Born machines,"M Ben-Dov, J Chen",2025.0,3,"Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target distribution, capable of capturing complex correlations with a compact parameterization. Despite their promise, the optimization of TNBMs presents several challenges. A key bottleneck of TNBMs is the logarithmic nature of the loss function commonly used for this problem. The single-tensor logarithmic optimization problem cannot be solved analytically, necessitating an iterative approach that slows down convergence and increases the risk of getting trapped in one of many non-optimal local minima. In this paper, we present an improved second-order optimization technique for TNBM training, which significantly enhances convergence rates and the quality of the optimized model. Our method employs a modified Newton's method on the manifold of normalized states, incorporating regularization of the loss landscape to mitigate local minima issues. We demonstrate the effectiveness of our approach by training a one-dimensional matrix product state (MPS) on both discrete and continuous datasets, showcasing its advantages in terms of stability and efficiency, and demonstrating its potential as a robust and scalable approach for optimizing quantum-inspired generative models.",SdKWFXivFoIJ,"M Ben-Dov, J Chen - arXiv preprint arXiv:2501.18691, 2025 - arxiv.org",['https://arxiv.org/pdf/2501.18691'],https://arxiv.org/abs/2501.18691,unknown,unknown,MPS 生成/Born机,2501.18691,['https://arxiv.org/pdf/2501.18691'],regularized second order optimization of tensor network born machines,MPS 生成/Born机,1,,
TensorSLM: Energy-efficient embedding compression of sub-billion parameter language models on low-end devices,"M Xu, YL Xu, DP Mandic",2025.0,3,"Small Language Models (SLMs, or on-device LMs) have significantly fewer parameters than Large Language Models (LLMs). They are typically deployed on low-end devices, like mobile phones and single-board computers. Unlike LLMs, which rely on increasing model size for better generalisation, SLMs designed for edge applications are expected to have adaptivity to the deployment environments and energy efficiency given the device battery life constraints, which are not addressed in datacenter-deployed LLMs. This paper addresses these two requirements by proposing a training-free token embedding compression approach using Tensor-Train Decomposition (TTD). Each pre-trained token embedding vector is converted into a lower-dimensional Matrix Product State (MPS). We comprehensively evaluate the extracted low-rank structures across compression ratio, language task performance, latency, and energy consumption on a typical low-end device, i.e. Raspberry Pi. Taking the sub-billion parameter versions of GPT-2/Cerebres-GPT and OPT models as examples, our approach achieves a comparable language task performance to the original model with around $2.0\times$ embedding layer compression, while the energy consumption of a single query drops by half.",tb9tSbpPghwJ,"M Xu, YL Xu, DP Mandic - arXiv preprint arXiv:2506.13514, 2025 - arxiv.org",['https://arxiv.org/pdf/2506.13514'],https://arxiv.org/abs/2506.13514,unknown,unknown,MPO/TT 压缩,2506.13514,['https://arxiv.org/pdf/2506.13514'],tensorslm energy efficient embedding compression of sub billion parameter language models on low end devices,MPO/TT 压缩,1,,
Tree Tensor Network Quantum-Classical Hybrid Neural Architecture for Efficient Data Classification,"NN Hidayat, M Akrom",2025.0,3,"… -Classical Neural Network (TTN-QNet), a hybrid architecture that leverages the hierarchical structure of Tree Tensor Networks … Liu, Quantum generative model with variable-depth circuit, …",PmTFsE7jZ74J,"NN Hidayat, M Akrom - Journal of Multiscale Materials …, 2025 - dl.futuretechsci.org",['https://dl.futuretechsci.org/id/eprint/121/1/JIMAT%20Template_5%20%2834-39%29.pdf'],https://dl.futuretechsci.org/id/eprint/121/,unknown,unknown,TTN/MERA/PEPS,,['https://dl.futuretechsci.org/id/eprint/121/1/JIMAT%20Template_5%20%2834-39%29.pdf'],tree tensor network quantum classical hybrid neural architecture for efficient data classification,TTN/MERA/PEPS,1,,
Compositional Concept Generalization with Variational Quantum Circuits,"H Hawashin, M Abbaszadeh, N Joseph…",2025.0,2,"… model (DisCoCat) introduced in [1] provides an explicitly compositional way of modelling language. It … advances, leading to the invention of Large Language Models. [4] is the first in this …",Ifbkvl5rqCkJ,"H Hawashin, M Abbaszadeh, N Joseph… - … on Quantum …, 2025 - ieeexplore.ieee.org",['https://arxiv.org/pdf/2509.09541?'],https://ieeexplore.ieee.org/abstract/document/11344646/,unknown,unknown,量子/混合LLM,,['https://arxiv.org/pdf/2509.09541?'],compositional concept generalization with variational quantum circuits,量子/混合LLM,1,,
Initialization and training of matrix product state probabilistic models,"X Tang, Y Khoo, L Ying",2025.0,2,"Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a common failure mode in training randomly initialized matrix product states (MPS) using gradient descent. The results show that the trained MPS models do not accurately predict the strong interactions between boundary sites in periodic spin chain models. In the case of the Born machine algorithm, we further identify a causality trap, where the trained MPS models resemble causal models that ignore the non-local correlations in the true distribution. We propose two complementary strategies to overcome the training failure -- one through optimization and one through initialization. First, we develop a natural gradient descent (NGD) method, which approximately simulates the gradient flow on tensor manifolds and significantly enhances training efficiency. Numerical experiments show that NGD avoids local minima in both Born machines and in general MPS tomography. Remarkably, we show that NGD with line search can converge to the global minimum in only a few iterations. Second, for the BM algorithm, we introduce a warm-start initialization based on the TTNS-Sketch algorithm. We show that gradient descent under a warm initialization does not encounter the causality trap and admits rapid convergence to the ground truth.",hW2EndstJo0J,"X Tang, Y Khoo, L Ying - arXiv preprint arXiv:2505.06419, 2025 - arxiv.org",['https://arxiv.org/pdf/2505.06419'],https://arxiv.org/abs/2505.06419,unknown,unknown,MPS 生成/Born机,2505.06419,['https://arxiv.org/pdf/2505.06419'],initialization and training of matrix product state probabilistic models,MPS 生成/Born机,1,,
Representation theorems for matrix product states,"E Guo, D Draper",2025.0,2,"… In this work, we investigate the universal representational capacity of matrix product states (… For specific MPS models, we construct equivalent NNs and show that nonlinear kernels, …",fy9Jp0tbwcEJ,"E Guo, D Draper - SIAM Journal on Mathematics of Data Science, 2025 - SIAM",['https://arxiv.org/pdf/2103.08277'],https://epubs.siam.org/doi/abs/10.1137/24M172010X,unknown,unknown,MPS 语言模型,,['https://arxiv.org/pdf/2103.08277'],representation theorems for matrix product states,MPS 语言模型,1,,
Saten: Sparse Augmented Tensor Networks for Post-Training Compression of Large Language Models.,"R Solgi, K Zhen, RV Swaminathan, N Susanj…",2025.0,2,… drops when using tensor factorization for LLM post-training compression. We have presented … component into tensor networks to improve model performance in compression. Saten has …,vJT3-TbrGxEJ,"R Solgi, K Zhen, RV Swaminathan, N Susanj… - EMNLP …, 2025 - aclanthology.org",['https://aclanthology.org/anthology-files/pdf/findings/2025.findings-emnlp.1287.pdf'],https://aclanthology.org/anthology-files/pdf/findings/2025.findings-emnlp.1287.pdf,unknown,unknown,MPO/TT 压缩,,['https://aclanthology.org/anthology-files/pdf/findings/2025.findings-emnlp.1287.pdf'],saten sparse augmented tensor networks for post training compression of large language models,MPO/TT 压缩,1,,
Share Token Tensorized Attention Fusion: Enhancing Audio-Visual Emotion Recognition for Consumer Electronics,"H Lu, D Liu, LT Yang, R Zhao, S Lv…",2025.0,2,"In today’s competitive market, smarter and higher-performing consumer electronics are increasingly attractive to the public. These products not only need to perform basic functions but also offer personalized services to enhance user experience and drive sales growth. To solve this problem, this paper proposes a multimodal emotion recognition model based on Share Token Tensorized Attention Fusion (STF), which improves the intelligence of electronic products by providing in-depth understanding of the user’s emotional state.The STF method constrains the modal feature fusion by introducing the share token and combines with the tensorized attention for feature fusion, which significantly improves the accuracy of emotion recognition, improves the robustness of the model, and reduces the learning cost compared to the Transformer-based multimodal emotion recognition model. The STF-based multimodal emotion recognition model can ensure model performance and faster response speed in noisy environments, and it is easier to meet the consumers’ pursuit of consumer electronics experience.",6RJUIIF2Qz0J,"H Lu, D Liu, LT Yang, R Zhao, S Lv… - IEEE Transactions on …, 2025 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/11128871/,unknown,unknown,张量化Transformer,,[],share token tensorized attention fusion enhancing audio visual emotion recognition for consumer electronics,张量化Transformer,1,IEEE Transactions on Consumer Electronics,
Tensorized attention for understanding multi-object relationships,"M Nakatsuji, Y Fujiwara, A Otsuka, N Nomoto…",2025.0,2,"… Tensorized Transformer in two key ways. First, TAM employs the Tucker decomposition with a core tensor, … used in this paper and introduce Tensorized Transformer (Ma et al. 2019). We …",Xa4mPTwIlDcJ,"M Nakatsuji, Y Fujiwara, A Otsuka, N Nomoto… - Proceedings of the …, 2025 - ojs.aaai.org",['https://ojs.aaai.org/index.php/AAAI/article/download/34675/36830'],https://ojs.aaai.org/index.php/AAAI/article/view/34675,unknown,unknown,张量化Transformer,,['https://ojs.aaai.org/index.php/AAAI/article/download/34675/36830'],tensorized attention for understanding multi object relationships,张量化Transformer,1,,
Towards robust scale-invariant mutual information estimators,"CT Leung, R Ghosh, M Motani",2025.0,2,"… : the scale of the variables (|X|). Specifically, for mutual information I(X; αT), where α ∈ R+ is a scaling … Toward fairness in text generation via mutual information minimization based on …",W5_hhBGiE-AJ,"CT Leung, R Ghosh, M Motani - Transactions on Machine Learning …, 2025 - openreview.net",['https://openreview.net/pdf?id=vB7Wvytko5'],https://openreview.net/forum?id=vB7Wvytko5,unknown,unknown,互信息/标度,,['https://openreview.net/pdf?id=vB7Wvytko5'],towards robust scale invariant mutual information estimators,互信息/标度,1,,
Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC,"E Puljak, M Pierini, A García-Sáez",2025.0,2,"Abstract The pursuit of discovering new phenomena at the Large Hadron Collider (LHC) requires constant innovation in algorithms and technologies. Tensor networks are mathematical models at the intersection of classical and quantum machine learning, which present a promising and efficient alternative for tackling these challenges. In this study, we propose a tensor network-based strategy for anomaly detection at the LHC and demonstrate its superior performance in identifying new phenomena compared to established quantum methods. Our model is a parameterized matrix product state with an isometric feature map, processing a latent representation of simulated LHC data generated by an autoencoder. Our results highlight the potential of tensor networks to enhance new-physics discovery.",,"E Puljak, M Pierini, A García-Sáez - Machine Learning Science and Technology",[],https://arxiv.org/abs/2506.00102,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2506.00102,['https://arxiv.org/pdf/2506.00102'],tensor network for anomaly detection in the latent space of proton collision events at the lhc,量子/混合LLM,1,Machine Learning Science and Technology,
Circuit partitioning using large language models for quantum compilation and simulations,"P Sinha, SK Jha, S Raj",2025.0,1,"We are in the midst of the noisy intermediate-scale quantum (NISQ) era, where quantum computers are limited by noisy gates, some of which are more error-prone than others and can render the final computation incomprehensible. Quantum circuit compilation algorithms attempt to minimize these noisy gates when mapping quantum algorithms onto quantum hardware but face computational challenges that restrict their application to circuits with no more than 5-6 qubits, necessitating the need to partition large circuits before the application of noisy quantum gate minimization algorithms. The existing generation of these algorithms is heuristic in nature and does not account for downstream gate minimization tasks. Large language models (LLMs) have the potential to change this and help improve quantum circuit partitions. This paper investigates the use of LLMs, such as Llama and Mistral, for partitioning quantum circuits by capitalizing on their abilities to understand and generate code, including QASM. Specifically, we teach LLMs to partition circuits using the quick partition approach of the Berkeley Quantum Synthesis Toolkit. Through experimental evaluations, we show that careful fine-tuning of open source LLMs enables us to obtain an accuracy of 53.4% for the partition task while over-the-shelf LLMs are unable to correctly partition circuits, using standard 1-shot and few-shot training approaches.",2v3m0pVrDkgJ,"P Sinha, SK Jha, S Raj - arXiv preprint arXiv:2505.07711, 2025 - arxiv.org",['https://arxiv.org/pdf/2505.07711'],https://arxiv.org/abs/2505.07711,unknown,unknown,量子/混合LLM,2505.07711,['https://arxiv.org/pdf/2505.07711'],circuit partitioning using large language models for quantum compilation and simulations,量子/混合LLM,1,,
Compression of Convolutional Neural Networks Employing Tensor Train and High Dimensional Model Representation,"B Yılmaz, S Tuna",2025.0,1,… This study investigates the compression of convolutional neural networks using Tensor … intends to compress deep networks and lower computing costs by means of Tensor Train (TT) …,WAXTCLmRPDcJ,"B Yılmaz, S Tuna - 2025 9th International Symposium on …, 2025 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/11101768/,unknown,unknown,MPO/TT 压缩,,[],compression of convolutional neural networks employing tensor train and high dimensional model representation,MPO/TT 压缩,1,,
Efficient Probabilistic Tensor Networks,"MGA Hameed, G Rabusseau",2025.0,1,"Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of marginals. However, existing approaches for learning parameters of PTNs are either computationally demanding and not fully compatible with automatic differentiation frameworks, or numerically unstable. In this work, we propose a conceptually simple approach for learning PTNs efficiently, that is numerically stable. We show our method provides significant improvements in time and space complexity, achieving 10x reduction in latency for generative modeling on the MNIST dataset. Furthermore, our approach enables learning of distributions with 10x more variables than previous approaches when applied to a variety of density estimation benchmarks. Our code is publicly available at github.com/marawangamal/ptn.",1EDj2xrrv1wJ,"MGA Hameed, G Rabusseau - arXiv preprint arXiv:2510.00382, 2025 - arxiv.org",['https://arxiv.org/pdf/2510.00382'],https://arxiv.org/abs/2510.00382,unknown,unknown,MPS/序列建模,2510.00382,['https://arxiv.org/pdf/2510.00382'],efficient probabilistic tensor networks,MPS/序列建模,1,,
Hybrid quantum transformer for language generation,"D Kong, X Cui, J Jin, J Xu, D Wang",2025.0,1,"Although quantum computing has been increasingly applied to replace classical computation, most existing quantum or hybrid models remain confined to simple tasks, with no successful application to large-scale natural language generation to date. In this work, we present the first hybrid quantum-classical large language model (LLM) for natural language generation, HyQuT, capable of performing coherent and context-aware dialogue. The proposed architecture integrates variational quantum circuits (VQCs) into the Transformer framework at both 8M and 150M parameter scales. Experimental results show that a minimal number of qubits (10 qubits with 80 quantum gates) can replace about 10% of the classical parameters in the 150M-parameter model, while achieving comparable convergence stability and generation quality. This study provides an early demonstration of the feasibility of integrating quantum computing to large-scale generative language models.",NJxb-OgYwy0J,"D Kong, X Cui, J Jin, J Xu, D Wang - arXiv preprint arXiv:2511.10653, 2025 - arxiv.org",['https://arxiv.org/pdf/2511.10653'],https://arxiv.org/abs/2511.10653,unknown,unknown,量子/混合LLM,2511.10653,['https://arxiv.org/pdf/2511.10653'],hybrid quantum transformer for language generation,量子/混合LLM,1,,
LLM-based code generation for optimized quantum circuits,L Jern,2025.0,1,"… This is followed by an introduction to the field of deep learning and large language models. Finally, we will present the state-… The VQE algorithm uses the variational principle of quantum …",7DpDtICZ16UJ,L Jern - 2025 - aaltodoc.aalto.fi,['https://aaltodoc.aalto.fi/bitstreams/275755ae-5be1-47b4-b38a-4704338a596b/download'],https://aaltodoc.aalto.fi/items/0937d12a-2da8-4114-96db-d3b960790133,unknown,unknown,量子/混合LLM,,['https://aaltodoc.aalto.fi/bitstreams/275755ae-5be1-47b4-b38a-4704338a596b/download'],llm based code generation for optimized quantum circuits,量子/混合LLM,1,,
Multilingual machine translation with quantum encoder decoder attention-based convolutional variational circuits,"S Dikshit, R Tiwari, P Jain",2025.0,1,"Cloud-based multilingual translation services like Google Translate and Microsoft Translator achieve state-of-the-art translation capabilities. These services inherently use large multilingual language models such as GRU, LSTM, BERT, GPT, T5, or similar encoder-decoder architectures with attention mechanisms as the backbone. Also, new age natural language systems, for instance ChatGPT and DeepSeek, have established huge potential in multiple tasks in natural language processing. At the same time, they also possess outstanding multilingual translation capabilities. However, these models use the classical computing realm as a backend. QEDACVC (Quantum Encoder Decoder Attention-based Convolutional Variational Circuits) is an alternate solution that explores the quantum computing realm instead of the classical computing realm to study and demonstrate multilingual machine translation. QEDACVC introduces the quantum encoder-decoder architecture that simulates and runs on quantum computing hardware via quantum convolution, quantum pooling, quantum variational circuit, and quantum attention as software alterations. QEDACVC achieves an Accuracy of 82% when trained on the OPUS dataset for English, French, German, and Hindi corpora for multilingual translations.",uAJbOMmkLU0J,"S Dikshit, R Tiwari, P Jain - arXiv preprint arXiv:2505.09407, 2025 - arxiv.org",['https://arxiv.org/pdf/2505.09407?'],https://arxiv.org/abs/2505.09407,unknown,unknown,量子/混合LLM,2505.09407,['https://arxiv.org/pdf/2505.09407?'],multilingual machine translation with quantum encoder decoder attention based convolutional variational circuits,量子/混合LLM,1,,
"Quantum Natural Language Processing: A Comprehensive Survey of Models, Architectures, and Evaluation Methods","A Vats, R Raja, A Kattamuri…",2025.0,1,"… different aspects of quantum mechanics to model linguistic struc… , circuit based models, variational approaches, quantum … parrots: Can language models be too big? In Proceedings of …",9P0Yb1NHuc0J,"A Vats, R Raja, A Kattamuri… - The 1st Workshop on …, 2025 - aclanthology.org",['https://aclanthology.org/anthology-files/anthology-files/pdf/quantumnlp/2025.quantumnlp-1.pdf#page=60'],https://aclanthology.org/anthology-files/anthology-files/pdf/quantumnlp/2025.quantumnlp-1.pdf#page=60,unknown,unknown,量子/混合LLM,,['https://aclanthology.org/anthology-files/anthology-files/pdf/quantumnlp/2025.quantumnlp-1.pdf#page=60'],quantum natural language processing a comprehensive survey of models architectures and evaluation methods,量子/混合LLM,1,,
Tensor-Based Compression of Neural Networks,"V Zvezdana, F Slavoljub, A Tatyana",2025.0,1,"… In the context of deep learning, weight tensors in neural networks often exhibit … techniques to achieve model compression. This section provides an overview of tensor representations, …",hpbdov-QT4YJ,"V Zvezdana, F Slavoljub, A Tatyana - Available at SSRN 5172392, 2025 - papers.ssrn.com",['https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=5172392'],https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5172392,unknown,unknown,MPO/TT 压缩,,['https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=5172392'],tensor based compression of neural networks,MPO/TT 压缩,1,,
LLM-Guided Ansätze Design for Quantum Circuit Born Machines in Financial Generative Modeling,"Y Gujju, R Harang, T Shibuya",2025.0,1,"Quantum generative modeling using quantum circuit Born machines (QCBMs) shows promising potential for practical quantum advantage. However, discovering ansätze that are both expressive and hardware-efficient remains a key challenge, particularly on noisy intermediate-scale quantum (NISQ) devices. In this work, we introduce a prompt-based framework that leverages large language models (LLMs) to generate hardware-aware QCBM architectures. Prompts are conditioned on qubit connectivity, gate error rates, and hardware topology, while iterative feedback, including Kullback-Leibler (KL) divergence, circuit depth, and validity, is used to refine the circuits. We evaluate our method on a financial modeling task involving daily changes in Japanese government bond (JGB) interest rates. Our results show that the LLM-generated ansätze are significantly shallower and achieve superior generative performance compared to the standard baseline when executed on real IBM quantum hardware using 12 qubits. These findings demonstrate the practical utility of LLM-driven quantum architecture search and highlight a promising path toward robust, deployable generative models for near-term quantum devices.",,"Y Gujju, R Harang, T Shibuya - arXiv preprint arXiv:2509.08385, 2025 - arxiv.org",[],https://arxiv.org/abs/2509.08385,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2509.08385,['https://arxiv.org/pdf/2509.08385'],llm guided ans tze design for quantum circuit born machines in financial generative modeling,MPS 语言模型 / MPS 生成/Born机,2,,
Efficient Deep Generative Models for Spatial Networks via Spanning Tree Sampler,"X Guo, Y Du, Z Zhang, L Zhao",2025.0,0,"… a novel disentangled and scalable deep generative model for spatial networks. Specifically, an objective for spatial-network joint disentangled representation learning is derived and …",FwwBdtwyxw0J,"X Guo, Y Du, Z Zhang, L Zhao - ACM Transactions on Knowledge …, 2025 - dl.acm.org",['https://dl.acm.org/doi/pdf/10.1145/3774416'],https://dl.acm.org/doi/abs/10.1145/3774416,unknown,unknown,TTN/MERA/PEPS,,['https://dl.acm.org/doi/pdf/10.1145/3774416'],efficient deep generative models for spatial networks via spanning tree sampler,TTN/MERA/PEPS,1,,
KARIPAP: Quantum-Inspired Tensor Network Compression of Large Language Models Using Infinite Projected Entangled Pair States and Tensor Renormalization …,A Nazri,2025.0,0,"Large Language Models (LLMs) like ChatGPT and LLaMA drive rapid progress in generative AI, yet their huge parameter scales create severe computational and environmental burdens. High training costs, energy use, and limited device deployment hinder accessibility. Existing compression - pruning, distillation, low-rank, and quantization - reduces size but ignores complex inter-layer correlations. We propose KARIPAP, a quantum-inspired tensor network compression using Infinite Projected Entangled Pair States (iPEPS) and Tensor Renormalization Group (TRG) contraction. Unlike 1D Matrix Product States, iPEPS captures multi-directional entanglement in attention and deep transformer layers. TRG ensures polynomial-time contraction, making tensorization feasible while preserving key correlation geometry. Experiments on LLaMA-2 7B show up to 93% memory and 70% parameter reduction, with 50% faster training, 25% faster inference, and only 2-3% accuracy loss. Layer-wise entanglement profiling reveals redundancy in deeper layers, confirming their suitability for tensor factorization. KARIPAP demonstrates that modern LLMs occupy low-dimensional entanglement manifolds, enabling scalable, energy-efficient, and quantum-aware AI architectures.",bOwPXK1zNM4J,"A Nazri - arXiv preprint arXiv:2510.21844, 2025 - arxiv.org",['https://arxiv.org/pdf/2510.21844'],https://arxiv.org/abs/2510.21844,unknown,unknown,MPO/TT 压缩,2510.21844,['https://arxiv.org/pdf/2510.21844'],karipap quantum inspired tensor network compression of large language models using infinite projected entangled pair states and tensor renormalization,MPO/TT 压缩,1,,
Tensor Train Recurrent Network Language Model Prediction,"A Murua‐Sazo, R Ramakrishnan, X Li, RH Yang…",2025.0,0,… Because our work focuses on language modelling and model compression rather than end-… canonical metric for intrinsic evaluation of probabilistic language models (Jelinek et al. 1977; …,g1kXhjmrYBcJ,"A Murua‐Sazo, R Ramakrishnan, X Li, RH Yang… - Stat, 2025 - Wiley Online Library",['https://onlinelibrary.wiley.com/doi/pdf/10.1002/sta4.70116'],https://onlinelibrary.wiley.com/doi/abs/10.1002/sta4.70116,unknown,unknown,MPO/TT 压缩,,['https://onlinelibrary.wiley.com/doi/pdf/10.1002/sta4.70116'],tensor train recurrent network language model prediction,MPO/TT 压缩,1,,
TNSPC: Learning from Partially Observed Data Using Tensor Network Structured Probabilistic Circuits,"M Mørup, MN Schmidt",2025.0,0,… is to exploit probabilistic circuit properties for tensor networks to develop an … the tensor network structured probabilistic circuit (TNSPC). TNSPC is able to train probabilistic circuit models …,B_qtjfCgrg8J,"M Mørup, MN Schmidt - 2025 IEEE 35th International …, 2025 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/11204307/,unknown,unknown,MPS/序列建模,,[],tnspc learning from partially observed data using tensor network structured probabilistic circuits,MPS/序列建模,1,,
tn4ml: Tensor Network Training and Customization for Machine Learning,"E Puljak, S Sanchez-Ramirez, S Masot-Llima, J Vallès-Muns, A Garcia-Saez, M Pierini",2025.0,0,"Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a novel library designed to seamlessly integrate Tensor Networks into optimization pipelines for Machine Learning tasks. Inspired by existing Machine Learning frameworks, the library offers a user-friendly structure with modules for data embedding, objective function definition, and model training using diverse optimization strategies. We demonstrate its versatility through two examples: supervised learning on tabular data and unsupervised learning on an image dataset. Additionally, we analyze how customizing the parts of the Machine Learning pipeline for Tensor Networks influences performance metrics.",,"E Puljak, S Sanchez-Ramirez, S Masot-Llima, J Vallès-Muns, A Garcia-Saez, M Pierini - arXiv preprint arXiv:2502.13090, 2025 - arxiv.org",[],https://arxiv.org/abs/2502.13090,manual,2026-09-26,MPS/序列建模,2502.13090,['https://arxiv.org/pdf/2502.13090'],tn4ml tensor network training and customization for machine learning,MPS/序列建模,1,,
A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics,"C A Amaral, V L Oliveira, J P L C Salazar, E I Duzzioni",2025.0,0,"Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively expensive under these conditions. Quantum computing and quantum-inspired methods have been investigated as promising alternatives. This review surveys advances at the intersection of quantum computing, quantum algorithms, machine learning, and tensor network techniques for CFD. We discuss the use of Variational Quantum Algorithms as hybrid quantum-classical solvers for PDEs, emphasizing their ability to incorporate nonlinearities through Quantum Nonlinear Processing Units. We further review Quantum Neural Networks and Quantum Physics-Informed Neural Networks, which extend classical machine learning frameworks to quantum hardware and have shown advantages in parameter efficiency and solution accuracy for certain CFD benchmarks. Beyond quantum computing, we examine tensor network methods, originally developed for quantum many-body systems and now adapted to CFD as efficient high-dimensional compression and solver tools. Reported studies include several orders of magnitude reductions in memory and runtime while preserving accuracy. Together, these approaches highlight quantum and quantum-inspired strategies that may enable more efficient CFD solvers. This review closes with perspectives: quantum CFD remains out of reach in the NISQ era, but quantum-inspired tensor networks already show practical benefits, with hybrid approaches offering the most promising near-term strategy.",,"C A Amaral, V L Oliveira, J P L C Salazar, E I Duzzioni - arXiv preprint arXiv:2510.14099, 2025 - arxiv.org",[],https://arxiv.org/abs/2510.14099,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2510.14099,['https://arxiv.org/pdf/2510.14099'],a review of quantum machine learning and quantum inspired applied methods to computational fluid dynamics,MPO/TT 压缩 / 量子/混合LLM / 量子启发综述,1,,
DeepQuantum: A PyTorch-based Software Platform for Quantum Machine Learning and Photonic Quantum Computing,"J He, K Hu, Y Zhu, G Yan, S Liang, X Zhao, D Wang, F Guo, Z Lan, X Shang, Z Yin, X Jiang, L Yang, H Tang, X Jin",2025.0,0,"We introduce DeepQuantum, an open-source, PyTorch-based software platform for quantum machine learning and photonic quantum computing. This AI-enhanced framework enables efficient design and execution of hybrid quantum-classical models and variational quantum algorithms on both CPUs and GPUs. For photonic quantum computing, DeepQuantum implements Fock, Gaussian, and Bosonic backends, catering to different simulation needs. To our knowledge, it is the first framework to realize closed-loop integration of three paradigms of quantum computing, namely quantum circuits, photonic quantum circuits, and measurement-based quantum computing, thereby enabling robust support for both specialized and universal photonic quantum algorithm design. Furthermore, DeepQuantum supports large-scale simulations based on tensor network techniques and a distributed parallel computing architecture. We demonstrate these capabilities through comprehensive benchmarks and illustrative examples. With its unique features, DeepQuantum is intended to be a powerful platform for both AI for Quantum and Quantum for AI.",,"J He, K Hu, Y Zhu, G Yan, S Liang, X Zhao, D Wang, F Guo, Z Lan, X Shang, Z Yin, X Jiang, L Yang, H Tang, X Jin - arXiv preprint arXiv:2512.18995, 2025 - arxiv.org",[],https://arxiv.org/abs/2512.18995,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2512.18995,['https://arxiv.org/pdf/2512.18995'],deepquantum a pytorch based software platform for quantum machine learning and photonic quantum computing,量子/混合LLM,2,,
Dimension reduction with structure-aware quantum circuits for hybrid machine learning,A Daskin,2025.0,0,"Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying Schmidt decompositions via SVD to all subsystems. Given a vector expressed as a linear combination of tensor products, using only the $k$ principal terms yields a $k$-rank approximation of the vector. Therefore, writing a vector in this reduced form allows to retain most important parts of the vector while removing small noises from it, analogous to SVD-based denoising. In this paper, we show that quantum circuits designed based on a value $k$ (determined from the tensor network decomposition of the mean vector of the training sample) can approximate the reduced-form representations of entire datasets. We then employ this circuit ansatz with a classical neural network head to construct a hybrid machine learning model. Since the output of the quantum circuit for an $2^n$ dimensional vector is an $n$ dimensional probability vector, this provides an exponential compression of the input and potentially can reduce the number of learnable parameters for training large-scale models. We use datasets provided in the Python scikit-learn module for the experiments. The results confirm the quantum circuit is able to compress data successfully to provide effective $k$-rank approximations to the classical processing component.",,"A Daskin - arXiv preprint arXiv:2508.00048, 2025 - arxiv.org",[],https://arxiv.org/abs/2508.00048,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2508.00048,['https://arxiv.org/pdf/2508.00048'],dimension reduction with structure aware quantum circuits for hybrid machine learning,MPO/TT 压缩 / 量子/混合LLM,1,,
Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning,"S A C Ordóñez, L F T Torres, M Bifulco, C A Durán, C Bosch, R S Carbajo",2025.0,0,"Quantum Support Vector Machines face scalability challenges due to high-dimensional quantum states and hardware limitations. We propose an embedding-aware quantum-classical pipeline combining class-balanced k-means distillation with pretrained Vision Transformer embeddings. Our key finding: ViT embeddings uniquely enable quantum advantage, achieving up to 8.02% accuracy improvements over classical SVMs on Fashion-MNIST and 4.42% on MNIST, while CNN features show performance degradation. Using 16-qubit tensor network simulation via cuTensorNet, we provide the first systematic evidence that quantum kernel advantage depends critically on embedding choice, revealing fundamental synergy between transformer attention and quantum feature spaces. This provides a practical pathway for scalable quantum machine learning that leverages modern neural architectures.",,"S A C Ordóñez, L F T Torres, M Bifulco, C A Durán, C Bosch, R S Carbajo - arXiv preprint arXiv:2508.00024, 2025 - arxiv.org",[],https://arxiv.org/abs/2508.00024,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2508.00024,['https://arxiv.org/pdf/2508.00024'],embedding aware quantum classical svms for scalable quantum machine learning,张量化Transformer / 量子/混合LLM,1,,
Enhancing Symbolic Machine Learning by Subsymbolic Representations,"S Roth, L Baur, D Boer, S Kramer",2025.0,0,"The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end learning. The versatility of systems like LTNs and DeepProbLog, however, makes them less efficient in simpler settings, for instance, for discriminative machine learning, in particular in domains with many constants. Therefore, we follow a different approach: We propose to enhance symbolic machine learning schemes by giving them access to neural embeddings. In the present paper, we show this for TILDE and embeddings of constants used by TILDE in similarity predicates. The approach can be fine-tuned by further refining the embeddings depending on the symbolic theory. In experiments in three real-world domain, we show that this simple, yet effective, approach outperforms all other baseline methods in terms of the F1 score. The approach could be useful beyond this setting: Enhancing symbolic learners in this way could be extended to similarities between instances (effectively working like kernels within a logical language), for analogical reasoning, or for propositionalization.",,"S Roth, L Baur, D Boer, S Kramer - arXiv preprint arXiv:2506.14569, 2025 - arxiv.org",[],https://arxiv.org/abs/2506.14569,arxiv-completion,2026-09-26 (citations:OpenAlex),,2506.14569,['https://arxiv.org/pdf/2506.14569'],enhancing symbolic machine learning by subsymbolic representations,,1,,
Fast and Expressive Multi-Byte Prediction with Probabilistic Circuits,"A Grivas, L Loconte, E v Krieken, P Nawrot, Y Zhao, E Wielewski, P Minervini, E Ponti, A Vergari",2025.0,0,"Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), especially in byte-level LLMs, which are tokeniser-free but prohibitively slow. However, many existing MTP methods either assume independence between future tokens, sacrificing expressiveness, or generate tokens one at a time within the window, increasing latency. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting circuit architectures, generalising classical models such as (hierarchical) mixture models, hidden Markov models, and tensor networks. We show the efficacy of MTPC by retrofitting existing byte-level LLMs, such as EvaByte, and byte-fied subword models, such as Llama3.2 3B. Our experiments show that, when combined with speculative decoding, MTPC substantially speeds up generation compared to MTP with independence assumptions, while guaranteeing to retain the performance of the original verifier LLM. We also rigorously study the optimal trade-off between expressiveness and latency when exploring the possible parameterisations of MTPC, such as PC architectures and partial layer sharing between the verifier and draft LLMs.",,"A Grivas, L Loconte, E v Krieken, P Nawrot, Y Zhao, E Wielewski, P Minervini, E Ponti, A Vergari - arXiv preprint arXiv:2511.11346, 2025 - arxiv.org",[],https://arxiv.org/abs/2511.11346,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2511.11346,['https://arxiv.org/pdf/2511.11346'],fast and expressive multi byte prediction with probabilistic circuits,MPS 语言模型,1,,
QCA-MolGAN: Quantum Circuit Associative Molecular GAN with Multi-Agent Reinforcement Learning,"A M Thomas, Y Chen, H O Valencia, S T Jose, R Wu",2025.0,0,"Navigating the vast chemical space of molecular structures to design novel drug molecules with desired target properties remains a central challenge in drug discovery. Recent advances in generative models offer promising solutions. This work presents a novel quantum circuit Born machine (QCBM)-enabled Generative Adversarial Network (GAN), called QCA-MolGAN, for generating drug-like molecules. The QCBM serves as a learnable prior distribution, which is associatively trained to define a latent space aligning with high-level features captured by the GANs discriminator. Additionally, we integrate a novel multi-agent reinforcement learning network to guide molecular generation with desired targeted properties, optimising key metrics such as quantitative estimate of drug-likeness (QED), octanol-water partition coefficient (LogP) and synthetic accessibility (SA) scores in conjunction with one another. Experimental results demonstrate that our approach enhances the property alignment of generated molecules with the multi-agent reinforcement learning agents effectively balancing chemical properties.",,"A M Thomas, Y Chen, H O Valencia, S T Jose, R Wu - arXiv preprint arXiv:2509.05051, 2025 - arxiv.org",[],https://arxiv.org/abs/2509.05051,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2509.05051,['https://arxiv.org/pdf/2509.05051'],qca molgan quantum circuit associative molecular gan with multi agent reinforcement learning,MPS 生成/Born机,1,,
Qiboml: towards the orchestration of quantum-classical machine learning,"M Robbiati, A Papaluca, A Pasquale, E Pedicillo, R M S Farias, A Sopena, M Robbiano, G Alramahi, S Bordoni, A Candido, N Laurora, J S Neto, Y P Tan, M Grossi, S Carrazza",2025.0,0,"We present Qiboml, an open-source software library for orchestrating quantum and classical components in hybrid machine learning workflows. Building on Qibo's quantum computing capabilities and integrating with popular machine learning frameworks such as TensorFlow and PyTorch, Qiboml enables the construction of quantum and hybrid models that can run on a broad range of backends: (i) multi-threaded CPUs, GPUs, and multi-GPU systems for simulation with statevector or tensor network methods; (ii) quantum processing units, both on-premise and through cloud providers. In this paper, we showcase its functionalities, including diverse simulation options, noise-aware simulations, and real-time error mitigation and calibration.",,"M Robbiati, A Papaluca, A Pasquale, E Pedicillo, R M S Farias, A Sopena, M Robbiano, G Alramahi, S Bordoni, A Candido, N Laurora, J S Neto, Y P Tan, M Grossi, S Carrazza - arXiv preprint arXiv:2510.11773, 2025 - arxiv.org",[],https://arxiv.org/abs/2510.11773,arxiv-completion,2026-09-26 (citations:OpenAlex),,2510.11773,['https://arxiv.org/pdf/2510.11773'],qiboml towards the orchestration of quantum classical machine learning,,2,,
Quantum Generative Models for Computational Fluid Dynamics: A First Exploration of Latent Space Learning in Lattice Boltzmann Simulations,"A Hsain, F M Abbou",2025.0,0,"This paper presents the first application of quantum generative models to learned latent space representations of computational fluid dynamics (CFD) data. While recent work has explored quantum models for learning statistical properties of fluid systems, the combination of discrete latent space compression with quantum generative sampling for CFD remains unexplored. We develop a GPU-accelerated Lattice Boltzmann Method (LBM) simulator to generate fluid vorticity fields, which are compressed into a discrete 7-dimensional latent space using a Vector Quantized Variational Autoencoder (VQ-VAE). The central contribution is a comparative analysis of quantum and classical generative approaches for modeling this physics-derived latent distribution: we evaluate a Quantum Circuit Born Machine (QCBM) and Quantum Generative Adversarial Network (QGAN) against a classical Long Short-Term Memory (LSTM) baseline. Under our experimental conditions, both quantum models produced samples with lower average minimum distances to the true distribution compared to the LSTM, with the QCBM achieving the most favorable metrics. This work provides: (1)~a complete open-source pipeline bridging CFD simulation and quantum machine learning, (2)~the first empirical study of quantum generative modeling on compressed latent representations of physics simulations, and (3)~a foundation for future rigorous investigation at this intersection.",,"A Hsain, F M Abbou - arXiv preprint arXiv:2512.22672, 2025 - arxiv.org",[],https://arxiv.org/abs/2512.22672,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2512.22672,['https://arxiv.org/pdf/2512.22672'],quantum generative models for computational fluid dynamics a first exploration of latent space learning in lattice boltzmann simulations,MPO/TT 压缩 / MPS 生成/Born机 / 量子/混合LLM,1,,
Quantum Machine Learning in Transportation: A Case Study of Pedestrian Stress Modelling,"B Rababah, B Farooq",2025.0,0,"Quantum computing has opened new opportunities to tackle complex machine learning tasks, for instance, high-dimensional data representations commonly required in intelligent transportation systems. We explore quantum machine learning to model complex skin conductance response (SCR) events that reflect pedestrian stress in a virtual reality road crossing experiment. For this purpose, Quantum Support Vector Machine (QSVM) with an eight-qubit ZZ feature map and a Quantum Neural Network (QNN) using a Tree Tensor Network ansatz and an eight-qubit ZZ feature map, were developed on Pennylane. The dataset consists of SCR measurements along with features such as the response amplitude and elapsed time, which have been categorized into amplitude-based classes. The QSVM achieved good training accuracy, but had an overfitting problem, showing a low test accuracy of 45% and therefore impacting the reliability of the classification model. The QNN model reached a higher test accuracy of 55%, making it a better classification model than the QSVM and the classic versions.",,"B Rababah, B Farooq - Proceedings of IEEE Intelligent Transportation Systems Conference, 2025",[],https://arxiv.org/abs/2507.01235,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2507.01235,['https://arxiv.org/pdf/2507.01235'],quantum machine learning in transportation a case study of pedestrian stress modelling,量子/混合LLM / TTN/MERA/PEPS,1,"Proceedings of IEEE Intelligent Transportation Systems Conference, 2025",
Quantum-Enhanced LLM Efficient Fine Tuning,"X Kong, L Li, Z Chen, C Xue, X Xu, H Liu, Y Wu, Y Fang, H Fang, K Chen, Y Yang, M Dou, G Guo",2025.0,0,"Low-Rank Adaptation (LoRA) enables efficient fine-tuning of pre-trained language models through low-rank matrix approximation, achieving effectiveness in many scenarios. However, its representation capacity is constrained in complex tasks or high-rank dependency settings, potentially limiting model adaptability. To overcome the expressive bottleneck in classical low-rank approximation for fine-tuning large language models (LLMs), we propose Quantum Tensor Hybrid Adaptation (QTHA), a parameter-efficient fine-tuning method that integrates a quantum neural network (QNN) with a tensor network. QTHA explores quantum tensor hybrid fine-tuning within low-rank spaces by decomposing pre-trained weights into quantum neural network and tensor network representations, leveraging quantum state superposition to overcome classical rank limitations. Experiments demonstrate that QTHA achieves performance comparable to or surpassing LoRA in parameter-efficient fine-tuning. Compared to LoRA, QTHA reduces trainable parameters by 76% while reducing training loss by up to 17% and improving test set performance by up to 17% within the same training steps. This research not only enables lightweight adaptation of quantum resources to the billion-parameter models but also validates the feasibility of quantum hardware optimization driven by LLM tasks. It establishes the first engineering-ready foundation for future quantum-enhanced Artificial General Intelligence (AGI) systems.",,"X Kong, L Li, Z Chen, C Xue, X Xu, H Liu, Y Wu, Y Fang, H Fang, K Chen, Y Yang, M Dou, G Guo - arXiv preprint arXiv:2503.12790, 2025 - arxiv.org",[],https://arxiv.org/abs/2503.12790,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2503.12790,['https://arxiv.org/pdf/2503.12790'],quantum enhanced llm efficient fine tuning,MPS 语言模型 / MPO/TT 压缩 / 量子/混合LLM,2,,
Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks,"Y Zhao, X Yu, X Xiao, Z Chen, Z Liu, G Kurczveil, R G Beausoleil, S Liu, Z Zhang",2025.0,,"Physics intelligence and digital twins often require rapid and repeated performance evaluation of various engineering systems (e.g. robots, autonomous vehicles, semiconductor chips) to enable (almost) real-time actions or decision making. This has motivated the development of accelerated partial differential equation (PDE) solvers, in resource-constrained scenarios if the PDE solvers are to be deployed on the edge. Physics-informed neural networks (PINNs) have shown promise in solving high-dimensional PDEs, but the training time on state-of-the-art digital hardware (e.g., GPUs) is still orders-of-magnitude longer than the latency required for enabling real-time decision making. Photonic computing offers a potential solution to address this huge latency gap because of its ultra-high operation speed. However, the lack of photonic memory and the large device sizes prevent training real-size PINNs on photonic chips. This paper proposes a completely back-propagation-free (BP-free) and highly salable framework for training real-size PINNs on silicon photonic platforms. Our approach involves three key innovations: (1) a sparse-grid Stein derivative estimator to avoid the BP in the loss evaluation of a PINN, (2) a dimension-reduced zeroth-order optimization via tensor-train decomposition to achieve better scalability and convergence in BP-free training, and (3) a scalable on-chip photonic PINN training accelerator design using photonic tensor cores. We validate our numerical methods on both low- and high-dimensional PDE benchmarks. Through pre-silicon simulation based on real device parameters, we further demonstrate the significant performance benefit (e.g., real-time training, huge chip area reduction) of our photonic accelerator.",,"Y Zhao, X Yu, X Xiao, Z Chen, Z Liu, G Kurczveil, R G Beausoleil, S Liu, Z Zhang - arXiv preprint arXiv:2502.12384, 2025 - arxiv.org",[],https://arxiv.org/abs/2502.12384,arxiv-completion,2026-09-26 (citations:OpenAlex),,2502.12384,['https://arxiv.org/pdf/2502.12384'],scalable back propagation free training of optical physics informed neural networks,,1,,
Sequence Modeling with Spectral Mean Flows,"J Kim, M Beier, P Bevanda, N Kim, S Hong",2025.0,,"A key question in sequence modeling with neural networks is how to represent and learn highly nonlinear and probabilistic state dynamics. Operator theory views such dynamics as linear maps on Hilbert spaces containing mean embedding vectors of distributions, offering an appealing but currently overlooked perspective. We propose a new approach to sequence modeling based on an operator-theoretic view of a hidden Markov model (HMM). Instead of materializing stochastic recurrence, we embed the full sequence distribution as a tensor in the product Hilbert space. A generative process is then defined as maximum mean discrepancy (MMD) gradient flow in the space of sequences. To overcome challenges with large tensors and slow sampling convergence, we introduce spectral mean flows, a novel tractable algorithm integrating two core concepts. First, we propose a new neural architecture by leveraging spectral decomposition of linear operators to derive a scalable tensor network decomposition of sequence mean embeddings. Second, we extend MMD gradient flows to time-dependent Hilbert spaces and connect them to flow matching via the continuity equation, enabling simulation-free learning and faster sampling. We demonstrate competitive results on a range of time-series modeling datasets. Code is available at https://github.com/jw9730/spectral-mean-flow.",,"J Kim, M Beier, P Bevanda, N Kim, S Hong - arXiv preprint arXiv:2510.15366, 2025 - arxiv.org",[],https://arxiv.org/abs/2510.15366,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2510.15366,['https://arxiv.org/pdf/2510.15366'],sequence modeling with spectral mean flows,MPS 生成/Born机 / MPS/序列建模 / 量子启发综述,1,,
The Born Ultimatum: Conditions for Classical Surrogation of Quantum Generative Models with Correlators,"M Herrero-Gonzalez, B Coyle, K McDowall, R Grassie, S Beentjes, A Khamseh, E Kashefi",2025.0,0,"Quantum Circuit Born Machines (QCBMs) are powerful quantum generative models that sample according to the Born rule, with complexity-theoretic evidence suggesting potential quantum advantages for generative tasks. Here, we identify QCBMs as a quantum Fourier model independently of the loss function. This allows us to apply known dequantization conditions when the optimal quantum distribution is available. However, realizing this distribution is hindered by trainability issues such as vanishing gradients on quantum hardware. Recent train-classical, deploy-quantum approaches propose training classical surrogates of QCBMs and using quantum devices only for inference. We analyze the limitations of these methods arising from deployment discrepancies between classically trained and quantumly deployed parameters. Using the Fourier decomposition of the Born rule in terms of correlators, we quantify this discrepancy analytically. Approximating the decomposition via distribution truncation and classical surrogation provides concrete examples of such discrepancies, which we demonstrate numerically. We study this effect using tensor-networks and Pauli-propagation-based classical surrogates. Our study examines the use of IQP circuits, matchcircuits, Heisenberg-chain circuits, and Haldane-chain circuits for the QCBM ansatz. In doing so, we derive closed-form expressions for Pauli propagation in IQP circuits and the dynamical Lie algebra of the Haldane chain, which may be of independent interest.",,"M Herrero-Gonzalez, B Coyle, K McDowall, R Grassie, S Beentjes, A Khamseh, E Kashefi - arXiv preprint arXiv:2511.01845, 2025 - arxiv.org",[],https://arxiv.org/abs/2511.01845,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2511.01845,['https://arxiv.org/pdf/2511.01845'],the born ultimatum conditions for classical surrogation of quantum generative models with correlators,MPO/TT 压缩 / MPS 生成/Born机,1,,
Typical Machine Learning Datasets as Low-Depth Quantum Circuits,"F J Kiwit, B Jobst, A Luckow, F Pollmann, C A Riofrío",2025.0,0,"Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading and the ability to scale to relevant problem sizes have prevented demonstrations of such advantages on practical problems. In particular, the encoding of arbitrary classical data into quantum states usually comes at a high computational cost, either in terms of qubits or gate count. However, real-world data typically exhibits some inherent structure (such as image data) which can be leveraged to load them with a much smaller cost on a quantum computer. This work further develops an efficient algorithm for finding low-depth quantum circuits to load classical image data as quantum states. To evaluate its effectiveness, we conduct systematic studies on the MNIST, Fashion-MNIST, CIFAR-10, and Imagenette datasets. The corresponding circuits for loading the full large-scale datasets are available publicly as PennyLane datasets and can be used by the community for their own benchmarks. We further analyze the performance of various quantum classifiers, such as quantum kernel methods, parameterized quantum circuits, and tensor-network classifiers, and we compare them to convolutional neural networks. In particular, we focus on the performance of the quantum classifiers as we introduce nonlinear functions of the input state, e.g., by letting the circuit parameters depend on the input state.",,"F J Kiwit, B Jobst, A Luckow, F Pollmann, C A Riofrío - Quantum Science and Technology 10 4, 045035 (2025)",[],https://arxiv.org/abs/2505.03399,arxiv-completion,2026-09-26 (citations:OpenAlex),量子/混合LLM,2505.03399,['https://arxiv.org/pdf/2505.03399'],typical machine learning datasets as low depth quantum circuits,量子/混合LLM,1,"Quantum Science and Technology 10 4, 045035 (2025)",
"Universality and kernel-adaptive training for classically trained, quantum-deployed generative models","A Kurkin, K Shen, S Pielawa, H Wang, V Dunjko",2025.0,0,"The instantaneous quantum polynomial (IQP) quantum circuit Born machine (QCBM) has been proposed as a promising quantum generative model over bitstrings. Recent works have shown that the training of IQP-QCBM is classically tractable w.r.t. the so-called Gaussian kernel maximum mean discrepancy (MMD) loss function, while maintaining the potential of a quantum advantage for sampling itself. Nonetheless, the model has a number of aspects where improvements would be important for more general utility: (1) the basic model is known to be not universal - i.e. it is not capable of representing arbitrary distributions, and it was not known whether it is possible to achieve universality by adding hidden (ancillary) qubits; (2) a fixed Gaussian kernel used in the MMD loss can cause training issues, e.g., vanishing gradients. In this paper, we resolve the first question and make decisive strides on the second. We prove that for an $n$-qubit IQP generator, adding $n + 1$ hidden qubits makes the model universal. For the latter, we propose a kernel-adaptive training method, where the kernel is adversarially trained. We show that in the kernel-adaptive method, the convergence of the MMD value implies weak convergence in distribution of the generator. We also analytically analyze the limitations of the MMD-based training method. Finally, we verify the performance benefits on the dataset crafted to spotlight improvements by the suggested method. The results show that kernel-adaptive training outperforms a fixed Gaussian kernel in total variation distance, and the gap increases with the dataset dimensionality. These modifications and analyses shed light on the limits and potential of these new quantum generative methods, which could offer the first truly scalable insights in the comparative capacities of classical versus quantum models, even without access to scalable quantum computers.",,"A Kurkin, K Shen, S Pielawa, H Wang, V Dunjko - arXiv preprint arXiv:2510.08476, 2025 - arxiv.org",[],https://arxiv.org/abs/2510.08476,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2510.08476,['https://arxiv.org/pdf/2510.08476'],universality and kernel adaptive training for classically trained quantum deployed generative models,MPS 生成/Born机,1,,
A Tensor-Train Decomposition based Compression of LLMs on Group Vector Systolic Accelerator,"S Huang, T Wang, A Li, A Shen, K Li, K Jiang, M Huang, H Yu",2025.0,0,"Large language models (LLMs) are both storage-intensive and computation-intensive, posing significant challenges when deployed on resource-constrained hardware. As linear layers in LLMs are mainly resource consuming parts, this paper develops a tensor-train decomposition (TTD) for LLMs with a further hardware implementation on FPGA. TTD compression is applied to the linear layers in ChatGLM3-6B and LLaMA2-7B models with compression ratios (CRs) for the whole network 1.94$\times$ and 1.60$\times$, respectively. The compressed LLMs are further implemented on FPGA hardware within a highly efficient group vector systolic array (GVSA) architecture, which has DSP-shared parallel vector PEs for TTD inference, as well as optimized data communication in the accelerator. Experimental results show that the corresponding TTD based LLM accelerator implemented on FPGA achieves 1.45$\times$ and 1.57$\times$ reduction in first token delay for ChatGLM3-6B and LLaMA2-7B models, respectively.",,"S Huang, T Wang, A Li, A Shen, K Li, K Jiang, M Huang, H Yu - arXiv preprint arXiv:2501.19135, 2025 - arxiv.org",[],https://arxiv.org/abs/2501.19135,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2501.19135,['https://arxiv.org/pdf/2501.19135'],a tensor train decomposition based compression of llms on group vector systolic accelerator,MPS 语言模型 / MPO/TT 压缩,1,,
Approximation and learning with compositional tensor trains,"M Eigel, C Miranda, A Nouy, D Sommer",2025.0,0,"We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools, such as (sparse) polynomials, deep neural networks (DNNs) with fixed width, or tensor networks with arbitrary permutation of the inputs, or more general affine coordinate transformations, with similar complexities. This format can be viewed as a DNN with width exponential in the input dimension and structured weights matrices. Compared to DNNs, this format enables controlled compression at the layer level using efficient tensor algebra. On the optimization side, we derive a layerwise algorithm inspired by natural gradient descent, allowing to exploit efficient low-rank tensor algebra. This relies on low-rank estimations of Gram matrices, and tensor structured random sketching. Viewing the format as a discrete dynamical system, we also derive an optimization algorithm inspired by numerical methods in optimal control. Numerical experiments on regression tasks demonstrate the expressivity of the new format and the relevance of the proposed optimization algorithms. Overall, CTTs combine the expressivity of compositional models with the algorithmic efficiency of tensor algebra, offering a scalable alternative to standard deep neural networks.",,"M Eigel, C Miranda, A Nouy, D Sommer - arXiv preprint arXiv:2512.18059, 2025 - arxiv.org",[],https://arxiv.org/abs/2512.18059,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2512.18059,['https://arxiv.org/pdf/2512.18059'],approximation and learning with compositional tensor trains,MPO/TT 压缩,1,,
"Compression, simulation, and synthesis of turbulent flows with tensor trains","S Pisoni, R D Peddinti, E Tiunov, S E Guzman, L Aolita",2025.0,,"Numerical simulations of turbulent fluids are paramount to real-life applications, from predicting and modeling flows to diagnostic purposes in engineering. However, they are also computationally challenging due to their intrinsically non-linear dynamics, which require a very high spatial resolution to accurately describe them. A promising idea is to represent flows on a discrete mesh using tensor trains (TTs), featuring a convenient scaling of the number of parameters with the mesh size. However, it is unclear how the compression power of TTs is affected by the complexity of the flows, as measured by the Reynolds number. In fact, no comprehensive analysis of how the TT representation affects the turbulent properties has yet been carried out. We fill this gap by analyzing TTs as an Ansatz to compress, simulate, and generate 3D snapshots with turbulent-like features. Specifically, we first investigate the effect of TT compression on key turbulence signatures, such as the energy spectrum, the PDF of velocity increments, and flatness. Second, we extend the 2D TT-solver introduced in [1] to a 3D cubic domain with periodic boundary conditions. We use it to simulate the incompressible Navier-Stokes dynamics at $Re_λ=315$ for a total of 9-10 Kolmogorov turnover times, showcasing the numerical stability of the TT-solver in fully developed turbulent regimes. Third, we develop a TT algorithm to synthesize artificial snapshots that exhibit turbulent-like features, with a logarithmic cost in the mesh size. Our analysis demonstrates the ability of the TT representation to capture the characteristic features of turbulence. This offers a powerful quantum-inspired toolkit for the computational treatment of turbulent flows.",,"S Pisoni, R D Peddinti, E Tiunov, S E Guzman, L Aolita - arXiv preprint arXiv:2506.05477, 2025 - arxiv.org",[],https://arxiv.org/abs/2506.05477,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2506.05477,['https://arxiv.org/pdf/2506.05477'],compression simulation and synthesis of turbulent flows with tensor trains,MPO/TT 压缩,1,,
Domain-Aware Tensor Network Structure Search,"G Iacovides, W Zhou, C Li, Q Zhao, D Mandic",2025.0,0,"Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art (SOTA) algorithms solve TN-SS as a purely numerical optimization problem and require extensive function evaluations, which is prohibitive for real-world applications. In addition, existing methods ignore the valuable domain information inherent in real-world tensor data and lack transparency in their identified TN structures. To this end, we propose a novel TN-SS framework, termed the tnLLM, which incorporates domain information about the data and harnesses the reasoning capabilities of large language models (LLMs) to directly predict suitable TN structures. The proposed framework involves a domain-aware prompting pipeline which instructs the LLM to infer suitable TN structures based on the real-world relationships between tensor modes. In this way, our approach is capable of not only iteratively optimizing the objective function, but also generating domain-aware explanations for the identified structures. Experimental results demonstrate that tnLLM achieves comparable TN-SS objective function values with much fewer function evaluations compared to SOTA algorithms. Furthermore, we demonstrate that the LLM-enabled domain information can be used to find good initializations in the search space for sampling-based SOTA methods to accelerate their convergence while preserving theoretical performance guarantees.",,"G Iacovides, W Zhou, C Li, Q Zhao, D Mandic - arXiv preprint arXiv:2505.23537, 2025 - arxiv.org",[],https://arxiv.org/abs/2505.23537,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2505.23537,['https://arxiv.org/pdf/2505.23537'],domain aware tensor network structure search,MPS 语言模型,1,,
FETTA: Flexible and Efficient Hardware Accelerator for Tensorized Neural Network Training,"J Lu, J Tian, H Li, I Young, Z Zhang",2025.0,,"The increasing demand for on-device training of deep neural networks (DNNs) aims to leverage personal data for high-performance applications while addressing privacy concerns and reducing communication latency. However, resource-constrained platforms face significant challenges due to the intensive computational and memory demands of DNN training. Tensor decomposition emerges as a promising approach to compress model size without sacrificing accuracy. Nevertheless, training tensorized neural networks (TNNs) incurs non-trivial overhead and severe performance degradation on conventional accelerators due to complex tensor shaping requirements. To address these challenges, we propose FETTA, an algorithm and hardware co-optimization framework for efficient TNN training. On the algorithm side, we develop a contraction sequence search engine (CSSE) to identify the optimal contraction sequence with the minimal computational overhead. On the hardware side, FETTA features a flexible and efficient architecture equipped with a reconfigurable contraction engine (CE) array to support diverse dataflows. Furthermore, butterfly-based distribution and reduction networks are implemented to perform flexible tensor shaping operations during computation. Evaluation results demonstrate that FETTA achieves reductions of 20.5x/100.9x, 567.5x/45.03x, and 11609.7x/4544.8x in terms of processing latency, energy, and energy-delay product (EDP) over GPU and TPU, respectively. Moreover, working on the tensorized training, FETTA outperforms prior accelerators with a speedup of 3.87~14.63x, and an energy efficiency improvement of 1.41~2.73x on average.",,"J Lu, J Tian, H Li, I Young, Z Zhang - arXiv preprint arXiv:2504.06474, 2025 - arxiv.org",[],https://arxiv.org/abs/2504.06474,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2504.06474,['https://arxiv.org/pdf/2504.06474'],fetta flexible and efficient hardware accelerator for tensorized neural network training,MPO/TT 压缩 / MPS/序列建模,1,,
Functional tensor train neural network for solving high-dimensional PDEs,"Y Feng, M K Ng, K Tang, Z Zhang",2025.0,0,"Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires uniform grids of regular domains, which limits its application on non-uniform grids or irregular domains. To address the limitation, we develop a functional tensor train neural network (FTTNN) for solving high-dimensional PDEs, which can represent PDE solutions on non-uniform grids or irregular domains. An essential ingredient of our approach is to represent the PDE solutions by the functional tensor train format whose TT-core functions are approximated by neural networks. To give the functional tensor train representation, we propose and study functional tensor train rank and employ it into a physics-informed loss function for training. Because of tensor train representation, the resulting high-dimensional integral in the loss function can be computed via one-dimensional integrals by Gauss quadrature rules. Numerical examples including high-dimensional PDEs on regular or irregular domains are presented to demonstrate that the performance of the proposed FTTNN is better than that of Physics Informed Neural Networks (PINN).",,"Y Feng, M K Ng, K Tang, Z Zhang - arXiv preprint arXiv:2510.13386, 2025 - arxiv.org",[],https://arxiv.org/abs/2510.13386,arxiv-completion,2026-09-26 (citations:OpenAlex),,2510.13386,['https://arxiv.org/pdf/2510.13386'],functional tensor train neural network for solving high dimensional pdes,,1,,
Grokking as an entanglement transition in tensor network machine learning,"D Pomarico, A Monaco, G Magnifico, A Lacalamita, E Pantaleo, L Bellantuono, S Tangaro, T Maggipinto, M L Rocca, E Picardi, N Amoroso, G Pesole, S Stramaglia, R Bellotti",2025.0,0,"Grokking is a intriguing phenomenon in machine learning where a neural network, after many training iterations with negligible improvement in generalization, suddenly achieves high accuracy on unseen data. By working in the quantum-inspired machine learning framework based on tensor networks, we numerically prove that grokking phenomenon can be related to an entanglement dynamical transition in the underlying quantum many-body systems, consisting in a one-dimensional lattice with each site hosting a qubit. Two datasets are considered as use case scenarios, namely fashion MNIST and gene expression communities of hepatocellular carcinoma. In both cases, we train Matrix Product State (MPS) to perform binary classification tasks, and we analyse the learning dynamics. We exploit measurement of qubits magnetization and correlation functions in the MPS network as a tool to identify meaningful and relevant gene subcommunities, verified by means of enrichment procedures.",,"D Pomarico, A Monaco, G Magnifico, A Lacalamita, E Pantaleo, L Bellantuono, S Tangaro, T Maggipinto, M L Rocca, E Picardi, N Amoroso, G Pesole, S Stramaglia, R Bellotti - arXiv preprint arXiv:2503.10483, 2025 - arxiv.org",[],https://arxiv.org/abs/2503.10483,arxiv-completion,2026-09-26 (citations:OpenAlex),,2503.10483,['https://arxiv.org/pdf/2503.10483'],grokking as an entanglement transition in tensor network machine learning,,1,,
Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective,"S M Subiñas, J M Martín, A M Ali, J Sedano, Á M García-Vico",2025.0,0,"In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal solution of the problems. As in other tensor network algorithms for combinatorial optimization problems, the method is based on imaginary time evolution and the implementation of restrictions in the tensor network. In addition, we introduce the use of symmetries and the reutilization of intermediate calculations, reducing the computational complexity for both problems. To show the efficiency of our implementations, we carry out some performance experiments and compare the results with those obtained by other classical algorithms.",,"S M Subiñas, J M Martín, A M Ali, J Sedano, Á M García-Vico - arXiv preprint arXiv:2506.11711, 2025 - arxiv.org",[],https://arxiv.org/abs/2506.11711,arxiv-completion,2026-09-26 (citations:OpenAlex),量子启发综述,2506.11711,['https://arxiv.org/pdf/2506.11711'],knapsack and shortest path problems generalizations from a quantum inspired tensor network perspective,量子启发综述,1,,
Minimality of Tree Tensor Network Ranks,"J Jovcheva, T Seynnaeve, N Vannieuwenhoven",2025.0,,"For a given tree tensor network $G$, we call a tuple of bond dimensions minimal if there exists a tensor $T$ that can be represented by this network but not on the same tree topology with strictly smaller bond dimensions. We establish necessary and sufficient conditions on the bond dimensions of a tree tensor network to be minimal, generalising a characterisation of Carlini and Kleppe about existence of tensors with a given multilinear rank. We also show that in a minimal tree tensor network, the non-minimal tensors form a Zariski closed subset, so minimality is a generic property in this sense.",,"J Jovcheva, T Seynnaeve, N Vannieuwenhoven - arXiv preprint arXiv:2509.09463, 2025 - arxiv.org",[],https://arxiv.org/abs/2509.09463,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2509.09463,['https://arxiv.org/pdf/2509.09463'],minimality of tree tensor network ranks,TTN/MERA/PEPS,1,,
PEPS: Quantum-Inspired Reinforcement Learning for Coherent Reasoning Traces in LLMs,"V Margapuri, G Kazanjian, N Kosaraju",2025.0,0,"Large Language Models (LLMs) often struggle with maintaining coherent multi-step reasoning traces, particularly in tasks that require a structured logical flow. This work introduces a quantum-inspired approach to address the challenge by incorporating a fidelity-based reward derived from Projected Entangled Pair States (PEPS) into Proximal Policy Optimization. Unlike prior approaches that use direct supervision or contrastive objectives, the proposed method guides learning through structural consistency, offering a novel approach to enforce global coherence in generated reasoning traces. The proposed framework is evaluated using multiple coherence-determining metrics on diverse datasets such as GSM8K, StrategyQA, and EntailmentBank spanning arithmetic, intuitive, and entailment-based reasoning. Results show that the proposed quantum-inspired approach offers significant improvements over supervised, contrastive, and pretrained baseline approaches, highlighting the effectiveness of quantum-inspired fidelity as a foundation to improve reasoning trace coherence in LLMs.",,"V Margapuri, G Kazanjian, N Kosaraju - arXiv preprint arXiv:2509.20105, 2025 - arxiv.org",[],https://arxiv.org/abs/2509.20105,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2509.20105,['https://arxiv.org/pdf/2509.20105'],peps quantum inspired reinforcement learning for coherent reasoning traces in llms,MPS 语言模型 / TTN/MERA/PEPS,2,,
QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks,"Y Werner, A Malemath, M Liu, V F Rey, N Palaiodimopoulos, P Lukowicz, M Kiefer-Emmanouilidis",2025.0,0,"Kolmogorov Arnold Networks (KANs), built upon the Kolmogorov Arnold representation theorem (KAR), have demonstrated promising capabilities in expressing complex functions with fewer neurons. This is achieved by implementing learnable parameters on the edges instead of on the nodes, unlike traditional networks such as Multi-Layer Perceptrons (MLPs). However, KANs potential in quantum machine learning has not yet been well explored. In this work, we present an implementation of these KAN architectures in both hybrid and fully quantum forms using a Quantum Circuit Born Machine (QCBM). We adapt the KAN transfer using pre-trained residual functions, thereby exploiting the representational power of parametrized quantum circuits. In the hybrid model we combine classical KAN components with quantum subroutines, while the fully quantum version the entire architecture of the residual function is translated to a quantum model. We demonstrate the feasibility, interpretability and performance of the proposed Quantum KAN (QuKAN) architecture.",,"Y Werner, A Malemath, M Liu, V F Rey, N Palaiodimopoulos, P Lukowicz, M Kiefer-Emmanouilidis - arXiv preprint arXiv:2506.22340, 2025 - arxiv.org",[],https://arxiv.org/abs/2506.22340,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2506.22340,['https://arxiv.org/pdf/2506.22340'],qukan a quantum circuit born machine approach to quantum kolmogorov arnold networks,MPS 生成/Born机 / 量子/混合LLM,1,,
Quantum Circuit Implementation of Two Matrix Product Operations and Elementary Column Transformations,"Y Liu, Y Tao, J Lan, S Fei",2025.0,0,"This paper focuses on quantum algorithms for three key matrix operations: Hadamard (Schur) product, Kronecker (tensor) product, and elementary column transformations each. By designing specific unitary transformations and auxiliary quantum measurement, efficient quantum schemes with circuit diagrams are proposed. Their computational depths are: O(1) for Kronecker product; O(max(m,n)) for Hadamard product (linked to matrix dimensions); and O(m) for elementary column transformations of (2^n X 2^m) matrices (dependent only on column count).Notably, compared to traditional column transformation via matrix transposition and row transformations, this scheme reduces computation steps and quantum gate usage, lowering quantum computing energy costs.",,"Y Liu, Y Tao, J Lan, S Fei - arXiv preprint arXiv:2511.02413, 2025 - arxiv.org",[],https://arxiv.org/abs/2511.02413,arxiv-completion,2026-09-26 (citations:OpenAlex),,2511.02413,['https://arxiv.org/pdf/2511.02413'],quantum circuit implementation of two matrix product operations and elementary column transformations,,1,,
Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates,"N v Hülst, P Siegl, P Over, S Bengoechea, T Hashizume, M G Cecile, T Rung, D Jaksch",2025.0,,"We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.",,"N v Hülst, P Siegl, P Over, S Bengoechea, T Hashizume, M G Cecile, T Rung, D Jaksch - arXiv preprint arXiv:2507.05222, 2025 - arxiv.org",[],https://arxiv.org/abs/2507.05222,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2507.05222,['https://arxiv.org/pdf/2507.05222'],quantum inspired tensor network fractional step method for incompressible flow in curvilinear coordinates,MPO/TT 压缩,1,,
Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning,"M Willner, M Trenti, D Lebiedz",2025.0,,"Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the quotient geometry underlying the TTN parameter space. Our framework allows for arbitrary horizontal distributions, and we develop efficient first- and second-order optimization algorithms that exploit this geometry. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative digit classification task and reveal an important tradeoff between two different horizontal distributions that are available for TTNs: while one offers cleaner geometric statements, the other ultimately leads to more efficient algorithms.",,"M Willner, M Trenti, D Lebiedz - arXiv preprint arXiv:2507.21726, 2025 - arxiv.org",[],https://arxiv.org/abs/2507.21726,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2507.21726,['https://arxiv.org/pdf/2507.21726'],riemannian optimization on tree tensor networks with application in machine learning,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
TeRA: Vector-based Random Tensor Network for High-Rank Adaptation of Large Language Models,"Y Gu, W Zhou, G Iacovides, D Mandic",2025.0,,"Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have significantly reduced the number of trainable parameters needed in fine-tuning large language models (LLMs). The developments of LoRA-style adapters have considered two main directions: (1) enhancing model expressivity with high-rank adapters, and (2) aiming for further parameter reduction, as exemplified by vector-based methods. However, these approaches come with a trade-off, as achieving the expressivity of high-rank weight updates typically comes at the cost of sacrificing the extreme parameter efficiency offered by vector-based techniques. To address this issue, we propose a vector-based random Tensor network for high-Rank Adaptation (TeRA), a novel PEFT method that achieves high-rank weight updates while retaining the parameter efficiency of vector-based PEFT adapters. This is achieved by parametrizing the tensorized weight update matrix as a Tucker-like tensor network (TN), whereby large randomly initialized factors are frozen and shared across layers, while only small layer-specific scaling vectors, corresponding to diagonal entries of factor matrices, are trained. Comprehensive experiments demonstrate that TeRA matches or even outperforms existing high-rank adapters, while requiring as few trainable parameters as vector-based methods. Theoretical analysis and ablation studies validate the effectiveness of the proposed TeRA method. The code is available at https://github.com/guyuxuan9/TeRA.",,"Y Gu, W Zhou, G Iacovides, D Mandic - arXiv preprint arXiv:2509.03234, 2025 - arxiv.org",[],https://arxiv.org/abs/2509.03234,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2509.03234,['https://arxiv.org/pdf/2509.03234'],tera vector based random tensor network for high rank adaptation of large language models,MPS 语言模型 / MPO/TT 压缩,1,,
Tensor Train Quantum State Tomography using Compressed Sensing,"S S Sofi, C Vermeylen, L D Lathauwer",2025.0,0,"Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become impractical due to the exponential growth of parameters in the state representation. In this work, we address this challenge by parameterizing the state using a low-rank block tensor train decomposition and demonstrate that our approach is both memory- and computationally efficient. This framework applies to a broad class of quantum states that can be well approximated by low-rank decompositions, including pure states, nearly pure states, and ground states of Hamiltonians.",,"S S Sofi, C Vermeylen, L D Lathauwer - 2025 33rd European Signal Processing Conference (EUSIPCO)",[],https://arxiv.org/abs/2506.23560,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2506.23560,['https://arxiv.org/pdf/2506.23560'],tensor train quantum state tomography using compressed sensing,MPO/TT 压缩,1,2025 33rd European Signal Processing Conference (EUSIPCO),
Time evolution of the quantum Ising model in two dimensions using Tree Tensor Networks,"W Krinitsin, N Tausendpfund, M Heyl, M Rizzi, M Schmitt",2025.0,0,"The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the dynamics of the quantum Ising model in two dimensions. Within the perturbative regime of small transverse fields, TTNs faithfully reproduce analytically known, but non-trivial and physically interesting results, for lattices up to $16 \times 16$ sites. Limitations of the method related to the rapid growth of entanglement entropy are explored within more general, paradigmatic quench settings. We provide and discuss comprehensive benchmarks regarding the benefit of \emph{GPU} acceleration and the impact of using local operator sums on the performance.",,"W Krinitsin, N Tausendpfund, M Heyl, M Rizzi, M Schmitt - arXiv preprint arXiv:2505.07612, 2025 - arxiv.org",[],https://arxiv.org/abs/2505.07612,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2505.07612,['https://arxiv.org/pdf/2505.07612'],time evolution of the quantum ising model in two dimensions using tree tensor networks,TTN/MERA/PEPS / 互信息/标度,1,,
Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models,"Z Tao, Y Takida, N Murata, Q Zhao, Y Mitsufuji",2025.0,,"Parameter-Efficient Fine-Tuning (PEFT) of text-to-image models has become an increasingly popular technique with many applications. Among the various PEFT methods, Low-Rank Adaptation (LoRA) and its variants have gained significant attention due to their effectiveness, enabling users to fine-tune models with limited computational resources. However, the approximation gap between the low-rank assumption and desired fine-tuning weights prevents the simultaneous acquisition of ultra-parameter-efficiency and better performance. To reduce this gap and further improve the power of LoRA, we propose a new PEFT method that combines two classes of adaptations, namely, transform and residual adaptations. In specific, we first apply a full-rank and dense transform to the pre-trained weight. This learnable transform is expected to align the pre-trained weight as closely as possible to the desired weight, thereby reducing the rank of the residual weight. Then, the residual part can be effectively approximated by more compact and parameter-efficient structures, with a smaller approximation error. To achieve ultra-parameter-efficiency in practice, we design highly flexible and effective tensor decompositions for both the transform and residual adaptations. Additionally, popular PEFT methods such as DoRA can be summarized under this transform plus residual adaptation scheme. Experiments are conducted on fine-tuning Stable Diffusion models in subject-driven and controllable generation. The results manifest that our method can achieve better performances and parameter efficiency compared to LoRA and several baselines.",,"Z Tao, Y Takida, N Murata, Q Zhao, Y Mitsufuji - arXiv preprint arXiv:2501.08727, 2025 - arxiv.org",[],https://arxiv.org/abs/2501.08727,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2501.08727,['https://arxiv.org/pdf/2501.08727'],transformed low rank adaptation via tensor decomposition and its applications to text to image models,MPO/TT 压缩 / MPS 生成/Born机,1,,
Tree Tensor Networks Methods for Efficient Calculation of Molecular Vibrational Spectra,"S Sun, R M Milbradt, S Knecht, C Kumar, C B Mendl",2025.0,,"We develop and employ general Tree Tensor Networks (TTNs) to compute the vibrational spectra for two model systems: a set of 64-dimensional coupled oscillators and acetonitrile. We explore various tree architectures, ranging from the simple linear structure of Matrix Product States (MPS), to trees where only the leaf nodes carry a physical leg -- as commonly seen in the underlying ansatz of the Multilayer Multiconfiguration Time-Dependent Hartree (ML-MCTDH) method -- and further to more general trees in which all nodes are allowed to possess a physical leg. In addition, we implement Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) methods and Inverse Iteration methods as eigensolvers. Benchmarking runtime and accuracy shows that all tested topologies can reach high accuracy. For acetonitrile, inverse-iteration refinement brings all 84 computed states below 1~cm$^{-1}$ error, while the fork-4 tree, a comb-like tree with four backbone nodes, provides the best overall balance between accuracy and cost. MPS remains computationally attractive, whereas more connected trees generally improve accuracy at fixed bond dimension. All numerical simulations were performed using PyTreeNet, a Python package designed for flexible tensor network computations.",,"S Sun, R M Milbradt, S Knecht, C Kumar, C B Mendl - J. Chem. Phys. 165, 034111 (2026)",[],https://arxiv.org/abs/2512.15875,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2512.15875,['https://arxiv.org/pdf/2512.15875'],tree tensor networks methods for efficient calculation of molecular vibrational spectra,TTN/MERA/PEPS,1,"J. Chem. Phys. 165, 034111 (2026)",
Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments,"X Chen, I Franco",2025.0,0,"We introduce an efficient method TTN-HEOM for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme to the bexcitonic generalization of the numerically-exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system-bath interaction. These master equations are constructed based on the time-dependent Dirac--Frenkel variational principle which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, Tensor Equations for Non-Markovian Structured Open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: Two fixed-rank methods that require a constant memory footprint during the dynamics, and one adaptive-rank method with variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude--Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable to simulate both dephasing and relaxation dynamics of driven quantum system interacting with structured baths, even those of chemical complexity, with affordable computational cost.",,"X Chen, I Franco - arXiv preprint arXiv:2505.00126, 2025 - arxiv.org",[],https://arxiv.org/abs/2505.00126,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2505.00126,['https://arxiv.org/pdf/2505.00126'],tree tensor network hierarchical equations of motion based on time dependent variational principle for efficient open quantum dynamics in structured thermal environments,TTN/MERA/PEPS,1,,
pyTTN: An Open Source Toolbox for Open and Closed System Quantum Dynamics Simulations Using Tree Tensor Networks,"L P Lindoy, D Rodrigo-Albert, Y Rath, I Rungger",2025.0,0,"We present the Python Tree Tensor Network package (pyTTN) for the evaluation of dynamical properties of closed and open quantum systems that makes use of Tree Tensor Network (TTN), or equivalently the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH), based representations of wavefunctions. This package includes several features allowing for easy setup of zero- and finite-temperature calculations for general Hamiltonians using single and multi-set TTN ansätze with an adaptive bond dimension through the use of subspace expansion techniques. All core features are implemented in C++ with Python bindings provided to simplify the use of this package. In addition to these core features, pyTTN provides several tools for setting up efficient simulation of open quantum system dynamics, including the use of the TTN ansatz to represent the auxiliary density operator space for the simulation of the Hierarchical Equation of Motion (HEOM) method and generalised pseudomode methods; furthermore we demonstrate that the two approaches are equivalent up to a non-unitary normal mode transformation acting on the pseudomode degrees of freedom. We present a set of applications of the package, starting with the widely used benchmark case of the photo-excitation dynamics of 24 mode pyrazine, following which we consider a more challenging model describing the exciton dynamics at the interface of a $n$-oligothiophene donor-C$_{60}$ fullerene acceptor system. Finally, we consider applications to open quantum systems, including the spin-boson model, a set of extended dissipative spin models, and an Anderson impurity model. By combining ease of use, an efficient implementation, as well as an extendable design allowing for the addition of future extensions, pyTTN can be integrated in a wide range of computational modelling software.",,"L P Lindoy, D Rodrigo-Albert, Y Rath, I Rungger - arXiv preprint arXiv:2503.15460, 2025 - arxiv.org",[],https://arxiv.org/abs/2503.15460,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2503.15460,['https://arxiv.org/pdf/2503.15460'],pyttn an open source toolbox for open and closed system quantum dynamics simulations using tree tensor networks,TTN/MERA/PEPS,1,,
Quantum-PEFT: Ultra parameter-efficient fine-tuning,"T Koike-Akino, F Tonin, Y Wu, F Z Wu, L N Candogan, V Cevher",2025.0,,"This paper introduces Quantum-PEFT that leverages quantum computations for parameter-efficient fine-tuning (PEFT). Unlike other additive PEFT methods, such as low-rank adaptation (LoRA), Quantum-PEFT exploits an underlying full-rank yet surprisingly parameter efficient quantum unitary parameterization. With the use of Pauli parameterization, the number of trainable parameters grows only logarithmically with the ambient dimension, as opposed to linearly as in LoRA-based PEFT methods. Quantum-PEFT achieves vanishingly smaller number of trainable parameters than the lowest-rank LoRA as dimensions grow, enhancing parameter efficiency while maintaining a competitive performance. We apply Quantum-PEFT to several transfer learning benchmarks in language and vision, demonstrating significant advantages in parameter efficiency.",,"T Koike-Akino, F Tonin, Y Wu, F Z Wu, L N Candogan, V Cevher - arXiv preprint arXiv:2503.05431, 2025 - arxiv.org",[],https://arxiv.org/abs/2503.05431,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2503.05431,['https://arxiv.org/pdf/2503.05431'],quantum peft ultra parameter efficient fine tuning,MPO/TT 压缩,1,,
MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning,"J Lopez-Piqueres, P Deshpande, A Ray, M J Villani, M Pistoia, N Kumar",2025.0,,"We present MetaTT, a Tensor Train (TT) adapter framework for fine-tuning of pre-trained transformers. MetaTT enables flexible and parameter-efficient model adaptation by using a single shared TT to factorize transformer sub-modules. This factorization indexes key structural dimensions, including layer and matrix type, and can optionally incorporate heads and tasks. This design allows MetaTT's parameter count to scale with the sum, rather than the product, of the modes, resulting in a substantially more compact adapter. Our benchmarks compare MetaTT with LoRA along with recent state-of-the-art matrix and tensor decomposition based fine-tuning methods. We observe that when tested on single-task standard language modeling benchmarks, MetaTT achieves competitive parameter efficiency to accuracy tradeoff. We further demonstrate that MetaTT performs competitively when compared to state-of-the-art methods on multi-task learning. Finally, we leverage the TT decomposition to design a rank adaptive optimizer inspired by the DMRG method from many-body physics. Our results demonstrate that integrating this approach with AdamW enhances optimization performance for a specified target rank.",,"J Lopez-Piqueres, P Deshpande, A Ray, M J Villani, M Pistoia, N Kumar - arXiv preprint arXiv:2506.09105, 2025 - arxiv.org",[],https://arxiv.org/abs/2506.09105,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2506.09105,['https://arxiv.org/pdf/2506.09105'],metatt a global tensor train adapter for parameter efficient fine tuning,MPS 语言模型 / 张量化Transformer,1,,
TensorLLM: Tensorising Multi-Head Attention for Enhanced Reasoning and Compression in LLMs,"Y Gu, W Zhou, G Iacovides, D Mandic",2025.0,,"The reasoning abilities of Large Language Models (LLMs) can be improved by structurally denoising their weights, yet existing techniques primarily focus on denoising the feed-forward network (FFN) of the transformer block, and can not efficiently utilise the Multi-head Attention (MHA) block, which is the core of transformer architectures. To address this issue, we propose a novel intuitive framework that, at its very core, performs MHA compression through a multi-head tensorisation process and the Tucker decomposition. This enables both higher-dimensional structured denoising and compression of the MHA weights, by enforcing a shared higher-dimensional subspace across the weights of the multiple attention heads. We demonstrate that this approach consistently enhances the reasoning capabilities of LLMs across multiple benchmark datasets, and for both encoder-only and decoder-only architectures, while achieving compression rates of up to $\sim 250$ times in the MHA weights, all without requiring any additional data, training, or fine-tuning. Furthermore, we show that the proposed method can be seamlessly combined with existing FFN-only-based denoising techniques to achieve further improvements in LLM reasoning performance.",,"Y Gu, W Zhou, G Iacovides, D Mandic - arXiv preprint arXiv:2501.15674, 2025 - arxiv.org",[],https://arxiv.org/abs/2501.15674,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2501.15674,['https://arxiv.org/pdf/2501.15674'],tensorllm tensorising multi head attention for enhanced reasoning and compression in llms,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩,1,,
LatentLLM: Attention-Aware Joint Tensor Compression,"T Koike-Akino, X Chen, J Liu, Y Wang, Pu, Wang, M Brand",2025.0,,Modern foundation models such as large language models (LLMs) and large multi-modal models (LMMs) require a massive amount of computational and memory resources. We propose a new framework to convert such LLMs/LMMs into a reduced-dimension latent structure. Our method extends a local activation-aware tensor decomposition to a global attention-aware joint tensor de-composition. Our framework can significantly improve the model accuracy over the existing model compression methods when reducing the latent dimension to realize computationally/memory-efficient LLMs/LLMs. We show the benefit on several benchmark including multi-modal reasoning tasks.,,"T Koike-Akino, X Chen, J Liu, Y Wang, Pu, Wang, M Brand - arXiv preprint arXiv:2505.18413, 2025 - arxiv.org",[],https://arxiv.org/abs/2505.18413,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2505.18413,['https://arxiv.org/pdf/2505.18413'],latentllm attention aware joint tensor compression,MPS 语言模型 / MPO/TT 压缩,1,,
Ultra Memory-Efficient On-FPGA Training of Transformers via Tensor-Compressed Optimization,"J Tian, J Lu, H Li, X Wang, C Hao, I Young, Z Zhang",2025.0,,"Transformer models have achieved state-of-the-art performance across a wide range of machine learning tasks. There is growing interest in training transformers on resource-constrained edge devices due to considerations such as privacy, domain adaptation, and on-device scientific machine learning. However, the significant computational and memory demands required for transformer training often exceed the capabilities of an edge device. Leveraging low-rank tensor compression, this paper presents the first on-FPGA accelerator for end-to-end transformer training. On the algorithm side, we present a bi-directional contraction flow for tensorized transformer training, significantly reducing the computational FLOPS and intra-layer memory costs compared to existing tensor operations. On the hardware side, we store all highly compressed model parameters and gradient information on chip, creating an on-chip-memory-only framework for each stage in training. This reduces off-chip communication and minimizes latency and energy costs. Additionally, we implement custom computing kernels for each training stage and employ intra-layer parallelism and pipe-lining to further enhance run-time and memory efficiency. Through experiments on transformer models within $36.7$ to $93.5$ MB using FP-32 data formats on the ATIS dataset, our tensorized FPGA accelerator could conduct single-batch end-to-end training on the AMD Alevo U50 FPGA, with a memory budget of less than $6$-MB BRAM and $22.5$-MB URAM. Compared to uncompressed training on the NVIDIA RTX 3090 GPU, our on-FPGA training achieves a memory reduction of $30\times$ to $51\times$. Our FPGA accelerator also achieves up to $3.6\times$ less energy cost per epoch compared with tensor Transformer training on an NVIDIA RTX 3090 GPU.",,"J Tian, J Lu, H Li, X Wang, C Hao, I Young, Z Zhang - arXiv preprint arXiv:2501.06663, 2025 - arxiv.org",[],https://arxiv.org/abs/2501.06663,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2501.06663,['https://arxiv.org/pdf/2501.06663'],ultra memory efficient on fpga training of transformers via tensor compressed optimization,张量化Transformer / MPO/TT 压缩,1,,
Tensorization of neural networks for improved privacy and interpretability,"J R P Monturiol, A Pozas-Kerstjens, D Pérez-García",2025.0,0,"We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the MPS representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing MPS in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.",,"J R P Monturiol, A Pozas-Kerstjens, D Pérez-García - SciPost Phys. Core 8, 095 (2025)",[],https://arxiv.org/abs/2501.06300,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2501.06300,['https://arxiv.org/pdf/2501.06300'],tensorization of neural networks for improved privacy and interpretability,MPO/TT 压缩,1,"SciPost Phys. Core 8, 095 (2025)",
Tensor product attention is all you need,"Y Zhang, Y Liu, H Yuan, Z Qin…",2026.0,57,"… Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to … Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new …",aqnvuPb5wZEJ,"Y Zhang, Y Liu, H Yuan, Z Qin… - Advances in Neural …, 2026 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2025/file/a301ec7cb9e07dc050403e2eb11d0041-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2025/hash/a301ec7cb9e07dc050403e2eb11d0041-Abstract-Conference.html,unknown,unknown,张量化Transformer,2501.06425,['https://proceedings.neurips.cc/paper_files/paper/2025/file/a301ec7cb9e07dc050403e2eb11d0041-Paper-Conference.pdf'],tensor product attention is all you need,张量化Transformer,1,,
A comprehensive survey of compression algorithms for language models,"S Park, J Choi, S Lee, U Kang",2026.0,35,"… In this section, we formally define the language model compression problem in Section 2.1, … of-the-art language models in Section 2.2, give an overview of language model compression …",PaxiKGAAjb0J,"S Park, J Choi, S Lee, U Kang - ACM Computing Surveys, 2026 - dl.acm.org",['https://dl.acm.org/doi/pdf/10.1145/3819816'],https://dl.acm.org/doi/abs/10.1145/3819816,unknown,unknown,MPO/TT 压缩,,['https://dl.acm.org/doi/pdf/10.1145/3819816'],a comprehensive survey of compression algorithms for language models,MPO/TT 压缩,1,,
A comprehensive survey on large language model compression for artificial intelligence applications in edge systems,"Y Liang, C Xu, Y Mei, H Zou, J Guo…",2026.0,18,"… Finally, we discuss the challenges of current model compression approaches and offer insights into future research directions, with a focus on edge-based LLM services. …",J86vAUrDStgJ,"Y Liang, C Xu, Y Mei, H Zou, J Guo… - IEEE Internet of …, 2026 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/11447275/,unknown,unknown,MPO/TT 压缩,,[],a comprehensive survey on large language model compression for artificial intelligence applications in edge systems,MPO/TT 压缩,1,,
LM: Mutual Information Scaling Law for Long-Context Language Modeling,"Z Chen, O Comas, Z Jin, D Luo…",2026.0,10,"… ANTN: Bridging autoregressive neural networks and tensor networks for quantum many-body … In the main text, we focused on the bipartite mutual information with equal splits. However, …",Cu0-6JIPJ_cJ,"Z Chen, O Comas, Z Jin, D Luo… - … in Neural Information …, 2026 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2025/file/c9da56addea9c977cf4ba873e1da979d-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2025/hash/c9da56addea9c977cf4ba873e1da979d-Abstract-Conference.html,unknown,unknown,互信息/标度,,['https://proceedings.neurips.cc/paper_files/paper/2025/file/c9da56addea9c977cf4ba873e1da979d-Paper-Conference.pdf'],lm mutual information scaling law for long context language modeling,互信息/标度,1,,
Entanglement detection and quantification through machine learning: A comprehensive review,"JM Varela, AB de Palhares Jr, DHG Duarte",2026.0,8,"… Next, we provide a brief overview of relevant machine learning paradigms. The final section then surveys the application of these ML techniques to the tasks of entanglement detection …",KojqSkO5dpAJ,"JM Varela, AB de Palhares Jr, DHG Duarte - Brazilian Journal of Physics, 2026 - Springer",[],https://link.springer.com/article/10.1007/s13538-025-01947-y,unknown,unknown,TTN/MERA/PEPS,,[],entanglement detection and quantification through machine learning a comprehensive review,TTN/MERA/PEPS,1,,
Generative Model Predictive Control in Manufacturing Processes: A Review,"SK Lee, RFP Stone, M Gao…",2026.0,5,"… As a result, integrating generative models with MPC could enable more proactive and … Within this taxonomy, generative ML-driven MPC is distinguished by its use of generative models …",DsWE-Chq2qoJ,"SK Lee, RFP Stone, M Gao… - … of Computing and …, 2026 - asmedigitalcollection.asme.org",['https://arxiv.org/pdf/2511.17865'],https://asmedigitalcollection.asme.org/computingengineering/article/26/8/080801/1232741,unknown,unknown,MPS 生成/Born机,,['https://arxiv.org/pdf/2511.17865'],generative model predictive control in manufacturing processes a review,MPS 生成/Born机,1,,
Generative modeling with gaussian boson sampling: classically trainable bosonic born machines,"Z Kolarovszki, B Bakó, M Oszmaniec, C Oh…",2026.0,5,"Quantum generative modeling has emerged as a promising application of quantum computers, aiming to model complex probability distributions beyond the reach of classical methods. In practice, however, training such models often requires costly gradient estimation performed directly on the quantum hardware. Crucially, for certain structured quantum circuits, expectation values of local observables can be efficiently evaluated on a classical computer, enabling classical training without calls to the quantum hardware in the optimization loop. In these models, sampling from the resulting circuits can still be classically hard, so inference must be performed on a quantum device, yielding a potential computational advantage. In this work, we introduce a photonic quantum generative model built on parametrized Gaussian Boson Sampling circuits. The training is based on the efficient classical evaluation of expectation values enabled by the Gaussian structure of the state, allowing scalable optimization of the model parameters through the maximum mean discrepancy loss function. We demonstrate the effectiveness of the approach through numerical experiments on photonic systems with up to 805 modes and over a million trainable parameters, highlighting its scalability and suitability for near-term photonic quantum devices.",ghVlMp_KZvEJ,"Z Kolarovszki, B Bakó, M Oszmaniec, C Oh… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2603.11195'],https://arxiv.org/abs/2603.11195,unknown,unknown,MPS 生成/Born机,2603.11195,['https://arxiv.org/pdf/2603.11195'],generative modeling with gaussian boson sampling classically trainable bosonic born machines,MPS 生成/Born机,1,,
On-device large language models: a survey of model compression and system optimization,"W Chen, J Wang, Y Zhang, Y Shi, T Jiang…",2026.0,5,"… Large language models are increasingly deployed on device and at the edge, where memo… On the model side, we present a clear taxonomy of quantization, pruning, knowledge …",YCYg-dxi7vcJ,"W Chen, J Wang, Y Zhang, Y Shi, T Jiang… - Artificial Intelligence …, 2026 - Springer",['https://link.springer.com/content/pdf/10.1007/s10462-026-11538-1.pdf'],https://link.springer.com/article/10.1007/s10462-026-11538-1,unknown,unknown,MPO/TT 压缩,,['https://link.springer.com/content/pdf/10.1007/s10462-026-11538-1.pdf'],on device large language models a survey of model compression and system optimization,MPO/TT 压缩,1,,
Tensorlens: End-to-end transformer analysis via high-order attention tensors,"IA Atad, I Zimerman, S Katz, L Wolf",2026.0,5,"Attention matrices are fundamental to transformer research, supporting a broad range of applications including interpretability, visualization, manipulation, and distillation.Yet, most existing analyses focus on individual attention heads or layers, failing to account for the model's global behavior.While prior efforts have extended attention formulations across multiple heads via averaging and matrix multiplications or incorporated components such as normalization and FFNs, a unified and complete representation that encapsulates all transformer blocks is still lacking.We address this gap by introducing TensorLens, a novel formulation that captures the entire transformer as a single, input-dependent linear operator expressed through a high-order attentioninteraction tensor.This tensor jointly encodes attention, FFNs, activations, normalizations, and residual connections, offering a theoretically coherent and expressive linear representation of the model's computation.TensorLens is theoretically grounded and our empirical validation shows that it yields richer representations than previous attention-aggregation methods.Our experiments demonstrate that the attention tensor can serve as a powerful foundation for developing tools aimed at interpretability and model understanding.",AclYujq6Ho8J,"IA Atad, I Zimerman, S Katz, L Wolf - … of the 64th Annual Meeting of …, 2026 - aclanthology.org",['https://aclanthology.org/2026.acl-long.156.pdf'],https://aclanthology.org/2026.acl-long.156/,unknown,unknown,张量化Transformer,,['https://aclanthology.org/2026.acl-long.156.pdf'],tensorlens end to end transformer analysis via high order attention tensors,张量化Transformer,1,,
LeSTD: LLM Compression via Learning-based Sparse Tensor Decomposition,"Y Li, Z Guo, M Yin, B Li",2026.0,4,"… synergy, showing that LeSTD consistently outperforms existing methods and establishes a new state of the art in the compression–accuracy trade-off for large language models. …",v4q2OdLtRV8J,"Y Li, Z Guo, M Yin, B Li - The Fourteenth International Conference …, 2026 - openreview.net",['https://openreview.net/pdf?id=0oHaazjMUX'],https://openreview.net/forum?id=0oHaazjMUX,unknown,unknown,MPO/TT 压缩,,['https://openreview.net/pdf?id=0oHaazjMUX'],lestd llm compression via learning based sparse tensor decomposition,MPO/TT 压缩,1,,
Plastic tensor networks for interpretable generative modeling,"KO Akamatsu, K Harada, T Okubo…",2026.0,4,"… We focus on binary tensor trees for modeling some discrete probability distribution P. A (full) … inputs are encoded as probabilities. For a Born machine, the tensor network elements are …",Mm2FgrQOlmUJ,"KO Akamatsu, K Harada, T Okubo… - … Learning: Science and …, 2026 - iopscience.iop.org",['https://iopscience.iop.org/article/10.1088/2632-2153/ae3048/pdf'],https://iopscience.iop.org/article/10.1088/2632-2153/ae3048/meta,unknown,unknown,MPS/序列建模,2504.06722,['https://iopscience.iop.org/article/10.1088/2632-2153/ae3048/pdf'],plastic tensor networks for interpretable generative modeling,MPS/序列建模 / TTN/MERA/PEPS,2,,
Information-Theoretic Scaling Laws of Neural Quantum States,"Y Lu, S Bharadwaj, D Rathore, D Luo",2026.0,3,"We establish an information-theoretic scaling law for generic autoregressive neural quantum states, determined by the middle-cut mutual information of the wavefunction amplitude. By formalizing the virtual bond as an effective information channel across a sequence bipartition, we rigorously prove that exact autoregressive representation of a quantum state requires the virtual-bond dimension to scale with the amplitude mutual information. For stabilizer-state families, we show that this law yields an explicit, analytical rank formula. Applying this framework across quantum-state tomography, ground-state and finite-temperature learning, our numerical experiments expose precise exponent matching, architecture-dependent scaling differences between recurrent and Transformer neural quantum state, and the critical role of autoregressive basis ordering. These results establish a rigorous physical link between the intrinsic structure of a quantum many-body state and the corresponding neural-network capacity required for its faithful representation.",RWgiwwd-LiYJ,"Y Lu, S Bharadwaj, D Rathore, D Luo - arXiv preprint arXiv:2603.23468, 2026 - arxiv.org",['https://arxiv.org/pdf/2603.23468'],https://arxiv.org/abs/2603.23468,unknown,unknown,互信息/标度,2603.23468,['https://arxiv.org/pdf/2603.23468'],information theoretic scaling laws of neural quantum states,互信息/标度,1,,
Quantum Circuit Generation via test-time learning with large language models,"A Macarone-Palmieri, RL Franco",2026.0,3,"Deploying large language models (LLMs) as optimizers for black-box scientific design problems requires efficient test-time refinement under expensive evaluations and without training data. We propose a \emph{memory-augmented test-time optimization} framework that combines episodic memory of high-scoring candidates, score-difference feedback, and restart-from-best sampling to improve iterative search. We evaluate the approach on quantum circuit synthesis, where the objective is to maximize the Meyer--Wallach (MW) global entanglement measure under an exponentially expensive black-box oracle. On 20-qubit circuits, the framework achieves $Q(ψ)=0.99$ without feedback. On the more challenging 25-qubit task, feedback and restart mechanisms enable multiple runs to reach $Q(ψ)=1.0$ within 45 oracle calls, while a budget-matched random hill-climbing baseline stalls below $Q(ψ)\approx0.29$. These results demonstrate that memory and evaluator feedback substantially improve the sample efficiency of LLM-based black-box optimization and establish quantum circuit synthesis as a challenging benchmark for test-time optimization.",x4_BLdFU1iwJ,"A Macarone-Palmieri, RL Franco - arXiv preprint arXiv:2602.03466, 2026 - arxiv.org",['https://arxiv.org/pdf/2602.03466'],https://arxiv.org/abs/2602.03466,unknown,unknown,量子/混合LLM,2602.03466,['https://arxiv.org/pdf/2602.03466'],quantum circuit generation via test time learning with large language models,量子/混合LLM,1,,
Spectral Born machines: classically trainable quantum generative models for discrete data,"A Huang, W Maxwell, V Belis, E Peters, J Pye…",2026.0,3,"We present \emph{spectral Born machines}, a class of quantum generative models that results from viewing and generalizing the class of IQP Born machines through the lens of group Fourier analysis. These quantum models exploit the quantum Fourier transform to create an inductive bias that make them naturally suited to learning integer-structured data, while remaining classically hard to sample from in general. Similar to IQP Born machines, spectral Born machines can be trained efficiently at scale on classical hardware via a maximum mean discrepancy loss based on graph spectral analysis, which we make available in a new \emph{tcdq} module of the PennyLane software platform. In numerical experiments, we show how the spectral bias of the model leads to significantly reduced parameter counts compared to unstructured approaches, and demonstrate the scalability of the software by training a 190-qubit model with over 1 million parameters to successfully learn a distribution of 93 nucleotide-long ribosomal RNA. Our results suggest that highly over-parameterized spectral Born machines may be immune to overfitting, even in strongly data-scarce regimes.",IUYKS3G332kJ,"A Huang, W Maxwell, V Belis, E Peters, J Pye… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2607.06675'],https://arxiv.org/abs/2607.06675,unknown,unknown,MPS 生成/Born机,2607.06675,['https://arxiv.org/pdf/2607.06675'],spectral born machines classically trainable quantum generative models for discrete data,MPS 生成/Born机,1,,
AI Agents for Variational Quantum Circuit Design,"M Knipfer, A Roman, KT Matchev, K Matcheva…",2026.0,2,"Variational quantum circuits (VQCs) constitute a central building block of near-term quantum machine learning (QML), yet the principled design of expressive and trainable architectures remains a major open challenge. The VQC design space grows combinatorially with the number of qubits, layers, entanglement structures, and gate parameterizations, rendering manual circuit construction inefficient and often suboptimal. We introduce an autonomous agent-based framework for VQC architecture search that integrates high-level reasoning with a quantum simulation environment. The agent proposes candidate circuit architectures, evaluates them through fully automated training and validation pipelines, and iteratively improves its design strategy via performance-driven feedback. Empirically, we show that the agent autonomously evolves circuit architectures from simple initial ansätze toward increasingly expressive designs, progressively trying to improve task performance. This demonstrates that agentic AI can effectively navigate and refine the VQC design landscape with minimal human intervention, providing a scalable methodology for automated quantum model development in the Noisy Intermediate-Scale Quantum (NISQ) regime.",Ah-6Hl4JO7IJ,"M Knipfer, A Roman, KT Matchev, K Matcheva… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2602.19387'],https://arxiv.org/abs/2602.19387,unknown,unknown,量子/混合LLM,2602.19387,['https://arxiv.org/pdf/2602.19387'],ai agents for variational quantum circuit design,量子/混合LLM,1,,
Compress large language models via collaboration between learning and matrix approximation,"Y Liao, Z Li, B Wu, Z Cheng, S Zhao…",2026.0,2,… matrix composite approximation has emerged as a promising paradigm for compressing large language models … compressing each matrix using matrix approximation techniques. Given …,JsA1Twsy478J,"Y Liao, Z Li, B Wu, Z Cheng, S Zhao… - Advances in …, 2026 - proceedings.neurips.cc",['https://proceedings.neurips.cc/paper_files/paper/2025/file/5752f9fd2d5c40174738d6f02c202e72-Paper-Conference.pdf'],https://proceedings.neurips.cc/paper_files/paper/2025/hash/5752f9fd2d5c40174738d6f02c202e72-Abstract-Conference.html,unknown,unknown,MPS 语言模型,,['https://proceedings.neurips.cc/paper_files/paper/2025/file/5752f9fd2d5c40174738d6f02c202e72-Paper-Conference.pdf'],compress large language models via collaboration between learning and matrix approximation,MPS 语言模型,1,,
Compressing Transformer Language Models via Matrix Product Operator Decomposition: A Case Study on PicoGPT,"Y Javanmard, T Pandit, M Mardani",2026.0,2,"Transformer-based language models achieve strong performance across NLP tasks, but their quadratic parameter scaling with hidden dimension makes deployment on resource-constrained hardware expensive. We study Matrix Product Operator (MPO) decomposition as a principled compression method for transformers. MPO factorises weight matrices into chains of low-rank cores, with approximation quality controlled by the bond dimension chi. We replace every nn.Linear layer in PicoGPT, a GPT-2-style character-level language model with about 1M parameters, with an MPOLinear module parameterised as an MPO chain. Cores are initialised either by TT-SVD from pretrained dense weights or from random initialisation, and trained using standard PyTorch autograd without a custom backward pass. We derive balanced factorisation schemes for the five distinct weight shapes in PicoGPT and evaluate bond dimensions chi in {4, 8, 16, 32} on Tiny Shakespeare. MPO compression achieves up to 13x compression per transformer block at chi = 4. At chi = 16, the model uses 191,872 parameters instead of 1,020,224 while retaining 97.7% of baseline token accuracy (51.6% vs 52.8%). Reconstruction error follows the expected trend and is lower for three-site than two-site factorisations at the same bond dimension. The chi = 8 model gives the best accuracy per parameter, exceeding the dense baseline by 2.7x on this metric. These results show that MPO parameterisation is a practical and theoretically grounded alternative to low-rank methods and unstructured pruning for transformer compression.",ZW_itJwz4FMJ,"Y Javanmard, T Pandit, M Mardani - arXiv preprint arXiv:2603.28534, 2026 - arxiv.org",['https://arxiv.org/pdf/2603.28534'],https://arxiv.org/abs/2603.28534,unknown,unknown,MPS 语言模型,2603.28534,['https://arxiv.org/pdf/2603.28534'],compressing transformer language models via matrix product operator decomposition a case study on picogpt,MPS 语言模型,1,arXiv (Cornell University),
Generative AI for quantum circuits and quantum code: A technical review and taxonomy,J Merilehto,2026.0,2,"We review thirteen generative systems and five supporting datasets for quantum circuit and quantum code generation, identified through a structured scoping review of Hugging Face, arXiv, and provenance tracing (January-February 2026). We organize the field along two axes: artifact type (Qiskit code, OpenQASM programs, circuit graphs); crossed with training regime (supervised fine-tuning, verifier-in-the-loop RL, diffusion/graph generation, agentic optimization); and systematically apply a three-layer evaluation framework covering syntactic validity, semantic correctness, and hardware executability. The central finding is that while all reviewed systems address syntax and most address semantics to some degree, none reports end-to-end evaluation on quantum hardware (Layer 3b), leaving a significant gap between generated circuits and practical deployment. Scope note: quantum code refers throughout to quantum program artifacts (QASM, Qiskit); we do not cover generation of quantum error-correcting codes (QEC).",-9T3j_HeFsQJ,"J Merilehto - arXiv preprint arXiv:2603.16216, 2026 - arxiv.org",['https://arxiv.org/pdf/2603.16216'],https://arxiv.org/abs/2603.16216,unknown,unknown,量子/混合LLM,2603.16216,['https://arxiv.org/pdf/2603.16216'],generative ai for quantum circuits and quantum code a technical review and taxonomy,量子/混合LLM,1,,
Rethinking the Role of Tensor Decompositions in Post-Training LLM Compression,"A Zagitov, A Miasnikov, M Krutikov, V Aletov…",2026.0,2,"Post-training compression is essential for deploying large language models (LLMs) under tight resource constraints. Tensor decompositions have emerged as a promising direction, offering compact parameterizations well suited to Transformer weight structures. However, existing studies evaluate these methods in narrow settings, leaving unclear whether tensorization is effective at large-scale deployment. We systematically evaluate tensor compression across dense and MoE architectures, establishing performance trade-offs grounded in both empirical analysis and theoretical analysis. We identify a fundamental mismatch between the shared subspaces assumed by tensor decompositions and the heterogeneous representations learned by modern LLMs, thereby delineating their practical limits and clarifying their viable role in large-scale deployment. The code is available at https://github.com/brain-lab-research/TT-LLM.",UZBb7oSIso8J,"A Zagitov, A Miasnikov, M Krutikov, V Aletov… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2606.03465'],https://arxiv.org/abs/2606.03465,unknown,unknown,MPO/TT 压缩,2606.03465,['https://arxiv.org/pdf/2606.03465'],rethinking the role of tensor decompositions in post training llm compression,MPO/TT 压缩,1,,
A Practical Tensor-Network Compression Pipeline for Production-Scale Large Language Models,"S Kozyrev, D Maiboroda",2026.0,1,"Large language models are limited in deployment by GPU memory and inference latency. We present Minima, a production compression pipeline that learns where and how to structurally compress a Transformer and turns that compression into real serving gains. Minima trains a lightweight convolutional predictor to estimate layer- and patch-level sensitivity, applies a mixture of Tucker, tensor-train, and tensor-ring decompositions to low-sensitivity regions, performs a short healing fine-tune, and executes the resulting operators with custom Triton and CUDA kernels. The reduced memory footprint enables speculative decoding with a small draft model and a larger verifier. On Qwen3-32B at an 8k-token context window, Minima reduces peak VRAM from 64 GiB to 40 GiB. For a single active request, throughput increases from 40 tokens per second (baseline) to 50 tokens per second (Minima) and 75 tokens per second (Minima with speculative decoding). Under 50 parallel requests, throughput is 34, 44, and 53 tokens per second respectively, showing that Minima remains effective under high concurrency even when speculative decoding gains compress. We position Minima relative to recent tensor-network, low-rank plus quantization, and cross-layer sharing methods, and argue that it is a practical step toward more aggressive structural compression via shared tensor backbones with tiny per-layer adapters.",BzpsEMoGFwQJ,"S Kozyrev, D Maiboroda - arXiv preprint arXiv:2602.01613, 2026 - arxiv.org",['https://arxiv.org/pdf/2602.01613'],https://arxiv.org/abs/2602.01613,unknown,unknown,MPO/TT 压缩,2602.01613,['https://arxiv.org/pdf/2602.01613'],a practical tensor network compression pipeline for production scale large language models,MPO/TT 压缩,1,,
"Area Laws and Tensor Networks for Maximally Mixed Ground States: I. Arad, R. Firanko, R. Jain","I Arad, R Firanko, R Jain",2026.0,1,"… We show an area law in the mutual information for the … looking at the scaling behavior of the mutual information between a … of local Hamiltonians, mutual information and entanglement …",XwqBbWFbfrEJ,"I Arad, R Firanko, R Jain - Communications in Mathematical Physics, 2026 - Springer",['https://link.springer.com/content/pdf/10.1007/s00220-026-05554-z.pdf'],https://link.springer.com/article/10.1007/s00220-026-05554-z,unknown,unknown,互信息/标度,,['https://link.springer.com/content/pdf/10.1007/s00220-026-05554-z.pdf'],area laws and tensor networks for maximally mixed ground states i arad r firanko r jain,互信息/标度,1,,
Artificial entanglement in the fine-tuning of large language models,"M Chen, Z Wang, C Chen, Z Wu, M Li, J Liu",2026.0,1,"Large language models (LLMs) can be adapted to new tasks using parameter-efficient fine-tuning (PEFT) methods that modify only a small number of trainable parameters, often through low-rank updates. In this work, we adopt a quantum-information-inspired perspective to understand their effectiveness. From this perspective, low-rank parameterizations naturally correspond to low-dimensional Matrix Product States (MPS) representations, which enable entanglement-based characterizations of parameter structure. Thereby, we term and measure ""Artificial Entanglement"", defined as the entanglement entropy of the parameters in artificial neural networks (in particular the LLMs). We first study the representative low-rank adaptation (LoRA) PEFT method, alongside full fine-tuning (FFT), using LLaMA models at the 1B and 8B scales trained on the Tulu3 and OpenThoughts3 datasets, and uncover: (i) Internal artificial entanglement in the updates of query and value projection matrices in LoRA follows a volume law with a central suppression (termed as the ""Entanglement Valley""), which is sensitive to hyper-parameters and is distinct from that in FFT; (ii) External artificial entanglement in attention matrices, corresponding to token-token correlations in representation space, follows an area law with logarithmic corrections and remains robust to LoRA hyper-parameters and training steps. Drawing a parallel to the No-Hair Theorem in black hole physics, we propose that although LoRA and FFT induce distinct internal entanglement signatures, such differences do not manifest in the attention outputs, suggesting a ""no-hair"" property that results in the effectiveness of low rank updates. We further provide theoretical support based on random matrix theory, and extend our analysis to an MPS Adaptation PEFT method, which exhibits qualitatively similar behaviors.",zHiZKtJ8Xq4J,"M Chen, Z Wang, C Chen, Z Wu, M Li, J Liu - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2601.06788'],https://arxiv.org/abs/2601.06788,unknown,unknown,互信息/标度,2601.06788,['https://arxiv.org/pdf/2601.06788'],artificial entanglement in the fine tuning of large language models,互信息/标度,1,,
IQP Born Machines under Data-dependent and Agnostic Initialization Strategies,"S Lerch, J Bowles, R Puig, E Armengol, Z Holmes, S Thanasilp",2026.0,1,"Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably classically hard in certain regimes. Recent proposals focus on training IQP-QCBMs using Maximum Mean Discrepancy (MMD) losses built from low-body Pauli-$Z$ correlators, but the effect of initialization on the resulting optimization landscape remains poorly understood. In this work, we address this by first proving that the MMD loss landscape suffers from barren plateaus for random full-angle-range initializations of IQP circuits. We then establish lower bounds on the loss variance for identity and an unbiased data-agnostic initialization. We then additionally consider a data-dependent initialization that is better aligned with the target distribution and, under suitable assumptions, yields provable gradients and generally converges quicker to a good minimum (as indicated by our training of circuits with 150 qubits on genomic data). Finally, as a by-product, the developed variance lower bound framework is applicable to a general class of non-linear losses, offering a broader toolset for analyzing warm-starts in quantum machine learning.",,"S Lerch, J Bowles, R Puig, E Armengol, Z Holmes, S Thanasilp - arXiv preprint arXiv:2603.14576, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.14576,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2603.14576,['https://arxiv.org/pdf/2603.14576'],iqp born machines under data dependent and agnostic initialization strategies,MPS 生成/Born机 / 量子/混合LLM,1,,
A general tensor-structured compression scheme for efficient large language models,"Y Lu, PF Zhou, QX Fang, P Zhang, SJ Ran…",2026.0,0,"Dense linear maps carry much of the parameter and computational burden of modern neural networks, yet their dense form leaves the organization of learned couplings implicit. Quantum many-body physics organizes exponentially large operators by writing a global Hamiltonian as a sum of local terms, \(\hat H=\sum_k\hat h_k\). Whether the same structural principle can carry learned neural maps is unknown. We introduce Tensor Mixture (MixT), which represents a dense map as a natively executable sum of overlapping local tensor operators without imposing an explicit matrix-rank constraint. The local-term count \(N_T\) sets the effective nonlocality and operator complexity, while the number of replaced Transformer blocks \(N_B\) extends this structural coordinate across network depth. Tests on Qwen3-8B and LLaMA2-7B reveal a broad recoverable regime followed by an abrupt, model-specific boundary that is remarkably stable against changes in \(N_T\). Accuracy and output-distribution statistics reorganize together across the boundary; in LLaMA2-7B, the same depth separates two scaling regimes of inter-layer geometry drift. The directly executed structure also reduces parameters, arithmetic, storage, and memory. These results establish the local-sum structure as a viable organizing principle for learned linear maps at billion-parameter scale and expose a sharp boundary in their tolerance to structural simplification.",3cDkWM1qQiIJ,"Y Lu, PF Zhou, QX Fang, P Zhang, SJ Ran… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2605.25344'],https://arxiv.org/abs/2605.25344,unknown,unknown,MPO/TT 压缩,2605.25344,['https://arxiv.org/pdf/2605.25344'],a general tensor structured compression scheme for efficient large language models,MPO/TT 压缩,1,,
A multi-scale information geometry reveals the structure of mutual information in neural populations,"S Azeglio, S Laquitaine, U Ferrari, M Chalk",2026.0,0,"Understanding how neural population responses represent sensory information is a central problem in systems neuroscience. One approach is to define a representational geometry on stimulus space in which distances reflect how reliably stimuli can be distinguished from neural activity. However, different constructions of these distances can lead to qualitatively different conclusions about the neural code. Here, we show that a unique Riemannian representational geometry emerges from first principles governing how distances contract as stimulus resolution is lost through coarse-graining. This results in a multi-scale extension of the Fisher information metric, capturing encoding structure from fine stimulus details to coarse global distinctions. The resulting geometry is exactly related to the mutual information encoded by the population: well encoded stimulus directions - those contributing more to mutual information - are expanded, whereas poorly encoded directions are contracted. The metric tensor can be estimated using diffusion models, making the framework practical for large neural populations and high-dimensional stimuli. Applied to visual cortical responses to natural images, the eigenvectors of the metric tensor identify stimulus variations that contribute most to information transmission, yielding interpretable features that are robust to modelling choices. Together, these results provide a principled, information-theoretic framework for characterising neural population codes.",iQip_CadDN4J,"S Azeglio, S Laquitaine, U Ferrari, M Chalk - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2605.06304'],https://arxiv.org/abs/2605.06304,unknown,unknown,互信息/标度,2605.06304,['https://arxiv.org/pdf/2605.06304'],a multi scale information geometry reveals the structure of mutual information in neural populations,互信息/标度,1,,
ACCELERATING LARGE LANGUAGE MODEL TRAINING USING HYBRID QUANTUM-CLASSICAL VARIATIONAL AUTOENCODERS WITH INTEGRATED …,PK Singh,2026.0,0,"… benefit from quantum superposition and interference. We designed a hybrid architecture that offloads variational encoder and decoder branches to a parameterized quantum circuit, …",tvLKCyqr-M4J,"PK Singh - Power System Protection and Control, 2026 - pspac.info",['http://pspac.info/index.php/dlbh/article/download/501/421'],http://pspac.info/index.php/dlbh/article/view/501,unknown,unknown,量子/混合LLM,,['http://pspac.info/index.php/dlbh/article/download/501/421'],accelerating large language model training using hybrid quantum classical variational autoencoders with integrated,量子/混合LLM,1,,
An LLM System for Autonomous Variational Quantum Circuit Design,"K Sakka, W Mizukami, K Mitarai",2026.0,0,"The design of high performing quantum circuits remains largely dependent on human expertise. We introduce an autonomous agentic framework that employs large language models (LLMs) to conduct iterative quantum circuit designs under explicit design constraints. Our system integrates seven components: Exploration, Generation, Discussion, Validation, Storage, Evaluation, and Review. These components form a closed-loop workflow that combines web-based knowledge acquisition, literature-grounded critique, executable code generation, and experimental feedback. We evaluate the framework on two tasks: quantum feature map construction for quantum machine learning and ansatz generation for variational quantum eigensolver applications in quantum chemistry. In image classification benchmarks, the best generated feature map outperforms representative quantum feature maps and, when scaled to larger qubit counts, surpasses the classical radial basis function kernel. In molecular ground state estimation across seven molecules, the generated ansatz attains competitive accuracy with widely used chemically inspired and hardware-efficient constructions while satisfying the imposed scaling constraints. These results establish LLM driven agentic system as a viable paradigm for automated quantum circuit design and illustrate how AI systems can participate in iterative scientific optimization workflows across scientific domains.",hcuN5Z9DT0sJ,"K Sakka, W Mizukami, K Mitarai - arXiv preprint arXiv:2606.13380, 2026 - arxiv.org",['https://arxiv.org/pdf/2606.13380'],https://arxiv.org/abs/2606.13380,unknown,unknown,量子/混合LLM,2606.13380,['https://arxiv.org/pdf/2606.13380'],an llm system for autonomous variational quantum circuit design,量子/混合LLM,1,,
Breaking the Entanglement-Structure Trade-off: Many-Body Localization Protects Emergent Holographic Geometry in Random Tensor Networks,Z Liang,2026.0,0,"We present a systematic numerical investigation of the ""entanglement geometry gravity"" chain in random tensor networks (RTN) established by the ER EPR conjecture and Jacobson's thermodynamic derivation. First, we verify the kinematic foundation: the entanglement first law $δ\langle K\rangle=δS$ (slope=1.000), the encoding of geometry by mutual information (correlation=0.92), and the locality of holographic perturbations (3.3x). We also confirm that gravitational dynamics (JT gravity) does not emerge, identifying a sharp kinematics-dynamics boundary. Second, and more importantly, we discover that many-body localization (MBL) is the mechanism that protects emergent holographic geometry from thermalization. Replacing Haar-random evolution (geometry lifetime $t\sim6$) with an XXZ Hamiltonian plus on-site disorder, we observe a finite-size crossover at disorder strength $W_c\approx10-12$ above which mutual-information-lattice correlations persist indefinitely ($r>0.5$ for $t>50$). We map the full parameter space: the optimal regime is a near-Ising anisotropy $Δ\approx50$ with $W=30$ yielding $r=0.779\pm0.002$ (confirmed by a fine scan over $Δ\in[30,70]$); only holographic (RTN) initial states sustain geometry, while product, Néel, and Bell-pair states do not. MBL preserves the spatial structure of entanglement (adjacent/non-adjacent MI ratio ~2.6-4.2x vs. 1.0x in the thermal phase), rather than its total amount. A comparison with classical cellular automata reveals that MBL uniquely breaks the entanglement-structure trade-off imposed by quantum monogamy: classical systems achieve spatial structure only at the cost of negligible mutual information, while MBL sustains both.",JiL4WbXEeQoJ,"Z Liang - arXiv preprint arXiv:2604.04596, 2026 - arxiv.org",['https://arxiv.org/pdf/2604.04596'],https://arxiv.org/abs/2604.04596,unknown,unknown,互信息/标度,2604.04596,['https://arxiv.org/pdf/2604.04596'],breaking the entanglement structure trade off many body localization protects emergent holographic geometry in random tensor networks,互信息/标度,1,,
DATT: Dimension-Augmented Tensor-Train Decomposition for Neural Network Compression,"YC Tai, CY Sie, CR Lee",2026.0,0,"… decomposition on permuted weight tensor with automatic rank determination,” in … : A multimodal tensor train decomposition with its application in convolutional neural networks for smart …",D0p6F9z13-8J,"YC Tai, CY Sie, CR Lee - 2026 IEEE 50th Annual Computers …, 2026 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/11645424/,unknown,unknown,MPO/TT 压缩,,[],datt dimension augmented tensor train decomposition for neural network compression,MPO/TT 压缩,1,,
Efficient Generative Modeling with Unitary Matrix Product States Using Riemannian Optimization,"H Duan, Z Chen, N Wong",2026.0,0,"Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical interpretability. This paper systematically studies matrix product states (MPS) for generative modeling and shows that unitary MPS, which is a tensor-network architecture that is both simple and expressive, offers clear benefits for unsupervised learning by reducing ambiguity in parameter updates and improving efficiency. To overcome the inefficiency of standard gradient-based MPS training, we develop a Riemannian optimization approach that casts probabilistic modeling as an optimization problem with manifold constraints, and further derive an efficient space-decoupling algorithm. Experiments on Bars-and-Stripes and EMNIST datasets demonstrate fast adaptation to data structure, stable updates, and strong performance while maintaining the efficiency and expressive power of MPS.",iSRR0FRFYy8J,"H Duan, Z Chen, N Wong - arXiv preprint arXiv:2603.12026, 2026 - arxiv.org",['https://arxiv.org/pdf/2603.12026'],https://arxiv.org/abs/2603.12026,unknown,unknown,MPS 生成/Born机,2603.12026,['https://arxiv.org/pdf/2603.12026'],efficient generative modeling with unitary matrix product states using riemannian optimization,MPS 生成/Born机,1,,
HVIA: A Hybrid Variational Ising Architecture for Quantum Language Modeling,"C Mao, H Li",2026.0,0,… two Ising-inspired hybrid quantum-classical language modeling architectures. These architectures integrate spin-coupling mechanisms with variational quantum circuits to enhance …,sjVWyK1H2XAJ,"C Mao, H Li - 2026 - assets-eu.researchsquare.com",['https://assets-eu.researchsquare.com/files/rs-9030361/v1_covered_6b06a8ca-8721-4847-be66-7bfce4bc81bb.pdf'],https://assets-eu.researchsquare.com/files/rs-9030361/v1_covered_6b06a8ca-8721-4847-be66-7bfce4bc81bb.pdf,unknown,unknown,量子/混合LLM,,['https://assets-eu.researchsquare.com/files/rs-9030361/v1_covered_6b06a8ca-8721-4847-be66-7bfce4bc81bb.pdf'],hvia a hybrid variational ising architecture for quantum language modeling,量子/混合LLM,1,,
Meaning Representations as Variational Quantum Circuits,"TG Limbäck-Stokin, TA Birdavade, KI Lo…",2026.0,0,"… Large language models are thought to be one of the most successful learning algorithms of our age. They are applied to a wide range of domains, from weather forecasting (Li et al., …",JDwdrOAExDIJ,"TG Limbäck-Stokin, TA Birdavade, KI Lo… - … (DMR 2026)@ LREC …, 2026 - aclanthology.org",['https://aclanthology.org/anthology-files/pdf/dmr/2026.dmr-1.pdf#page=125'],https://aclanthology.org/anthology-files/pdf/dmr/2026.dmr-1.pdf#page=125,unknown,unknown,量子/混合LLM,,['https://aclanthology.org/anthology-files/pdf/dmr/2026.dmr-1.pdf#page=125'],meaning representations as variational quantum circuits,量子/混合LLM,1,,
Model Checking Matrix Product States Against Linear Chain Logic,"M Xu, Y Chen, J Guan",2026.0,0,"… on periodic matrix product states; for brevity, we will refer to them simply as matrix product states (MPS). … Matrix Product State (MPS) is a popular formalism for representing quantum …",YCUqQNvDZfwJ,"M Xu, Y Chen, J Guan - International Conference on Computer Aided …, 2026 - Springer",['https://link.springer.com/content/pdf/10.1007/978-3-032-32537-2_17.pdf'],https://link.springer.com/chapter/10.1007/978-3-032-32537-2_17,unknown,unknown,MPS 语言模型,,['https://link.springer.com/content/pdf/10.1007/978-3-032-32537-2_17.pdf'],model checking matrix product states against linear chain logic,MPS 语言模型,1,,
On the Approximation Complexity of Matrix Product Operator Born Machines,"C Li, Z Tao, Y Cong, J Xu, Q Zhao",2026.0,0,"Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive perspectives. First, we prove that KL approximation is NP-hard for MPO-BMs in the continuous setting, ruling out universal efficient approximation in the worst case. Second, for score-based variational inference, we show that, under a locality and spectral-gap conditions on the loss-induced Hamiltonian, structured targets (e.g., path-graph Markov random fields) admit MPO-BM approximations with polynomial bond dimension and provable KL guarantees. Third, under the same locality structure, we prove that polynomially many score queries suffice to estimate the induced Hamiltonian and obtain such guarantees. Our results provide a theoretical characterization of when MPO-BMs are fundamentally hard to approximate and when they become efficiently learnable.",Dsk1JwrRh8sJ,"C Li, Z Tao, Y Cong, J Xu, Q Zhao - arXiv preprint arXiv:2605.11471, 2026 - arxiv.org",['https://arxiv.org/pdf/2605.11471'],https://arxiv.org/abs/2605.11471,unknown,unknown,MPS 生成/Born机,2605.11471,['https://arxiv.org/pdf/2605.11471'],on the approximation complexity of matrix product operator born machines,MPS 生成/Born机,1,,
Quantum Circuit Vision: Cost-Aware Evaluation of Visual AI Agents for Quantum Code Generation,"D Liu, A Zhang, L Zhang",2026.0,0,"Can AI agents visually comprehend quantum circuit diagrams and generate verified executable code--and at what cost? We present Quantum Circuit Vision, a cost-aware evaluation framework for multimodal AI agents on quantum circuit visual understanding. We construct a 132-circuit benchmark spanning 13 categories ($1$--$10$ qubits) with executable Amazon Braket code and unitary-fidelity verification. Evaluating three frontier Claude-family models at different capability-cost tiers with $n=5$ repeated trials, we find that the mid-tier model (Sonnet 4.6, $1.30\times$ credits) offers the most favorable balance on the cost-accuracy frontier: 91% pass rate on the core subset at 18% of the per-call cost of the strongest model (Opus 4.6), whose accuracy advantage is not statistically significant (paired $t$: $p=0.083$). Logistic regression confirms that circuit depth--not qubit count--is the primary predictor of failure ($p<0.001$). Chain-of-thought prompting shows no statistically significant effect (all $p>0.18$, $n=5$), suggesting that visual pattern recognition outweighs explicit reasoning strategy for structurally coupled diagrams. We propose a cascade routing strategy (cheap $\rightarrow$ expensive models) that achieves 84% accuracy at 38% of single-model cost, demonstrating that model routing dominates prompt engineering as a cost lever. We release QCV-Dataset (132 circuits, 5 modalities, 1,931 files) on Hugging Face Hub as an open evaluation infrastructure with structured metadata for discoverability, interoperability, and responsible AI documentation, and all evaluation code, cost logs, and verification scripts on GitHub for full reproducibility.",e7k6jofT_Q4J,"D Liu, A Zhang, L Zhang - arXiv preprint arXiv:2607.10057, 2026 - arxiv.org",['https://arxiv.org/pdf/2607.10057'],https://arxiv.org/abs/2607.10057,unknown,unknown,量子/混合LLM,2607.10057,['https://arxiv.org/pdf/2607.10057'],quantum circuit vision cost aware evaluation of visual ai agents for quantum code generation,量子/混合LLM,1,,
"Quantum Computing Meets Large Language Models: Insights, Challenges, and Future Directions","TR Gadekallu, K Fang, H Feng, W Wang, Y Xia, J Cai…",2026.0,0,"… , explore variational and hybrid models that blend quantum circuits with classical … of quantum computing and large language models. Early research shows that quantum methods could …",ueDA4wl9VF8J,"TR Gadekallu, K Fang, H Feng, W Wang, Y Xia, J Cai… - 2026 - techrxiv.org",['https://www.techrxiv.org/doi/pdf/10.36227/techrxiv.177004376.69666864/v1'],https://www.techrxiv.org/doi/abs/10.36227/techrxiv.177004376.69666864/v1,unknown,unknown,量子/混合LLM,,['https://www.techrxiv.org/doi/pdf/10.36227/techrxiv.177004376.69666864/v1'],quantum computing meets large language models insights challenges and future directions,量子/混合LLM,1,,
Quantum-inspired tensor networks in machine learning models,"G Valverde, I GarcÃa-Olaizola, G Scarpa…",2026.0,0,"Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.",bTDUxPFRXQAJ,"G Valverde, I GarcÃa-Olaizola, G Scarpa… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2604.14287'],https://arxiv.org/abs/2604.14287,unknown,unknown,量子启发综述,2604.14287,['https://arxiv.org/pdf/2604.14287'],quantum inspired tensor networks in machine learning models,量子启发综述,1,,
Quantum2Prompt: Representing Quantum Circuits as Language Prompts for Linear System Solving,Y Yang,2026.0,0,"… large language models can serve as efficient, interpretable surrogates for VQLS, offering a scalable path toward language-driven quantum … Following prior work on variational quantum …",sH1w1dyvtOoJ,Y Yang - 2026 - assets-eu.researchsquare.com,['https://assets-eu.researchsquare.com/files/rs-8187619/v1_covered_25faca44-5500-4f1c-9aab-674aadb6b384.pdf'],https://assets-eu.researchsquare.com/files/rs-8187619/v1_covered_25faca44-5500-4f1c-9aab-674aadb6b384.pdf,unknown,unknown,量子/混合LLM,,['https://assets-eu.researchsquare.com/files/rs-8187619/v1_covered_25faca44-5500-4f1c-9aab-674aadb6b384.pdf'],quantum2prompt representing quantum circuits as language prompts for linear system solving,量子/混合LLM,1,Research Square,
Reduced Matrix Multiplication: Input-Adaptive Matrix-Product Reduction for LLM Inference,"Z Lan, Y Li, J Zhou",2026.0,0,"Transformer-based language models achieve strong performance but incur substantial inference cost due to repeated high-dimensional matrix multiplications. We propose Reduced Matrix Multiplication (RMM), a training-free, input-adaptive inference method that reduces Transformer matrix products by selecting informative slices along their contraction dimensions, without modifying model weights. Under a simple retention-ratio control, RMM provides a smooth and predictable accuracy-efficiency trade-off. Across language models ranging from 1B to 70B parameters, we find that reduction tolerance depends on the model family, task, component, and retention ratio, although it often improves with model scale. Under moderate reduction, RMM remains robust across the evaluated discriminative, autoregressive generation, and long-context settings. We further show that the same principle extends to multimodal vision-language inference. Mechanistic ablations reveal a structural asymmetry within Transformers: attention-side computations are substantially more reducible than MLP components. Finally, wall-clock benchmarks with custom kernels on an NVIDIA A100 show that these computational savings can translate into practical runtime gains, especially at longer sequence lengths. Together, these results position RMM as a scalable direction for input-adaptive inference-time optimization.",4LYeki8qLGYJ,"Z Lan, Y Li, J Zhou - arXiv preprint arXiv:2608.13426, 2026 - arxiv.org",['https://arxiv.org/pdf/2608.13426'],https://arxiv.org/abs/2608.13426,unknown,unknown,MPS 语言模型,2608.13426,['https://arxiv.org/pdf/2608.13426'],reduced matrix multiplication input adaptive matrix product reduction for llm inference,MPS 语言模型,1,,
Sparse Tensor Attention for Hyperspectral Unmixing,"J Wang, F Xiong, Z Wen, Z Zhao…",2026.0,0,"… convolutional neural networks, Transformer-based approaches … coefficients are reorganized into tensorized cores that … formulates tensorized selfattention as a Tucker decomposition for …",7vgVsqKdwBwJ,"J Wang, F Xiong, Z Wen, Z Zhao… - IEEE Transactions on …, 2026 - ieeexplore.ieee.org",[],https://ieeexplore.ieee.org/abstract/document/11693948/,unknown,unknown,张量化Transformer,,[],sparse tensor attention for hyperspectral unmixing,张量化Transformer,1,,
Stochastic Optimization of Tree Tensor Networks,"M Willner, M Scharf, A Uschmajew, T Felser…",2026.0,0,"Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks (TTNs) on both their parameter and quotient manifolds, including adaptive and learning-rate-free schemes suitable for minibatch training. Using a hybrid CNN-TTN architecture, we evaluate the methods on Fashion-MNIST, CIFAR10, and Imagenette. The proposed optimizers achieve predictive performance comparable to unconstrained optimization while enabling numerically stable downstream compression.",IhNJ7aNwJMIJ,"M Willner, M Scharf, A Uschmajew, T Felser… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2609.00870'],https://arxiv.org/abs/2609.00870,unknown,unknown,TTN/MERA/PEPS,2609.00870,['https://arxiv.org/pdf/2609.00870'],stochastic optimization of tree tensor networks,TTN/MERA/PEPS,1,,
Surviving Resource-constraint Compression: Capability Retention under Tensor-train Decomposition for Sub-billion Parameter Language Models,"M Xu, YL Xu, DP Mandic",2026.0,0,… a training-free model compression approach based on the tensor-train decomposition (… language capabilities are preserved under training-free compression at different compression …,K7gOVM8lADsJ,"M Xu, YL Xu, DP Mandic - Machine Intelligence Research, 2026 - Springer",['https://link.springer.com/content/pdf/10.1007/s11633-026-1653-x.pdf'],https://link.springer.com/article/10.1007/s11633-026-1653-x,unknown,unknown,MPO/TT 压缩,,['https://link.springer.com/content/pdf/10.1007/s11633-026-1653-x.pdf'],surviving resource constraint compression capability retention under tensor train decomposition for sub billion parameter language models,MPO/TT 压缩,1,,
Tensor Brain: Structured Probabilistic Modeling for Neural Population Activity with Tensor Networks,"Y Huang, F Wu, D Chen, X Gu, Z Sun…",2026.0,0,"… direct modeling computationally intractable. We propose Tensor Brain (TB), a tensor-network-based probabilistic framework that factorizes the full joint distribution into structured tensor …",_uVjd-DHZZUJ,"Y Huang, F Wu, D Chen, X Gu, Z Sun… - 人工知能学会全国大会論文 …, 2026 - jstage.jst.go.jp",['https://www.jstage.jst.go.jp/article/pjsai/JSAI2026/0/JSAI2026_1YinA49/_pdf'],https://www.jstage.jst.go.jp/article/pjsai/JSAI2026/0/JSAI2026_1YinA49/_article/-char/ja/,unknown,unknown,MPS/序列建模,,['https://www.jstage.jst.go.jp/article/pjsai/JSAI2026/0/JSAI2026_1YinA49/_pdf'],tensor brain structured probabilistic modeling for neural population activity with tensor networks,MPS/序列建模,1,,
Tensor decomposition based lightweight residual fusion for Multimodal sentiment understanding,"F Wan, R Zhi",2026.0,0,"… named Light Tensor-based Disentangling and Multi-scale Fusion (… Third, we propose a contrastive mutual information … raw text tokens, and θt is the network parameters for the text …",NGSBUwqUBb4J,"F Wan, R Zhi - Journal of Intelligent Information Systems, 2026 - Springer",[],https://link.springer.com/article/10.1007/s10844-026-01039-6,unknown,unknown,互信息/标度,,[],tensor decomposition based lightweight residual fusion for multimodal sentiment understanding,互信息/标度,1,,
"Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability","M Tarasov, S Ahmadi-Asl, ALF de Almeida…",2026.0,0,"Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is underexploited by the conventional matrix-centric view. Tensor decompositions and tensor networks provide a principled algebraic language for this structure, yet the literature often treats them as isolated compression mechanisms. This survey organizes tensor methods for LLMs through two complementary views: a seven-stage lifecycle taxonomy covering tokenization, embeddings, pre-training, adaptation, compression, inference, and interpretability, and a component view covering embeddings, attention, and feed-forward networks. We provide unified notation and theoretical foundations, analyze tensorization strategies for individual Transformer components, and compare methods at each lifecycle stage while making differences in evaluation protocols and model scales explicit. We further connect tensor methods to neighboring efficiency techniques and probabilistic tensor networks. Finally, we synthesize open challenges and introduce $ρ_{\rm gap}$, a metric for the compression-realization gap between theoretical memory reduction and measured system-level speedup. By treating tensorization as a common structural principle, the survey provides a structured entry point to tensorized language models and clarifies when parameter savings can plausibly translate into memory efficiency, computational efficiency, or interpretability. The GitHub page dedicated to this paper is accessible at \href{https://github.com/ma-tt-a/awesome-tensor-methods-for-llms}{this https URL}.",xC6m69fuNkEJ,"M Tarasov, S Ahmadi-Asl, ALF de Almeida… - arXiv preprint arXiv …, 2026 - arxiv.org",['https://arxiv.org/pdf/2608.30505'],https://arxiv.org/abs/2608.30505,unknown,unknown,MPO/TT 压缩,2608.30505,['https://arxiv.org/pdf/2608.30505'],tensor methods for language models from token representation to training adaptation inference compression and interpretability,MPO/TT 压缩 / 张量化Transformer,2,,
Tensor-Network Markov-Chain Monte Carlo: Efficient Sampling of Three-Dimensional Spin Glasses,"T Chen, J Liu, Y Deng, P Zhang",2026.0,0,"… into 2D tensor networks, we generate whole-slice spin configurations via tensor-network … For each scheme, the conditional probability P(s\σ) is computed approximately with a tensor …",2_5jZxyKTLkJ,"T Chen, J Liu, Y Deng, P Zhang - Physical Review Letters, 2026 - APS",['https://link.aps.org/pdf/10.1103/96lr-z7tb'],https://link.aps.org/doi/10.1103/96lr-z7tb,unknown,unknown,MPS/序列建模,,['https://link.aps.org/pdf/10.1103/96lr-z7tb'],tensor network markov chain monte carlo efficient sampling of three dimensional spin glasses,MPS/序列建模,1,,
Tensortrim: dynamic tensor-train decomposition for efficient neural network compression,"S Luo, M Liu, Y Lou, P Sun, Y Yu, S Ren…",2026.0,0,"… higher compression ratio alongside a Under the unified cost C, we include Tensor Train … as a baseline, where fully training a compressed model from scratch is counted as a cost of e. …",m5L-p7ceFHwJ,"S Luo, M Liu, Y Lou, P Sun, Y Yu, S Ren… - International Journal of …, 2026 - Springer",[],https://link.springer.com/article/10.1007/s13042-025-02819-2,unknown,unknown,MPO/TT 压缩,,[],tensortrim dynamic tensor train decomposition for efficient neural network compression,MPO/TT 压缩,1,,
"A Coherent Memory Register for Sequential Quantum Generative Modeling, with Application to Calorimeter Showers","J S S Monaco, R Xue, D Kruecker, K Borras",2026.0,0,"Simulating the showers that particles deposit in a calorimeter, the detector that records their energy across many cells, is one of the largest computing costs in high-energy physics, and fast generative surrogates are needed. Quantum circuits have been proposed as such surrogates, but demonstrations on calorimeter data have either required a register that grows with the image, roughly one qubit per cell, or have passed the information between parts of the image through a classical channel. We remove both constraints for this problem, using a construction drawn from the sequential-generation and hidden-quantum-Markov-model literature. A shower image is generated block by block on a fixed register of six qubits. Three of them, the memory, are never measured. They hold what the circuit knows about the blocks already generated as a quantum state, so the correlations between distant parts of the image cross each block boundary as unmeasured amplitudes. The other three are measured and reset once per block, and each outcome selects the energy pattern of one block. The register size is set by the block, so adding cells to the image adds steps to the sequence, not qubits. We call the model a coherent-memory Born machine (CoMB), a Born machine being a circuit whose measurement statistics are the generated distribution. Its training loss grows only linearly with the number of blocks and never requires enumerating the image distribution, and a depth-two instance runs on an IBM superconducting processor. On a twelve-cell benchmark the model reproduces the energy distribution of every cell, the correlation matrix between cells, and the total-energy spectrum. Removing the three memory qubits, with everything else unchanged, produces independent blocks. Every correlation between blocks is carried by the unmeasured qubits and by nothing else.",,"J S S Monaco, R Xue, D Kruecker, K Borras - arXiv preprint arXiv:2609.23050, 2026 - arxiv.org",[],https://arxiv.org/abs/2609.23050,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2609.23050,['https://arxiv.org/pdf/2609.23050'],a coherent memory register for sequential quantum generative modeling with application to calorimeter showers,MPS 生成/Born机 / MPS/序列建模,1,,
Autonomous Quantum Simulation through Large Language Model Agents,"W Li, J Ren, L Cheng, C Gong",2026.0,0,"We demonstrate that large language model (LLM) agents can autonomously perform tensor network simulations of quantum many-body systems, achieving approximately 90% success rate across representative benchmark tasks. Tensor network methods are powerful tools for quantum simulation, but their effective use requires expertise typically acquired through years of graduate training. By combining in-context learning with curated documentation and multi-agent decomposition, we create autonomous AI agents that can be trained in specialized computational domains within minutes. We benchmark three configurations (baseline, single-agent with in-context learning, and multi-agent with in-context learning) on problems spanning quantum phase transitions, open quantum system dynamics, and photochemical reactions. Systematic evaluation using DeepSeek-V3.2, Gemini 2.5 Pro, and Claude Opus 4.5 demonstrates that both in-context learning and multi-agent architecture are essential. Analysis of failure modes reveals characteristic patterns across models, with the multi-agent configuration substantially reducing implementation errors and hallucinations compared to simpler architectures.",,"W Li, J Ren, L Cheng, C Gong - arXiv preprint arXiv:2601.10194, 2026 - arxiv.org",[],https://arxiv.org/abs/2601.10194,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2601.10194,['https://arxiv.org/pdf/2601.10194'],autonomous quantum simulation through large language model agents,MPS 语言模型 / 量子/混合LLM,2,,
Classical Limits of Spectral Filtering in Quantum Generative Models,M Roth,2026.0,0,"Spectral filtering has been proposed as a route to regularization in quantum generative models: the quantum Fourier transform exposes the amplitude spectrum of a quantum circuit Born machine, and a diagonal filter suppresses the high frequencies associated with finite-sample noise, an operation whose classical counterpart seemingly requires manipulating an exponentially long amplitude vector. We examine whether this coherent operation produces anything that classical post-processing of samples from the unfiltered model cannot match. Measuring the filter against convolution with a symmetric probability kernel at matched sampling cost, which accounts for the post-selection overhead of attenuation, we derive necessary and sufficient conditions for the gap between the two to vanish. Magnitude (attenuating) filters obey a dichotomy: at a fixed affordability threshold, the filtered output is either a constant-size Fourier object with an efficient classical sampler, or the passband must widen until no fixed frequency is attenuated and the filter no longer smooths. In neither case does the filter create a quantum-classical separation. Whatever separation survives is inherited from the spectral phase of the input state. Numerical experiments on trained circuit Born machines confirm the classification and show that the deciding phases are invisible to the Born-rule training loss and set by the initialization. Within the diagonal family, pure phase filters remain the only spectral operations exempt from these constraints.",,"M Roth - arXiv preprint arXiv:2608.14169, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.14169,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2608.14169,['https://arxiv.org/pdf/2608.14169'],classical limits of spectral filtering in quantum generative models,MPS 生成/Born机,1,,
Distilling Datasets into Shallow Circuits for Quantum Machine Learning,"G Lin, Q Zhao",2026.0,0,"In quantum machine learning, training a quantum model requires each sample to be prepared as a quantum state by a loading circuit that must be re-executed for every shot at every training step. The total burden therefore scales with both the number of samples and the cost of preparation. Existing approaches reduce the loading cost of individual inputs or distill data and compress their representations before applying a separate quantum encoding. This separation can leave resulting samples costly to prepare or cause additional loss of the information during subsequent compilation into shallow circuits. We propose quantum dataset distillation (QDD), which distills the full dataset directly into a small set of shallow circuits. Each synthetic sample is parameterized as a staircase circuit corresponding to a low-rank tensor network, making the sample and its loading circuit the same object. The circuit parameters are optimized classically with exact gradients using distribution matching under an explicit loading budget, without post-hoc state-preparation synthesis. On MNIST and Fashion-MNIST, only 10 circuits per class ($0.0017\times$ the full dataset size) achieve accuracy comparable to full-data training and outperform selection baselines under matched sample and loading budgets. In finite-shot training, QDD reaches 95\% of the full-data accuracy with more than $100\times$ fewer cumulative shots. Additionally, we validate QDD on real quantum hardware, demonstrating its practical deployment potential.",,"G Lin, Q Zhao - arXiv preprint arXiv:2609.28229, 2026 - arxiv.org",[],https://arxiv.org/abs/2609.28229,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2609.28229,['https://arxiv.org/pdf/2609.28229'],distilling datasets into shallow circuits for quantum machine learning,MPO/TT 压缩 / 量子/混合LLM,1,,
Do Transformations Reveal the Truth? Generative Residual Learning for Generalized AI-Generated Image Detection,"K Uddin, N Tasnim, A Khan, M U Farooq, K Malik",2026.0,0,"The rapid advancement of generative AI has enabled the creation of highly realistic deepfake media, posing significant threats, including misinformation, digital identity theft, fraud, and manipulation of public opinion. AI-generated image (AIGI) detection is reliably challenging due to the diversity of generative methods and the subtle artifacts they leave behind. In this work, we propose GenRes, a novel framework for generative residual learning via a neural tensor network, which models fine-grained relational features between original and transformed samples to enhance generalization. To address scenarios involving multiple generative transformations, we introduce GenRes++, which employs a learnable attention mechanism to aggregate relational features across multiple transformed samples and enables the model to focus on the most informative cues. Both models leverage PE-Core as a feature extractor, providing generalized and semantically rich embeddings that improve cross-domain performance and enable the detection of AIGI generated by unseen methods. Comprehensive experiments on multiple benchmark datasets demonstrate that the proposed GenRes++ approach outperforms existing methods.",,"K Uddin, N Tasnim, A Khan, M U Farooq, K Malik - arXiv preprint arXiv:2607.08674, 2026 - arxiv.org",[],https://arxiv.org/abs/2607.08674,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2607.08674,['https://arxiv.org/pdf/2607.08674'],do transformations reveal the truth generative residual learning for generalized ai generated image detection,张量化Transformer / MPS 生成/Born机,1,,
Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection,"E Chen, J Li, Z Zheng, J Pei",2026.0,0,"Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a *Dual-Channel Tensor Neural Network* (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a *structure-aware conformal ROC* procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a *conformal structure selector* that, to our knowledge, is the *first distribution-free procedure* for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.",,"E Chen, J Li, Z Zheng, J Pei - arXiv preprint arXiv:2605.19122, 2026 - arxiv.org",[],https://arxiv.org/abs/2605.19122,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2605.19122,['https://arxiv.org/pdf/2605.19122'],dual channel tensor neural networks finite sample theory and conformal structure selection,MPO/TT 压缩,1,,
EinSort: Sorting is All We Need for Tensorizing LLM,"T Koike-Akino, J Liu, Y Wang",2026.0,0,"Tensor networks provide efficient representations for compressing large neural networks. By carefully designing shapes and topologies, they can significantly reduce memory and computational costs. However, identifying implicit low-rank structures in large foundation models remains challenging due to their enormous scale and un-structured weight distributions. We propose an adaptive tensorization method that discovers inherent low-rank structure in a target tensor by index ordering. Experiments on weight and KV-cache compression demonstrate improved reconstruction quality compared to baselines.",,"T Koike-Akino, J Liu, Y Wang - arXiv preprint arXiv:2606.08565, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.08565,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2606.08565,['https://arxiv.org/pdf/2606.08565'],einsort sorting is all we need for tensorizing llm,MPO/TT 压缩,1,,
Encoding Numerical Data for Generative Quantum Machine Learning,"M Krebsbach, F Reiter, T Wellens, H Kowalski, A Abedi",2026.0,0,"Generative quantum machine learning models are trained to deduce the probability distribution underlying a given dataset, and to produce new, synthetic samples from it. The majority of such models proposed in the literature, like the Quantum Circuit Born Machine (QCBM), fundamentally work on a binary level. Real-world data, however, is often numeric, requiring the models to translate between binary and continuous representations. We analyze how this transition influences the performance of quantum models and show that it requires the models to learn correlations that are solely an artifact of the way the data is encoded, and not related to the data itself. At the same time, structure of the original data, like continuity, can be obscured in the binary representation, hindering generalization. To mitigate these effects, we propose a strategy based on Gray-codes that can be implemented with essentially no overhead, conserves structures in the data, and avoids artificial correlations in situations in which the standard approach creates them. Considering datasets drawn from various low-dimensional probability distributions, we verify that, in most cases, QCBMs using the reflected Gray code learn faster and more accurately than those with standard binary code. This shows that, as complement to specifically tailored circuit ansätze or data pre-processing, binary encodings can be used to introduce inductive biases into generative machine learning models.",,"M Krebsbach, F Reiter, T Wellens, H Kowalski, A Abedi - arXiv preprint arXiv:2603.23407, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.23407,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2603.23407,['https://arxiv.org/pdf/2603.23407'],encoding numerical data for generative quantum machine learning,MPS 生成/Born机 / 量子/混合LLM,1,,
"LLMs Interpret, Embeddings Organize, Graphs Emerge: Agent-Driven Compilation of Scientific Knowledge","S Ran, K Zhang, X Wu, L Yang, W Li",2026.0,0,"Sustained scientific work requires a knowledge substrate that carries interpretation across tasks and preserves paths to source evidence. We call this process \emph{scientific knowledge compilation} and implement it in ASKS, the \emph{Agent-Driven Scientific Knowledge System}. For each source, an LLM produces a readable Wiki view and machine-facing semantics. Deterministic checks convert the latter into a document-local GraphDelta, and embedding geometry together with explicit graph rules integrates the proposed changes into persistent state. Each ingest is an inspectable state transition over accumulated knowledge, with compiled Wiki and graph views linked to the preserved source record. We examine this process by chronologically compiling 56 published papers from one research program. Branch survival, cross-paper support, lineage, coverage, and churn yield a source-traceable author research portrait centered on tensor-network methods, with branches into quantum many-body research, tensor-network machine learning, and quantum-AI-oriented directions. In this run, higher-level Hub organization remains stable and low-churn. Canonical-node growth is predominantly additive. Graph-level measurements and navigation paths retain links to the source records from which they were compiled.",,"S Ran, K Zhang, X Wu, L Yang, W Li - arXiv preprint arXiv:2608.29612, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.29612,arxiv-completion,2026-09-26 (citations:OpenAlex),,2608.29612,['https://arxiv.org/pdf/2608.29612'],llms interpret embeddings organize graphs emerge agent driven compilation of scientific knowledge,,1,,
Learning Quantum-Samplers for Stochastic Processes with Quantum Sequence Models,"X Wang, C Yang, C A Somasundaram, J Thompson, M Gu",2026.0,0,"Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing such circuits from data face immense challenges, given the exponential growth in the size of the associated probability vectors as the desired simulation time horizon increases. Here, we introduce quantum sequence models that leverage a recurrent quantum circuit structure to generate coherent superpositions with circuit complexity that grows linearly with the desired time horizon; together with a recurrent variant of the parameter-shift rule, we train these models from observational data. When benchmarked against baseline quantum Born machines, our constructions exhibit orders-of-magnitude improvements in model accuracy in data-sparse regimes.",,"X Wang, C Yang, C A Somasundaram, J Thompson, M Gu - arXiv preprint arXiv:2603.24069, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.24069,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2603.24069,['https://arxiv.org/pdf/2603.24069'],learning quantum samplers for stochastic processes with quantum sequence models,MPS 生成/Born机 / MPS/序列建模,1,,
Neural Network Pruning via QUBO Optimization,"O Orabi, A Zagitov, H Salloum, V A Lobachev, K Khubiev, Y Kholodov",2026.0,,"Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic Unconstrained Binary Optimization (QUBO) provide a principled alternative but have so far underperformed due to oversimplified objective formulations based on metrics like the L1-norm. In this work, we propose a unified Hybrid QUBO framework that bridges heuristic importance estimation with global combinatorial optimization. Our formulation integrates gradient-aware sensitivity metrics - specifically first-order Taylor and second-order Fisher information - into the linear term, while utilizing data-driven activation similarity in the quadratic term. This allows the QUBO objective to jointly capture individual filter relevance and inter-filter functional redundancy. We further introduce a dynamic capacity-driven search to strictly enforce target sparsity without distorting the optimization landscape. Finally, we employ a two-stage pipeline featuring a Tensor-Train (TT) Refinement stage - a gradient-free optimizer that fine-tunes the QUBO-derived solution directly against the true evaluation metric. Experiments on the SIDD image denoising dataset demonstrate that the proposed Hybrid QUBO significantly outperforms both greedy Taylor pruning and traditional L1-based QUBO, with TT Refinement providing further consistent gains at appropriate combinatorial scales. This highlights the potential of hybrid combinatorial formulations for robust, scalable, and interpretable neural network compression.",,"O Orabi, A Zagitov, H Salloum, V A Lobachev, K Khubiev, Y Kholodov - arXiv preprint arXiv:2604.05856, 2026 - arxiv.org",[],https://arxiv.org/abs/2604.05856,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2604.05856,['https://arxiv.org/pdf/2604.05856'],neural network pruning via qubo optimization,MPO/TT 压缩,1,,
Parity Supervision as a Driver of Generalization in Quantum Generative Modeling,"M Baumann, D Hein, S Udluft, T Rohe, C Linnhoff-Popien, J Stein",2026.0,0,"Generative models learn probability distributions in order to produce new samples beyond a finite training set. Their usefulness therefore depends on assigning probability to valid but previously unseen states. In a controlled benchmark, we test whether parity-based training provides an inductive bias for this kind of generalization in instantaneous quantum polynomial-time (IQP) circuit Born machines. We compare the same IQP circuit trained with parity supervision and coordinate-wise mean-squared error (MSE), together with classical controls. Parity supervision improves exact distributional fit and recovery of unseen high-value states over IQP-MSE. A circuit-free spectral reconstruction shows that the matched parity moments already transfer evidence from observed samples to structurally compatible unseen states, while the IQP circuit further refines this structure. These results identify parity supervision as both a tractable training signal and a generalization mechanism when the target distribution, training objective, and circuit architecture are spectrally aligned.",,"M Baumann, D Hein, S Udluft, T Rohe, C Linnhoff-Popien, J Stein - arXiv preprint arXiv:2605.10258, 2026 - arxiv.org",[],https://arxiv.org/abs/2605.10258,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2605.10258,['https://arxiv.org/pdf/2605.10258'],parity supervision as a driver of generalization in quantum generative modeling,MPS 生成/Born机,1,,
SAR and InSAR Change Detection with Quantum Generative Models,"S K Sekwao, S De, A Hocken, S Staniewicz, E Epifanovsky, C Stringham, G Farquharson, M Roetteler, P K Barkoutsos, J Iaconis",2026.0,0,"Change detection in synthetic aperture radar (SAR) and interferometric synthetic aperture radar (InSAR) underpins disaster response, infrastructure monitoring and land-use enforcement. Detection is limited by the background estimator, which conventionally forms a conditional expectation directly from observed pixel statistics and degrades where those statistics are sparse, including the regime produced by the heavy-tailed marginals of sub-meter-resolution radars. In this work, we integrate state-of-the-art satellite imagery with quantum machine learning on IonQ trapped-ion-based quantum processors. By replacing the empirical conditional with a quantum circuit Born machine (QCBM)-sampled generative model in Copula space, we substantially improve change detection on sparse real-world images. On Capella Space satellite image acquisitions, the generative estimator matches conventional methods when the observed statistics are adequate, and substantially outperforms them when they are not. Executing the trained model on IonQ trapped-ion based hardware reproduces the results of the ideal and noisy simulations and demonstrates up to par, or even better, performance with the classical state-of-the-art methods. For a SAR dataset of an airport, QPU circuit evaluations for both training and inference achieved a maximized filtered F1 score of 0.32, compared with 0.16 and 0.24 for the two classical baselines. For an InSAR dataset of a volcanic lava flow, all three methods reached a maximum filtered F1 of approximately 0.66. These experiments demonstrate the feasibility of executing a QCBM-based background estimator on trapped-ion hardware. We further demonstrate that the QCBM method successfully extends to interferometric coherence data, achieving performance comparable to classical approaches.",,"S K Sekwao, S De, A Hocken, S Staniewicz, E Epifanovsky, C Stringham, G Farquharson, M Roetteler, P K Barkoutsos, J Iaconis - arXiv preprint arXiv:2609.05313, 2026 - arxiv.org",[],https://arxiv.org/abs/2609.05313,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2609.05313,['https://arxiv.org/pdf/2609.05313'],sar and insar change detection with quantum generative models,MPS 生成/Born机 / 量子/混合LLM,1,,
"Universality of Classically Trainable, Quantum-Deployed Boson-Sampling Generative Models","A Kurkin, U Chabaud, Z Kolarovszki, B Bakó, Z Zimborás, V Dunjko",2026.0,0,"Recent work on the instantaneous quantum polynomial-time (IQP) quantum-circuit Born machine (QCBM) highlights a promising paradigm for generative modeling: train classically, deploy quantumly. In this setting, the training objective can be evaluated efficiently on a classical computer, while sampling from the resulting model may still be classically intractable. Furthermore, in the IQP-QCBM framework, extending the model family with ancillary qubits has been proven to yield universality. This paper asks whether similar results hold for linear-optical generative models. To this end, we introduce the Boson Sampling Born Machine (BSBM). Our analysis retraces analogous steps as were found for IQP-QCBMs with twists. Using recent results that enable classical approximation of broad classes of expectation values in linear optics, we show that BSBMs can be trained classically for wide families of loss functions. Next, we argue that ""basic"" BSBMs are not universal generative models, and that universality can be achieved by expanding the model while preserving efficient classical training and sampling hardness. In our approach, we introduce and analyze the role of constant-function postprocessing, generalizing the construction for IQP-QCBMs, which under suitable conditions can lead to universality while preserving the hardness of classically simulating the models. We showcase a family of BSBMs, characterized by a single hyperparameter, that allows for a monotonic increase in expressivity toward universality while retaining the capacity to represent ostensibly hard distributions. Furthermore, we discuss the possible modalities for the efficient classical training, in the sense of efficient estimation of gradients of the loss function.",,"A Kurkin, U Chabaud, Z Kolarovszki, B Bakó, Z Zimborás, V Dunjko - arXiv preprint arXiv:2603.11014, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.11014,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2603.11014,['https://arxiv.org/pdf/2603.11014'],universality of classically trainable quantum deployed boson sampling generative models,MPS 生成/Born机,1,,
A Hybrid Quantum Circuit Born Machine Framework for Financial Volatility Forecasting: Quantum-Assisted Training and Classical Inference,Y Chen,2026.0,0,"Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic ``Drop-Prior"" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of ``quantum-assisted training with classical-efficient inference"", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.",,"Y Chen - arXiv preprint arXiv:2603.09789, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.09789,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2603.09789,['https://arxiv.org/pdf/2603.09789'],a hybrid quantum circuit born machine framework for financial volatility forecasting quantum assisted training and classical inference,MPS 生成/Born机 / MPS/序列建模,1,,
A tensor-train multidimensional inverse Laplace transform,"M Mikkelsen, M Kastoryano",2026.0,0,"Laplace transforms and their numerical inverses arise throughout applied mathematics, physics, finance, and probability theory. Numerical inversion, however, quickly becomes intractable in high dimensions because the number of quadrature evaluations grows exponentially with dimension. We develop a tensor train (TT) formulation of the multidimensional inverse Laplace transform. The method constructs a TT approximation of the transformed function on the complex quadrature grid and then performs the inversion through a sequence of tensor contractions. Under suitable low-rank assumptions, this reduces the computational cost from exponential to polynomial in the dimension, provided that the relevant bond dimensions remain bounded. The method has only a small number of tunable parameters and admits error estimations. We demonstrate its performance in numerical experiments, benchmarked against Monte Carlo estimates and exact references, for multivariate normal-inverse Gaussian, Wishart, and correlated Gamma-type distributions.",,"M Mikkelsen, M Kastoryano - arXiv preprint arXiv:2606.06093, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.06093,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2606.06093,['https://arxiv.org/pdf/2606.06093'],a tensor train multidimensional inverse laplace transform,MPO/TT 压缩 / MPS/序列建模,1,,
Algorithmic algorithm development with LLMs: A Case Study on LLM-Usage for Contraction Order Optimization in Tensor Networks,"F Hoppe, M Röhrig-Zöllner, P Knechtges",2026.0,0,"We consider LLM-based algorithm development through a case study on contractionorder optimisation for tensor networks with OpenEvolve. We pay particular attention to the choice of the LLM as well as design choices such as evaluation metric and test instances. Our results highlight both the promise of verifier-guided evolutionary coding agents for algorithm development/improvement and the continuing importance of evaluation, validation, and interpretation -- and corresponding challenges -- by the human scientist.",,"F Hoppe, M Röhrig-Zöllner, P Knechtges - arXiv preprint arXiv:2606.01975, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.01975,arxiv-completion,2026-09-26 (citations:OpenAlex),,2606.01975,['https://arxiv.org/pdf/2606.01975'],algorithmic algorithm development with llms a case study on llm usage for contraction order optimization in tensor networks,,1,,
An IQP Born Machine for Calorimeter Image Generation at 64 Qubits with Compiled-IQP Deployment,"J Slim, S Monaco, F Rehm, D Krücker, K Borras",2026.0,0,"The challenge to scaling quantum generative models on near-term hardware is training. Variational circuit Born machines require repeated quantum sampling and are prone to barren plateaus. Instantaneous Quantum Polynomial-time (IQP) Born machines sidestep both, since their loss is built from low-order Pauli-Z correlators that admit an unbiased classical estimator, while sampling from worst-case circuits in the class is conjectured to be classically hard. We take this train-on-classical, deploy-on-quantum workflow to a real high-energy-physics generative task, learning calorimeter shower profiles at 64 qubits and running the trained model on an IBM Heron r2 superconducting processor at 67 physical qubits. Three ingredients make it work. A uniform mixture of IQP circuits (MoIQP) widens the model class at single-circuit training cost. The Pearson-Stabilized Correlation Kernel (PSCK) biases descent toward the pairwise correlations that carry the shower-development physics, which the standard heat kernel systematically compresses. An exact deferred-measurement compilation collapses the mixture into a single IQP circuit, realized on hardware as a constant-depth dynamic circuit with zero SWAP insertions on the device's native heavy-hex graph. The trained model reconstructs the correlation structure to within 0.016 of the floor imposed by the encoding itself. Raw device samples reproduce the per-cell energy spectra and the full pairwise correlation structure at Pearson r = 0.989, up to a single global amplitude compression of depolarizing origin. A Gaussian copula fitted to the same training split matches the pairwise target more accurately than the quantum model at negligible cost. The contribution is therefore the classical trainability, exact compilation, and hardware deployability of a quantum generative model at this scale, not superiority over classical surrogates.",,"J Slim, S Monaco, F Rehm, D Krücker, K Borras - arXiv preprint arXiv:2605.27735, 2026 - arxiv.org",[],https://arxiv.org/abs/2605.27735,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2605.27735,['https://arxiv.org/pdf/2605.27735'],an iqp born machine for calorimeter image generation at 64 qubits with compiled iqp deployment,MPO/TT 压缩 / MPS 生成/Born机,1,,
Automatically Differentiable Nonlinear Tensor Networks (ADNTNs) for Exponential Parameter Compression of Deep Neural Networks,"A Cichocki, M Wietczak",2026.0,0,"Large deep neural networks are costly to store and deploy because inference must move and evaluate many parameters. This paper studies \emph{Automatically Differentiable Nonlinear Tensor Networks} (ADNTNs), compact differentiable weight generators for replacing selected dense, convolutional, and attention layers. An ADNTN maps a small set of trainable tensor cores to a full weight tensor through hierarchical contractions and learnable nonlinearities; the generated layer is then used as an ordinary linear or convolutional operator. We investigate three multilayered topologies: Tree Tensor Networks, augmented Tree Tensor Networks with boundary disentanglers, and MERA-style multi-scale decoders. Compared with flat brick-wall automatically differentiable tensor networks, these hierarchies provide logarithmic-depth communication between tensorised modes and optional lateral mixing, which can improve long-range structure without large increases in stored parameters. We give a unified forward--adjoint formulation showing how reverse-mode automatic differentiation computes pre-activation adjoints and contracted-environment gradients for all trainable cores. The formulation supports task losses, reconstruction losses, distillation, quantisation-aware terms, batching, and modern optimisers. Proof-of-concept experiments on selected AlexNet and VGG-16 layers on CIFAR-10 datasets achieve per-layer parameter-compression ratios from about $2{,}000\times$ to $430{,}000\times$. Several VGG-16 compressed models match or slightly exceed the dense baseline, whereas AlexNet shows moderate degradation under more restrictive redundancy. These results indicate that nonlinear tensor-network generators are a promising structured route to compact pattern-recognition models, while also showing that contraction schedules and hardware-aware implementations remain essential for practical speedups.",,"A Cichocki, M Wietczak - arXiv preprint arXiv:2606.00130, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.00130,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2606.00130,['https://arxiv.org/pdf/2606.00130'],automatically differentiable nonlinear tensor networks adntns for exponential parameter compression of deep neural networks,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
Basis-update and Galerkin time integration in canonical matrix-product-state form,"M Fröhlich, R M Milbradt, M Eigel, A Sander, R Wille, C B Mendl",2026.0,0,"Matrix product state algorithms must enlarge their bond spaces as entanglement grows and compress them to control cost. We formulate basis-update and Galerkin (BUG) time integration as a sequence of canonical MPS sweeps for Hamiltonians represented as matrix product operators. We show when two natural basis updates produce the same trial space and when transporting coefficients between successive bases preserves the represented state. Under these conditions, the existing first-order error bound for uncompressed tree-tensor-network BUG also applies to the alternating-endpoint MPS schedule. We verify the uncompressed implementation against an independent six-site calculation. We then compare BUG with two-site TDVP for 16-site transverse-field Ising and Haldane-Shastry dynamics. At matched timestep and truncation settings, BUG performs fewer local exponential actions and has lower runtime. These settings do not produce equal accuracy. The runtime versus accuracy curves cross for the Ising model and are close for the Haldane-Shastry model. The comparison therefore identifies model-dependent trade-offs rather than a general advantage for either method.",,"M Fröhlich, R M Milbradt, M Eigel, A Sander, R Wille, C B Mendl - arXiv preprint arXiv:2608.16994, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.16994,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2608.16994,['https://arxiv.org/pdf/2608.16994'],basis update and galerkin time integration in canonical matrix product state form,MPO/TT 压缩 / MPS/序列建模,1,,
Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines,"K Shen, S Pielawa, V Dunjko, H Wang",2026.0,0,"Instantaneous quantum polynomial quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models with a classically tractable training objective based on the maximum mean discrepancy (MMD) and a potential quantum advantage motivated by sampling-complexity arguments, making them an exciting model worth deeper investigation. While recent works have further proven the universality of a (slightly generalized) model, the next immediate question pertains to its trainability, i.e., whether it suffers from the exponentially vanishing loss gradients, known as the barren plateau issue, preventing effective use, and how regimes of trainability overlap with regimes of possible quantum advantage. Here, we provide significant strides in these directions. To study the trainability at initialization, we analytically derive closed-form expressions for the variances of the partial derivatives of the MMD loss function and provide general upper and lower bounds. With uniform initialization, we show that barren plateaus depend on the generator set and the spectrum of the chosen kernel. We identify regimes in which low-weight-biased kernels avoid exponential gradient suppression in structured topologies. Also, we prove that a small-variance Gaussian initialization ensures polynomial scaling for the gradient under mild conditions. As for the potential quantum advantage, we further argue, based on previous complexity-theoretic arguments, that sparse IQP families can output a probability distribution family that is classically intractable, and that this distribution remains trainable at initialization at least at lower-weight frequencies.",,"K Shen, S Pielawa, V Dunjko, H Wang - arXiv preprint arXiv:2602.11042, 2026 - arxiv.org",[],https://arxiv.org/abs/2602.11042,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2602.11042,['https://arxiv.org/pdf/2602.11042'],characterizing trainability of instantaneous quantum polynomial circuit born machines,MPS 生成/Born机,1,,
Classical Tensor Network and Quantum Fourier Transform Approaches for Large-Scale Carr-Madan Option Pricing,"S Hauck, I Turkalj",2026.0,0,"Fourier-based methods are among the most widely used techniques for pricing European options when the characteristic function of the underlying asset process is available. Their applicability to increasingly fine discretizations, however, is limited by the rapidly growing memory requirements of classical Fourier transforms, which become a computational bottleneck for large-scale pricing problems. In this work, we overcome this limitation by reformulating the Carr-Madan pricing framework using tensor networks. Specifically, we employ the Superfast Fourier Transform (SFFT), a compressed Tensor Train representation of the Quantum Fourier Transform (QFT), and apply it directly to tensorized option pricing without ever explicitly constructing exponentially large vectors or Fourier operators. This formulation also enables a direct comparison between the classical tensor network algorithm and its quantum counterpart through QFT-based option pricing on quantum simulators and quantum hardware. Numerical experiments for European call options demonstrate that the proposed SFFT method maintains pricing accuracy while substantially reducing memory requirements and achieving subexponential computational scaling compared with conventional FFT-based pricing. The accompanying quantum simulations and hardware executions enable a direct comparison between the classical tensor network formulation and its QFT-based quantum counterpart, showing that both approaches avoid the exponential scaling of conventional Fourier implementations and provide complementary perspectives on large-scale option pricing. Together, these results establish a unified framework connecting classical Fourier pricing, tensor network algorithms, and quantum computing approaches, demonstrating how tensorized Fourier methods can provide scalable alternatives for high-dimensional financial computations.",,"S Hauck, I Turkalj - arXiv preprint arXiv:2607.28435, 2026 - arxiv.org",[],https://arxiv.org/abs/2607.28435,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2607.28435,['https://arxiv.org/pdf/2607.28435'],classical tensor network and quantum fourier transform approaches for large scale carr madan option pricing,MPO/TT 压缩 / 量子启发综述,1,,
Completely Positive and Trace Preserving Schemes with Tensor Train Compression for the Lindblad Equation,"P DelMastro, D Appelö, Y Cheng",2026.0,0,"We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into the product of tall-skinny matrices, and the columns of these matrices are further represented using the tensor train (TT) format, also know as matrix product states (MPS). This two-level low-rank format fits naturally into our existing Kraus is King scheme (arXiv:2409.08898v2 [math.NA]) for the Lindblad equation, whose underlying operations are arithmetic on the columns of the tall-skinny matrices. We show how these operations can be performed efficiently in the TT/MPS format, with particular emphasis on density matrix rank-truncation. We conclude with extensive numerical experiments demonstrating the convergence of this scheme and its efficiency in simulating systems with up to $10^{19}$ degrees of freedom using only modest compute resources.",,"P DelMastro, D Appelö, Y Cheng - arXiv preprint arXiv:2605.01494, 2026 - arxiv.org",[],https://arxiv.org/abs/2605.01494,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2605.01494,['https://arxiv.org/pdf/2605.01494'],completely positive and trace preserving schemes with tensor train compression for the lindblad equation,MPO/TT 压缩,1,,
Compressibility of micromagnetic solutions in tensor train format,"T Valet, N Vukadinovic",2026.0,0,"For three-dimensional (3D) magnetic objects with linear size $L$ exceeding a few exchange lengths, the micromagnetic state exhibits pronounced informational sparsity: low-dimensional, high-gradient regions (e.g., domain walls) coexist with near-uniformly magnetized volumetric domains. Because standard micromagnetic simulation methods discretize the magnetization on near-uniform 3D grids with linear cell size $a$, they cannot take advantage of this sparsity. The computational problem scales as $\sim L^3$ and $\sim (1/a)^3$. In this Letter, we establish that direct tensor-train (TT) representations overcome these poor scalings by exploiting the spatial sparsity optimally, while preserving accuracy in a controlled way. Focusing on representative flux-closure configurations in soft-magnetic rectangular prisms, in the near-micrometer regime, we demonstrate that the parameter count of TT-compressed micromagnetic data scales approximately as $L^{1.8}$ and $(1/a)^{1.2}$. Hence the relative advantage over dense discretizations rapidly grows with the problem size and refinement level. These first results provide a strong motivation for future developments of micromagnetic solvers in TT format which could transcend the limitations of traditional simulators, with far reaching potential impacts on fundamental research and technology development.",,"T Valet, N Vukadinovic - arXiv preprint arXiv:2604.28008, 2026 - arxiv.org",[],https://arxiv.org/abs/2604.28008,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2604.28008,['https://arxiv.org/pdf/2604.28008'],compressibility of micromagnetic solutions in tensor train format,MPO/TT 压缩,1,,
Continuous unitary transformations using tensor network representations access the full many-body localized spectrum,"Q Liu, J Herre, D M Kennes, C Karrasch",2026.0,0,"We develop variational continuous unitary transformations (VCUTs), which integrate Wegner-Wilson flow equations with tensor network techniques to approximately diagonalize many-body localized (MBL) Hamiltonians. The diagonalizing unitary is represented as a matrix product operator whose bond dimension controls the accuracy. For the disordered Heisenberg chain, VCUTs accurately reproduces the full spectrum across the ergodic-to-MBL crossover at small system sizes and scales to $L = 48$ sites. Beyond eigenenergies, the method can track the spatial entanglement structure of the diagonalizing unitary $U(l)$ at each flow step, enabling identification of local integrals of motion deep in the MBL phase.",,"Q Liu, J Herre, D M Kennes, C Karrasch - arXiv preprint arXiv:2603.12851, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.12851,arxiv-completion,2026-09-26 (citations:OpenAlex),,2603.12851,['https://arxiv.org/pdf/2603.12851'],continuous unitary transformations using tensor network representations access the full many body localized spectrum,,1,,
"Coupling Tensor Trains with Graph of Convex Sets: Effective Compression, Exploration, and Planning in the C-Space","G Reinerth, R Laha, M Romano",2026.0,0,"We present TANGO (Tensor ANd Graph Optimization), a novel motion planning framework that integrates tensor-based compression with structured graph optimization to enable efficient and scalable trajectory generation. While optimization-based planners such as the Graph of Convex Sets (GCS) offer powerful tools for generating smooth, optimal trajectories, they typically rely on a predefined convex characterization of the high-dimensional configuration space-a requirement that is often intractable for general robotic tasks. TANGO builds further by using Tensor Train decomposition to approximate the feasible configuration space in a compressed form, enabling rapid discovery and estimation of task-relevant regions. These regions are then embedded into a GCS-like structure, allowing for geometry-aware motion planning that respects both system constraints and environmental complexity. By coupling tensor-based compression with structured graph reasoning, TANGO enables efficient, geometry-aware motion planning and lays the groundwork for more expressive and scalable representations of configuration space in future robotic systems. Rigorous simulation studies on planar and real robots reinforce our claims of effective compression and higher quality trajectories.",,"G Reinerth, R Laha, M Romano - arXiv preprint arXiv:2603.11658, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.11658,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2603.11658,['https://arxiv.org/pdf/2603.11658'],coupling tensor trains with graph of convex sets effective compression exploration and planning in the c space,MPO/TT 压缩,1,,
Efficient Application of Tensor Network Operators to Tensor Network States,"R M Milbradt, S Sun, C B Mendl, J Gray, G K - Chan",2026.0,0,"The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states inspired by the density matrix method and the Cholesky decomposition. This application procedure is a common subroutine in tensor network methods. We explicitly include the special case of tensor train structures and demonstrate how to extend methods commonly used in this context to general tree structures. We compare our newly developed method with the existing ones in a benchmark scenario with random tensor network states and operators. We find our Cholesky-based compression (CBC) performs equivalently to the current state-of-the-art method, while outperforming most established methods by at least an order of magnitude in runtime. We then apply our knowledge to perform circuit simulation of tree-like circuits, in order to test our method in a more realistic scenario. Here, we find that more complex tree structures can outperform simple linear structures and achieve lower errors than those possible with the simple structures. Additionally, our CBC still performs among the most successful methods, showing less dependence on the different bond dimensions of the operator.",,"R M Milbradt, S Sun, C B Mendl, J Gray, G K - Chan - arXiv preprint arXiv:2601.19650, 2026 - arxiv.org",[],https://arxiv.org/abs/2601.19650,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2601.19650,['https://arxiv.org/pdf/2601.19650'],efficient application of tensor network operators to tensor network states,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
Equations of Tree Tensor Network Varieties,"S Hoşten, N C Paul, O T P Schmidt, D Skurt",2026.0,0,"We show that tree tensor network varieties, including tensor train varieties, are general Markov models associated to spaced trees. This allows us to prove that the prime ideals of these varieties are generated by minors of matrix flattenings. In the case of tensor train varieties, we discuss whether these minors form a Gröbner basis and provide a combinatorial method to compute the degree for order $3$ tensor trains.",,"S Hoşten, N C Paul, O T P Schmidt, D Skurt - arXiv preprint arXiv:2608.19071, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.19071,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2608.19071,['https://arxiv.org/pdf/2608.19071'],equations of tree tensor network varieties,TTN/MERA/PEPS,1,,
Hierarchical Search of Tree Tensor Networks for High-Dimensional Data,"Z Guo, A Deshpande, X Wang, B C Kiedrowski, A A Gorodetsky",2026.0,0,"Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this limitation by formalizing the structural rounding problem for tree tensor networks and introducing a hierarchical search algorithm HIST, which automatically identifies optimized structures with index reshaping for input tree tensor networks. To navigate the combinatorial explosion of the structural search space, HIST integrates stochastic sub-network sampling with hierarchical refinement. This approach utilizes entropy-guided index clustering to reduce dimensionality and targeted reshaping to expose latent data correlations. Numerical experiments on analytical functions and real-world physics applications, including thermal radiation transport, neutron diffusion, and computational fluid dynamics, demonstrate that HIST exhibits empirical polynomial scaling with dimensionality relative to the sampling budget, bypassing the scalability barriers in prior work. HIST achieves compression ratios $2.5\times$ to $100\times$ higher than standard fixed formats such as Tensor Trains and Hierarchical Tuckers (peaking at $1000\times$). Furthermore, HIST discovers structures that generalize effectively: applying a structure optimized for one data instance to a related target data typically maintains compression performance within $10\%$ of the result obtained by performing structure search on that target data. These results highlight HIST as a robust, automated tool for adaptive data representation and high-dimensional simulation compression with tensor network methods.",,"Z Guo, A Deshpande, X Wang, B C Kiedrowski, A A Gorodetsky - arXiv preprint arXiv:2603.27856, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.27856,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2603.27856,['https://arxiv.org/pdf/2603.27856'],hierarchical search of tree tensor networks for high dimensional data,MPO/TT 压缩 / MPS 生成/Born机 / TTN/MERA/PEPS,1,,
High-Resolution Tensor-Network Fourier Methods for Exponentially Compressed Non-Gaussian Aggregate Distributions,"J J Rodríguez-Aldavero, J J García-Ripoll",2026.0,0,"Characteristic functions of weighted sums of independent random variables exhibit low-rank structure in the quantized tensor train (QTT) representation, also known as matrix product states (MPS), enabling up to exponential compression of their fully non-Gaussian probability distributions. Under variable independence, the global characteristic function factorizes into local terms. Its low-rank QTT structure arises from intrinsic spectral smoothness in continuous models, or from spectral energy concentration as the number of components $D$ grows in discrete models. We demonstrate this on weighted sums of Bernoulli and lognormal random variables. In the former, despite an adversarial, incompressible small-$D$ regime, the characteristic function undergoes a sharp bond-dimension collapse for $D \gtrsim 300$ components, enabling polylogarithmic time and memory scaling. In the latter, the approach reaches high-resolution discretizations of $N = 2^{30}$ frequency modes on standard hardware, far beyond the $N = 2^{24}$ ceiling of dense implementations. These compressed representations enable efficient computation of Value at Risk (VaR) and Expected Shortfall (ES), supporting applications in quantitative finance and beyond.",,"J J Rodríguez-Aldavero, J J García-Ripoll - arXiv preprint arXiv:2603.23106, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.23106,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2603.23106,['https://arxiv.org/pdf/2603.23106'],high resolution tensor network fourier methods for exponentially compressed non gaussian aggregate distributions,MPO/TT 压缩,1,,
Incremental Tensor-Train Compression from Streaming TT-Formatted Data: Applications to Reduced-Order Modeling,"W Guo, Z Peng",2026.0,0,"High-dimensional tensor data streams arise naturally in scientific and engineering applications, such as simulations of kinetic equations and quantum systems, where samples become available sequentially and are often already represented in compressed low-rank tensor formats. Existing streaming tensor-train (TT) algorithms typically construct or update representations from dense tensor data or randomized sketches. However, when high-dimensional data are generated directly in TT or related low-rank formats, reconstructing dense tensors solely for the purpose of compression is unnecessary and computationally prohibitive. We develop a deterministic incremental TT compression algorithm that operates directly on streaming TT-formatted data. Given a new TT tensor, the proposed method updates an accumulated TT representation through core-wise projection, residual orthogonalization, and adaptive enrichment, retaining only the complementary information that cannot be represented within a prescribed tolerance. By operating entirely at the level of TT cores, the algorithm avoids reconstructing either the incoming tensor or the accumulated full tensor. We establish approximation error bounds for the proposed incremental approach. Moreover, we show that the accumulated TT representation corresponds to a compressed analogue of standard proper orthogonal decomposition for full-order snapshot data, enabling reduced-order models to be constructed directly from streaming low-rank solution data through operations on TT cores, without first reconstructing full snapshots. Numerical experiments on parametric radiative transfer equations demonstrate that the proposed method achieves comparable reconstruction accuracy with substantially reduced wall time and yields efficient and accurate ROMs directly from compressed low-rank data.",,"W Guo, Z Peng - arXiv preprint arXiv:2606.26900, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.26900,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2606.26900,['https://arxiv.org/pdf/2606.26900'],incremental tensor train compression from streaming tt formatted data applications to reduced order modeling,MPO/TT 压缩,1,,
Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions,"X Wang, T Hashizume, P Siegl, D Jaksch",2026.0,0,"Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise evaluation of elementary and nonlinear filtering functions on data encoded as tensor trains (TTs), a class of tensor networks. Our approach operates entirely in the compressed domain, enabling efficient computation on exponentially large datasets while maintaining a controlled computational cost. We demonstrate its power in two key areas: (I) evaluating highly nonlinear elementary and filtering functions on a 3D reactive flow field, enabling high-fidelity reaction rate computation and region filtering, and (II) finding extrema in complex optimization problems, such as solving Max-SAT instances on spaces up to $2^{70}$ configurations. These results establish ITNT as a foundational tool that provides tensor network methods with the capability for general-purpose data science and large-scale optimization.",,"X Wang, T Hashizume, P Siegl, D Jaksch - arXiv preprint arXiv:2608.17135, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.17135,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2608.17135,['https://arxiv.org/pdf/2608.17135'],iterative tensor network transformations for element wise evaluation of elementary and filtering functions,MPO/TT 压缩,1,,
Lattice in Line: Optimized DMRG ordering for complex lattice geometries,R Rausch,2026.0,0,"The density-matrix renormalization group (DMRG) is a one-dimensional tensor-network technique, but it is not limited to one-dimensional systems: it can be applied to periodic 2D and 3D clusters and molecules, provided their sites are first enumerated along a line; a step one may call ""lattice compilation"". This paper discusses three proxy loss functions for finding this optimal enumeration: the graph bandwidth $B$ (maximum interaction range), the cutwidth $C$ (maximum number of bonds crossing a cut), and the average interaction range $R$. Constructing the Hamiltonian MPO (matrix-product operator) for a large set of clusters that are of interest in frustrated magnetism, I find that $C$ determines the peak SU(2) Heisenberg MPO bond dimension and $R$ the average one. Targeting $(C,R)$ lexicographically yields the best energies. Targeting $B$ indirectly reduces $C$, but not as efficiently as targeting $C$ directly. Otherwise, the value of $B$ itself is largely irrelevant in the sense that good DMRG energies can have large $B$. To perform the optimization, classic heuristics (e.g. reverse Cuthill--McKee) prove unreliable even for small clusters, and I find that a QUBO formulation improves them only marginally. Instead I propose a staged optimization built on Boolean satisfiability (SAT) and constraint-programming (CP) solvers, chiefly CP-SAT of Google's OR-Tools, a hybrid of CP propagation and SAT clause learning. This approach yields significantly better orderings together with rigorous bounds. The corresponding Lattice in Line code is available at https://github.com/spinflip/lattice_in_line and was designed with extensive use of the Fable 5 large language model.",,"R Rausch - arXiv preprint arXiv:2609.25384, 2026 - arxiv.org",[],https://arxiv.org/abs/2609.25384,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2609.25384,['https://arxiv.org/pdf/2609.25384'],lattice in line optimized dmrg ordering for complex lattice geometries,MPS 语言模型,1,,
LiQSS: Post-Transformer Linear Quantum-Inspired State-Space Tensor Networks for Real-Time 6G,"F Rezazadeh, H Chergui, A A Gargari, M Bennis, H Song, L Liu, M Debbah",2026.0,0,"Proactive and agentic control in Sixth-Generation (6G) Open Radio Access Networks (O-RAN) requires control-grade prediction under stringent Near-Real-Time (Near-RT) latency and computational constraints. While Transformer-based models are effective for sequence modeling, their quadratic complexity limits scalability in Near-RT RAN Intelligent Controller (RIC) analytics. This paper investigates a post-Transformer design paradigm for efficient radio telemetry forecasting. We propose a quantum-inspired many-body state-space tensor network that replaces self-attention with stable structured state-space dynamics kernels, enabling linear-time sequence modeling. Tensor-network factorizations in the form of Tensor Train (TT) / Matrix Product State (MPS) representations are employed to reduce parameterization and data movement in both input projections and prediction heads, while lightweight channel gating and mixing layers capture non-stationary cross-Key Performance Indicator (KPI) dependencies. The proposed model is instantiated as an agentic perceive-predict xApp and evaluated on a bespoke O-RAN KPI time-series dataset comprising 59,441 sliding windows across 13 KPIs, using Reference Signal Received Power (RSRP) forecasting as a representative use case. Our proposed Linear Quantum-Inspired State-Space (LiQSS) model is 10.8x-15.8x smaller and approximately 1.4x faster than prior structured state-space baselines. Relative to Transformer-based models, LiQSS achieves up to a 155x reduction in parameter count and up to 2.74x faster inference, without sacrificing forecasting accuracy.",,"F Rezazadeh, H Chergui, A A Gargari, M Bennis, H Song, L Liu, M Debbah - arXiv preprint arXiv:2601.12375, 2026 - arxiv.org",[],https://arxiv.org/abs/2601.12375,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2601.12375,['https://arxiv.org/pdf/2601.12375'],liqss post transformer linear quantum inspired state space tensor networks for real time 6g,张量化Transformer / MPS/序列建模,2,,
Multi-agent Autoformalization of Tensor Network Theory,"S Lu, E Tjoa, J I Cirac",2026.0,0,"We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration. The agents, coordinated through a structured mathematical blueprint and periodic human review, orchestrated and executed the full formalization autonomously. For some statements, the agents were able to explore new proof routes that are not part of the standard literature. Along the way the agents produced extensive tensor-network and quantum-information libraries not previously available in Mathlib, Lean's mathematical library. As a physical application, the formalization also extends towards symmetry-protected topological phases in one dimension. We find that the main bottleneck in large-scale autoformalization is enforcing mathematical intent and we provide a detailed study of the full process and various subtleties involved. We release the codebase as the library \href{https://github.com/LionSR/TNLean}{TNLean}, together with a \nChapters{}-chapter \href{https://lionsr.github.io/TNLean/blueprint/}{blueprint} of the formalization effort.",,"S Lu, E Tjoa, J I Cirac - arXiv preprint arXiv:2607.07857, 2026 - arxiv.org",[],https://arxiv.org/abs/2607.07857,arxiv-completion,2026-09-26 (citations:OpenAlex),量子启发综述,2607.07857,['https://arxiv.org/pdf/2607.07857'],multi agent autoformalization of tensor network theory,量子启发综述,1,,
Multiscale Structural Reliability Analysis in high dimensions with Tensor Trains and Physics-Augmented Neural Networks,"A Tyagi, A d Beer, T Cui, J N Fuhg",2026.0,,"Structural reliability evaluation for composites constitutes a fundamentally high-dimensional multiscale problem, as microscale material uncertainties must propagate to the macroscale and can be quantified as high-dimensional random fields. Conventional approaches are computationally intractable, as they rely on repeatedly solving coupled partial differential equation systems across scales while contending with the exponential complexity inherent in high-dimensional uncertainty quantification. This work introduces a scalable and physically consistent framework that addresses both bottlenecks simultaneously in the case of separation of scales and (anisotropic) linear elasticity. In particular, we couple a physics-augmented Voigt--Reuss Neural Network (VRNN) with the Deep Inverse Rosenblatt Transport (DIRT) method to estimate the posterior probability of structural failure. The VRNN is used to resolve the computationally expensive FE$^2$ scheme by providing a near-instantaneous evaluation of the homogenized stiffness tensor that is guaranteed to be symmetric, positive-definite, and strictly bounded within the Voigt--Reuss limits, enabling fast evaluation of the homogenized responses. The DIRT method constructs a sequence of functional tensor train approximations to efficiently store an approximation of the high-dimensional optimal importance sampling distribution for estimating the probability of failure. This mitigates the curse of dimensionality arising from the Karhunen--Loève expansion of the random fields. The framework is demonstrated on a three-dimensional heterogeneous benchmark problem, where the uncertainty in the microscale material properties is characterized by a Bayesian posterior distribution obtained from limited strain observations. Our results show that the proposed framework can provide low-variance estimates of failure probabilities in dimensions up to 150.",,"A Tyagi, A d Beer, T Cui, J N Fuhg - arXiv preprint arXiv:2604.18776, 2026 - arxiv.org",[],https://arxiv.org/abs/2604.18776,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS/序列建模,2604.18776,['https://arxiv.org/pdf/2604.18776'],multiscale structural reliability analysis in high dimensions with tensor trains and physics augmented neural networks,MPS/序列建模,1,,
Multiscale passive scalar turbulence in a compressed subspace via tensor trains,"S Pisoni, E Tiunov, C Calascibetta",2026.0,0,"Capturing the multiscale statistics of turbulence in compressed form remains a central challenge for reduced-order modeling. We introduce a hybrid Tensor Train (TT) approach for a highly intermittent passive scalar. The hybrid TT matches Galerkin, wavelet, and standard TT decompositions for the structure functions while improving the representation of intermittent, non-Gaussian fluctuations. These results open a route toward evolving the linear dynamics of passive scalars directly in compressed tensor form, with potential applications to quantum algorithms for fluid transport.",,"S Pisoni, E Tiunov, C Calascibetta - arXiv preprint arXiv:2608.00194, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.00194,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2608.00194,['https://arxiv.org/pdf/2608.00194'],multiscale passive scalar turbulence in a compressed subspace via tensor trains,MPO/TT 压缩,1,,
Optimizing Tensor Train Decomposition in DNNs for RISC-V Architectures Using Design Space Exploration and Compiler Optimizations,"T Anthimopoulos, M Kokhazadeh, V Kelefouras, B Himpel, G Keramidas",2026.0,0,"Deep neural networks (DNNs) have become indispensable in many real-life applications like natural language processing, and autonomous systems. However, deploying DNNs on resource-constrained devices, e.g., in RISC-V platforms, remains challenging due to the high computational and memory demands of fully connected (FC) layers, which dominate resource consumption. Low-rank factorization (LRF) offers an effective approach to compressing FC layers, but the vast design space of LRF solutions involves complex trade-offs among FLOPs, memory size, inference time, and accuracy, making the LRF process complex and time-consuming. This paper introduces an end-to-end LRF design space exploration methodology and a specialized design tool for optimizing FC layers on RISC-V processors. Using Tensor Train Decomposition (TTD) offered by TensorFlow T3F library, the proposed work prunes the LRF design space by excluding first, inefficient decomposition shapes and second, solutions with poor inference performance on RISC-V architectures. Compiler optimizations are then applied to enhance custom T3F layer performance, minimizing inference time and boosting computational efficiency. On average, our TT-decomposed layers run 3x faster than IREE and 8x faster than Pluto on the same compressed model. This work provides an efficient solution for deploying DNNs on edge and embedded devices powered by RISC-V architectures.",,"T Anthimopoulos, M Kokhazadeh, V Kelefouras, B Himpel, G Keramidas - ACM Transactions on Embedded Computing Systems 24, 6, Article 171 (October 2025), 34 pages",[],https://arxiv.org/abs/2602.01996,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2602.01996,['https://arxiv.org/pdf/2602.01996'],optimizing tensor train decomposition in dnns for risc v architectures using design space exploration and compiler optimizations,MPS 语言模型 / MPO/TT 压缩,1,"ACM Transactions on Embedded Computing Systems 24, 6, Article 171 (October 2025), 34 pages",
Quantum Scrambling Born Machine,M Płodzień,2026.0,0,"Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling Born Machine in which a fixed entangling unitary -- acting as a scrambling reservoir -- provides multi-qubit entanglement, while only single-qubit rotations are optimized. We consider three entangling unitaries -- a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution under nearest-neighbor spin-chain Hamiltonians -- and show that, for the benchmark distributions and system sizes considered, once the entangler produces near-Haar-typical entanglement the model learns the target distribution with weak sensitivity to the scrambler's microscopic origin. Finally, promoting the Hamiltonian couplings to trainable parameters casts the generative task as a variational Hamiltonian problem, with performance competitive with representative classical generative models at matched parameter count.",,"M Płodzień - Phys. Rev. A 114, 012464 (2026)",[],https://arxiv.org/abs/2602.17281,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2602.17281,['https://arxiv.org/pdf/2602.17281'],quantum scrambling born machine,MPS 生成/Born机,1,"Phys. Rev. A 114, 012464 (2026)",
Quantum-Enhanced Synthetic Data Generation Using Quantum Circuit Born Machines for Imbalanced Tabular Learning,"T Nuatho, N Sangnakara, P Prechaprapranwong, R Sarochawikasit",2026.0,0,"Data scarcity and class imbalance are persistent challenges in machine learning that degrade model generalization and introduce predictive bias. We present a hybrid quantum-classical framework for synthetic data generation using a Quantum Circuit Born Machine (QCBM) to address these limitations. The proposed approach exploits quantum mechanical properties -- superposition and entanglement -- within a parameterized variational quantum circuit to model complex probability distributions that are difficult for classical generative methods to capture. Experiments are conducted on two tabular benchmark datasets: the Iris dataset and the Telco Customer Churn dataset. Preprocessing includes normalization and PCA-based dimensionality reduction to enable efficient basis encoding for quantum circuits. The QCBM is trained by minimizing Kullback-Leibler (KL) divergence between real and generated data distributions using a gradient-based parameter-shift optimization rule. Augmenting training data with QCBM-generated synthetic samples at 40-50% of the minority class improves F1-score by approximately 5-15% and minority-class recall by 10-25%. Cross-domain evaluations (Train on Synthetic, Test on Real; and Train on Real, Test on Synthetic) reveal a performance gap of only 3-10%, indicating strong distributional fidelity. Comparative analysis against classical oversampling methods -- SMOTE, Borderline-SMOTE, KMeansSMOTE, and SVM-SMOTE -- shows that QCBM achieves competitive classification performance and produces lower Maximum Mean Discrepancy (MMD) on the Telco dataset, suggesting superior structural similarity in certain imbalanced settings. These findings establish QCBM as a viable complementary tool for data augmentation, particularly for low-dimensional structured tabular data with class imbalance.",,"T Nuatho, N Sangnakara, P Prechaprapranwong, R Sarochawikasit - arXiv preprint arXiv:2607.09113, 2026 - arxiv.org",[],https://arxiv.org/abs/2607.09113,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2607.09113,['https://arxiv.org/pdf/2607.09113'],quantum enhanced synthetic data generation using quantum circuit born machines for imbalanced tabular learning,MPS 生成/Born机,1,,
Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach,"E Gurkanli, M Spannowsky",2026.0,0,"We investigate whether a multiscale tensor-network architecture can provide a useful inductive bias for reconstruction-based anomaly detection in collider jets. Jets are produced by a branching cascade, so their internal structure is naturally organised across angular and momentum scales. This motivates an autoencoder that compresses information hierarchically and can reorganise short-range correlations before coarse-graining. Guided by this picture, we formulate a MERA-inspired autoencoder acting directly on ordered jet constituents. To the best of our knowledge, a MERA-inspired autoencoder has not previously been proposed, and this architecture has not been explored in collider anomaly detection. We compare this architecture to a dense autoencoder, the corresponding tree-tensor-network limit, and standard classical baselines within a common background-only reconstruction framework. The paper is organised around two main questions: whether locality-aware hierarchical compression is genuinely supported by the data, and whether the disentangling layers of MERA contribute beyond a simpler tree hierarchy. To address these questions, we combine benchmark comparisons with a training-free local-compressibility diagnostic and a direct identity-disentangler ablation. The resulting picture is that the locality-preserving multiscale structure is well matched to jet data, and that the MERA disentanglers become beneficial precisely when the compression bottleneck is strongest. Overall, the study supports locality-aware hierarchical compression as a useful inductive bias for jet anomaly detection.",,"E Gurkanli, M Spannowsky - arXiv preprint arXiv:2604.06541, 2026 - arxiv.org",[],https://arxiv.org/abs/2604.06541,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2604.06541,['https://arxiv.org/pdf/2604.06541'],quantum inspired tensor network autoencoders for anomaly detection a mera based approach,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
Quantum-Inspired Tensor Networks for Approximating PDE Flow Maps,"N B Dehaghani, B Q Tran, R Wisniewski, S Mengel, A P Aguiar",2026.0,,"We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized transport and diffusion dynamics, we encode PDE states as matrix product states (MPS) and represent the evolution operator as a structured low-rank matrix product operator (MPO) in tensor-train form (e.g., arising from finite-difference discretizations assembled in MPO form). The MPO is applied directly in MPS form, and rank growth is controlled via canonicalization and SVD-based truncation after each step. We provide theoretical context through standard matrix product properties, including exact MPS representability bounds, local optimality of SVD truncation, and a Lipschitz-type multi-step error propagation estimate. Experiments on one- and two-dimensional linear advection-diffusion and nonlinear viscous Burgers equations demonstrate accurate short-horizon prediction, favorable scaling in smooth diffusive regimes, and error growth in nonlinear multi-step predictions.",,"N B Dehaghani, B Q Tran, R Wisniewski, S Mengel, A P Aguiar - arXiv preprint arXiv:2602.15906, 2026 - arxiv.org",[],https://arxiv.org/abs/2602.15906,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2602.15906,['https://arxiv.org/pdf/2602.15906'],quantum inspired tensor networks for approximating pde flow maps,MPO/TT 压缩 / MPS 生成/Born机,1,,
"Quantum-inspired Tensor Network for QUBO, QUDO and Tensor QUDO Problems with k-neighbors","S M Subiñas, A M Ali, J M Martín, M F Hernando, J Sedano, Á M García-Vico",2026.0,0,"This work presents a novel tensor network algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, Quadratic Unconstrained Discrete Optimization (QUDO) problems, and Tensor Quadratic Unconstrained Discrete Optimization (T-QUDO) problems. The proposed algorithm is based on the MeLoCoToN methodology, which solves combinatorial optimization problems by employing superposition, imaginary time evolution, and projective measurements. Additionally, two different approaches are presented to solve QUBO and QUDO problems with k-neighbors interactions in a lineal chain, one based on 4-order tensor contraction and the other based on matrix-vector multiplication, including sparse computation and a new technique called ""Waterfall"". Furthermore, the performance of both implementations is compared with a quadratic optimization solver to demonstrate the performance of the method, showing advantages in several problem instances.",,"S M Subiñas, A M Ali, J M Martín, M F Hernando, J Sedano, Á M García-Vico - arXiv preprint arXiv:2603.28065, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.28065,arxiv-completion,2026-09-26 (citations:OpenAlex),,2603.28065,['https://arxiv.org/pdf/2603.28065'],quantum inspired tensor network for qubo qudo and tensor qudo problems with k neighbors,,1,,
Semantic Uncertainty Quantification of Hallucinations in LLMs: A Quantum Tensor Network Based Method,"P Vipulanandan, K Premaratne, D Sarkar",2026.0,0,"Large language models (LLMs) exhibit strong generative capabilities but remain vulnerable to confabulations, fluent yet unreliable outputs that vary arbitrarily even under identical prompts. Leveraging a quantum tensor network based pipeline, we propose a quantum physics inspired uncertainty quantification framework that accounts for aleatoric uncertainty in token sequence probability for semantic equivalence based clustering of LLM generations. This offers a principled and interpretable scheme for hallucination detection. We further introduce an entropy maximization strategy that prioritizes high certainty, semantically coherent outputs and highlights entropy regions where LLM decisions are likely to be unreliable, offering practical guidelines for when human oversight is warranted. We evaluate the robustness of our scheme under different generation lengths and quantization levels, dimensions overlooked in prior studies, demonstrating that our approach remains reliable even in resource constrained deployments. A total of 116 experiments on TriviaQA, NQ, SVAMP, and SQuAD across multiple architectures including Mistral-7B, Mistral-7B-instruct, Falcon-rw-1b, LLaMA-3.2-1b, LLaMA-2-13b-chat, LLaMA-2-7b-chat, LLaMA-2-13b, and LLaMA-2-7b show consistent improvements in AUROC and AURAC over state of the art baselines.",,"P Vipulanandan, K Premaratne, D Sarkar - ICLR2026",[],https://arxiv.org/abs/2601.20026,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2601.20026,['https://arxiv.org/pdf/2601.20026'],semantic uncertainty quantification of hallucinations in llms a quantum tensor network based method,MPS 语言模型 / MPO/TT 压缩 / MPS 生成/Born机 / MPS/序列建模 / 量子启发综述,2,ICLR2026,
TENSO: Software Package for Numerically Exact Open Quantum Dynamics Based on Efficient Tree Tensor Network Decomposition of the Hierarchical Equations of Motion,"J C Rodriguez-Betancourt, M C Anderson, L Niu, X Chen, I Franco",2026.0,0,"TENSO is a versatile and powerful open-source software package for numerically exact simulations of the dynamics of quantum systems immersed in structured thermal environments. It is based on a tree tensor network decomposition of the hierarchical equations of motion (HEOM) that efficiently curbs its curse of dimensionality with bath complexity. As such, TENSO enables exact non-Markovian open quantum dynamics simulations even with complex environments typical of chemistry and quantum information science. TENSO allows for time-dependent drive in the system, and for non-commuting fluctuations. More generally, TENSO efficiently propagates the dynamics for any method with a generator of the dynamics that can be expressed in a sum-of-products form, including the HEOM and multi-layer multiconfigurational time-dependent Hartree methods. TENSO enables simulations using tensor trees and trains of arbitrary order, and implements three propagation strategies for the coupled master equations; two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive rank method with a variable memory footprint controlled by the target level of computational error. In contrast to the accompanying theory and algorithmic paper [J. Chem. Phys. 163, 104109 (2025)] the focus here is on the practical usage and applications of TENSO with underlying theoretical concepts introduced only as needed.",,"J C Rodriguez-Betancourt, M C Anderson, L Niu, X Chen, I Franco - arXiv preprint arXiv:2603.17711, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.17711,arxiv-completion,2026-09-26 (citations:OpenAlex),TTN/MERA/PEPS,2603.17711,['https://arxiv.org/pdf/2603.17711'],tenso software package for numerically exact open quantum dynamics based on efficient tree tensor network decomposition of the hierarchical equations of motion,TTN/MERA/PEPS,1,,
TT-net: Quantum Inspired Tensor Network Denoising in Conditional GANs,"M A Sterzel, M J Rančić",2026.0,0,"Developed as a workhorse for classical simulations of quantum algorithms and quantum many-body systems, Tensor Network methods have entered the scientific mainstream in quantum physics. Among various types of tensor networks, Tensor Trains (commonly know as Matrix Product States in the quantum computing community) have already found applications in machine learning. These methods often rely on a powerful linear algebra tool called the Singular Value Decomposition (SVD). Several conditional GAN architectures for image denoising incorporate SVD as a single-cut decomposition step applied to generator feature maps. In this work we introduce TT-Net, which replaces the per-channel SVD denoising block with a two-cut tensor-train decomposition capable of accessing cross-channel information directly, a capability absent from contemporary alternatives. In a controlled comparison differing only in this decomposition mechanism, TT-Net outperforms SVD-Net on PSNR and SSIM across all three noise types tested (Gaussian, motion blur, and salt-and-pepper), supporting the hypothesis that cross-channel access improves denoising quality. Training-dynamics analysis further shows that TT-Net's adversarial loss term consistently saturates to a stagnant state across all three noise types, more so than SVD-Net's, while reconstruction quality continues to improve regardless, raising an open question about the adversarial component's contribution that this work identifies but does not resolve. Furthermore, for Gaussian noise our method outperforms both the EigenGAN and the state of the art Pix2pix method which does not assume any linear algebra decompositions and does not retain any linear algebra information. Our manuscript shows how quantum inspired tools can be used as practical real world feature filters for deep learning applications.",,"M A Sterzel, M J Rančić - arXiv preprint arXiv:2608.19789, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.19789,arxiv-completion,2026-09-26 (citations:OpenAlex),量子启发综述,2608.19789,['https://arxiv.org/pdf/2608.19789'],tt net quantum inspired tensor network denoising in conditional gans,量子启发综述,1,,
Tensor Decomposition of Transformer Key-Value Caches: Spectral Structure and Format Comparison,"R Krishnan, V Schulz",2026.0,0,"The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers. We measure the singular-value spectra of all four mode unfoldings on Mistral-7B-v0.3 and LLaMA-2-13B and compare four standard tensor decompositions: Tucker, CP, tensor train, and t-SVD, at matched storage. The spectra partition the four axes into two classes. The token and feature modes carry low-rank structure, particularly for keys. The head and layer modes are nearly full-rank and resist compression at any practical error level. Among the four decompositions, Tucker achieves the lowest reconstruction error at every compression ratio from $2\times$ to $5\times$, because it can leave the full-rank modes untouched. Comparisons with two-dimensional unfolding baselines show that the preferred representation differs between keys and values: 2D methods achieve lower key error, while four-way Tucker achieves lower value error at matched storage. A mode-pinning theorem certifies the full-rank preservation from the measured spectra alone. Two further spectral properties affect the compressible modes without touching the full-rank ones: values reach a higher error floor than keys at every ratio, and post-RoPE keys lose $41\%$ - $64\%$ of their pre-RoPE compressibility on both models.",,"R Krishnan, V Schulz - arXiv preprint arXiv:2609.28029, 2026 - arxiv.org",[],https://arxiv.org/abs/2609.28029,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2609.28029,['https://arxiv.org/pdf/2609.28029'],tensor decomposition of transformer key value caches spectral structure and format comparison,MPS 语言模型 / 张量化Transformer / MPO/TT 压缩 / MPS/序列建模,1,,
Tensor Network Generator-Enhanced Optimization for Traveling Salesman Problem,"R Sakai, C Liu",2026.0,0,"We present an application of the tensor network generator-enhanced optimization (TN-GEO) framework to address the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. Our approach employs a tensor network Born machine based on automatically differentiable matrix product states (MPS) as the generative model, using the Born rule to define probability distributions over candidate solutions. Unlike approaches based on binary encoding, which require $N^2$ variables and penalty terms to enforce valid tour constraints, we adopt a permutation-based formulation with integer variables and use autoregressive sampling with masking to guarantee that every generated sample is a valid tour by construction. We also introduce a $k$-site MPS variant that learns distributions over $k$-grams (consecutive city subsequences) using a sliding window approach, enabling parameter-efficient modeling for larger instances. Experimental validation on TSPLIB benchmark instances with up to 52 cities demonstrates that TN-GEO can outperform classical heuristics including swap and 2-opt hill-climbing. The $k$-site variants, which put more focus on local correlations, show better results compared to the full-MPS case.",,"R Sakai, C Liu - arXiv preprint arXiv:2602.20175, 2026 - arxiv.org",[],https://arxiv.org/abs/2602.20175,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2602.20175,['https://arxiv.org/pdf/2602.20175'],tensor network generator enhanced optimization for traveling salesman problem,MPS 生成/Born机 / MPS/序列建模,1,,
Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification,"A Saiapin, K Batselier",2026.0,0,"Developing nonlinear models that are both expressive and computationally efficient remains a challenge in machine learning and nonlinear system identification. Tensor network kernel machines (TNKM) address this challenge by combining nonlinear feature representations with compact low-rank tensor-network parameterizations. However, practical and extensible software frameworks for developing TNKM models remain limited. In this work, we introduce ""tnkm"", an open-source Python library for constructing and training TNKM models using JAX. The library provides a unified interface for combining different feature maps, tensor-network architectures, and optimization strategies, including alternating least squares and gradient-based methods. We demonstrate the capabilities of ""tnkm"" on nonlinear benchmark problems, showing that the implemented models achieve competitive prediction accuracy while retaining compact parameterizations and efficient training. The proposed framework facilitates reproducible development and application of tensor-network-based learning methods.",,"A Saiapin, K Batselier - arXiv preprint arXiv:2608.07043, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.07043,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2608.07043,['https://arxiv.org/pdf/2608.07043'],tensor network kernel machines a jax framework for machine learning and nonlinear system identification,MPO/TT 压缩,2,,
Tensor Network Machine Learning for Wildfire Susceptibility Mapping: from Grokking Dynamics to Quantum Mixedness of Class Representations,"D Pomarico, A Costantino, G R Sanchez, L Bellantuono, D D Alò, M Elia, A Fania, F Giordano, N Kheirkhahan, R Lafortezza, E Pantaleo, S Tangaro, R Bellotti, A Monaco, N Amoroso",2026.0,0,"A quantum-inspired tensor network framework for wildfire susceptibility classification in the Gargano region is introduced, leveraging AlphaEarth embeddings and Matrix Product State models. The approach combines scalable geospatial representations with an interpretable quantum mask, enabling both binary and multiclass classification of wildfire susceptibility. Beyond predictive performance, the study reveals a pronounced grokking transition in the binary case and provides a detailed analysis of inter-class confusion in the multiclass setting. By introducing level-resolved mixedness diagnostics based on reduced density matrices, we show that the MPS classifier naturally encodes a hierarchy of class distinguishability, with non-adjacent categories becoming more separable than neighboring ones. These results demonstrate that tensor network models not only achieve competitive classification accuracy but also offer a physically grounded framework to quantify and interpret class separability in complex environmental datasets.",,"D Pomarico, A Costantino, G R Sanchez, L Bellantuono, D D Alò, M Elia, A Fania, F Giordano, N Kheirkhahan, R Lafortezza, E Pantaleo, S Tangaro, R Bellotti, A Monaco, N Amoroso - arXiv preprint arXiv:2607.19503, 2026 - arxiv.org",[],https://arxiv.org/abs/2607.19503,arxiv-completion,2026-09-26 (citations:OpenAlex),,2607.19503,['https://arxiv.org/pdf/2607.19503'],tensor network machine learning for wildfire susceptibility mapping from grokking dynamics to quantum mixedness of class representations,,1,,
Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension,"M D Horner, C W Duncan, O T Brown, S M d B Kops, M G Meena",2026.0,0,"High performance computers produce extreme-scale data sets that require sampling or compression if they are to be used to their full potential. Existing data compression techniques typically exploit features such as sparsity in the data, homogeneity in the data, or {\it a priori} knowledge of what subsets of data are of most interest. Fluid dynamics data in general do not exhibit these features and so are attractive test beds for generic compression techniques that are objective, robust, and tuneable with respect to information lost due to compression. Presented here is a method based on tensor networks, specifically matrix product states or tensor trains, that meets these requirements. The method is demonstrated for compression in one-dimension and is extensible to higher dimensionality. Lossless compression is demonstrated for random Fourier series for sufficiently high bond dimension of the tensor network, with the memory required to store the tensor network scaling directly proportional to the bond dimension. The lossy compression exhibited at lower bond dimension can be well within the relative error of many fluid simulations. The compression algorithm is tested for the time evolution of Burger's equation with excellent results. We additionally demonstrate the capability to perform computations in the compressed form through a tensor network periodic convolution that can be orders of magnitude faster than using fast Fourier transforms and the convolution theorem. In addition to being an attractive method for working with data sets generated by existing computers, the tensor network methods utilised are directly translatable to the emerging paradigm of quantum computing.",,"M D Horner, C W Duncan, O T Brown, S M d B Kops, M G Meena - arXiv preprint arXiv:2606.17064, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.17064,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2606.17064,['https://arxiv.org/pdf/2606.17064'],tensor network compression using fluid dynamics as a testbed analytical foundations in one dimension,MPO/TT 压缩 / TTN/MERA/PEPS,1,,
Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization,G D Luca,2026.0,0,"Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.",,"G D Luca - arXiv preprint arXiv:2606.10179, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.10179,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 生成/Born机,2606.10179,['https://arxiv.org/pdf/2606.10179'],trainability of iqp quantum circuit born machines under gaussian initialization,MPS 生成/Born机 / 量子/混合LLM,1,,
Transform-Based Multilinear Algebra via Tensor Decomposition,"Y Mei, S Mei, Z He, C Chen",2026.0,0,"Transform-based tensor products, including the T-product and its more general form, namely the higher-order tensor-tensor product, have become fundamental tools for multilinear data analysis in applications such as image processing, signal reconstruction, and robotics. While invertible transforms enable tensor computations to be carried out via matrix operations in the transform domain, the resulting storage and computational costs remain prohibitive for high-dimensional, higher-order tensors. To address this challenge, we integrate low-rank tensor decomposition techniques, specifically tensor train decomposition (TTD) and hierarchical Tucker decomposition (HTD), into transform-based multilinear algebra to improve computational and memory efficiency. In particular, we develop TTD- and HTD-based formulations for the T-product and its associated key algebra, such as block diagonalization and tensor singular value decomposition, by operating directly on the factor matrices or tensors of the decompositions. The framework is further generalized to the higher-order tensor-tensor product and applied to multilinear model order reduction problems. We demonstrate the effectiveness and efficiency of our framework with numerical examples.",,"Y Mei, S Mei, Z He, C Chen - arXiv preprint arXiv:2608.23366, 2026 - arxiv.org",[],https://arxiv.org/abs/2608.23366,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2608.23366,['https://arxiv.org/pdf/2608.23366'],transform based multilinear algebra via tensor decomposition,MPO/TT 压缩,1,,
Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques,"X Waintal, C Huang, C W Groth",2026.0,,"This is a set of lectures on tensor networks with a strong emphasis on the core algorithms involving Matrix Product States (MPS) and Matrix Product Operators (MPO). Compared to other presentations, particular care has been given to disentangle aspects of tensor networks from the quantum many-body problem: MPO/MPS algorithms are presented as a way to deal with linear algebra on extremely (exponentially) large matrices and vectors, regardless of any particular application. The lectures include well-known algorithms to find eigenvectors of MPOs (the celebrated DMRG), solve linear problems, and recent learning algorithms that allow one to map a known function into an MPS (the Tensor Cross Interpolation, or TCI, algorithm). The lectures end with a discussion of how to represent functions and perform calculus with tensor networks using the ""quantics"" representation. They include the detailed analytical construction of important MPOs such as those for differentiation, indefinite integration, convolution, and the quantum Fourier transform. Three concrete applications are discussed in detail: the simulation of a quantum computer (either exactly or with compression), the simulation of a quantum annealer, and techniques to solve partial differential equations (e.g. Poisson, diffusion, or Gross-Pitaevskii) within the ""quantics"" representation. The lectures have been designed to be accessible to a first-year PhD student and include detailed proofs of all statements.",,"X Waintal, C Huang, C W Groth - SciPost Phys. Lect. Notes 133 (2026)",[],https://arxiv.org/abs/2601.03035,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,2601.03035,['https://arxiv.org/pdf/2601.03035'],who can compete with quantum computers lecture notes on quantum inspired tensor networks computational techniques,MPO/TT 压缩 / MPS 生成/Born机 / 量子启发综述,1,SciPost Phys. Lect. Notes 133 (2026),
Tensorizing Engram: Sharing Latents Across N-Gram Embeddings is Beneficial in LLMs,"W Zhou, Y Gu, G Iacovides, Y Qiu, Q Zhao, D Mandic",2026.0,,"Modern language models represent text using discrete token-level embeddings, which forces recurring multi-token patterns to be learned implicitly across Transformer layers. Both Over-tokenized Transformers and Engram attempt to address this limitation by explicitly incorporating multi-token (n-gram) memories. However, they rely on separate hash tables for each n-gram order, which introduces hash collisions and prevents nested n-grams from sharing the underlying latent structures. To address these issues, we propose Tensorized Engram (TN-gram), a compact memory module that represents tensorized n-gram embeddings through shared factors in the Canonical Polyadic (CP) form. TN-gram learns shared token-position factors together with order-absorption vectors to encode the embeddings of different n-gram order. Comprehensive experiments demonstrate that TN-gram matches or even outperforms Engram-style n-gram modules while requiring much fewer parameters.",,"W Zhou, Y Gu, G Iacovides, Y Qiu, Q Zhao, D Mandic - arXiv preprint arXiv:2606.08347, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.08347,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2606.08347,['https://arxiv.org/pdf/2606.08347'],tensorizing engram sharing latents across n gram embeddings is beneficial in llms,MPS 语言模型 / 张量化Transformer,1,,
Tucker Attention: A generalization of approximate attention mechanisms,"T Klein, J Kusch, S Sager, S Schnake, S Schotthöfer",2026.0,,"The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods leverage specialized low-rank factorizations across embedding dimensions or attention heads. From the point of view of classical low-rank approximation, these methods are unconventional and raise questions of which objects they really approximate and how to interpret the low-rank behavior of the resulting representations. To answer these questions, this work proposes a generalized view on the weight objects in the self-attention layer and a factorization strategy, which allows us to construct a parameter efficient scheme, called Tucker Attention. Tucker Attention requires an order of magnitude fewer parameters for comparable validation metrics, compared to GQA and MLA, as evaluated in LLM and ViT test cases. Additionally, Tucker Attention~encompasses GQA, MLA, MHA as special cases and is fully compatible with flash-attention and rotary position embeddings (RoPE). This generalization strategy yields insights of the actual ranks achieved by MHA, GQA, and MLA, and further enables simplifications for MLA.",,"T Klein, J Kusch, S Sager, S Schnake, S Schotthöfer - arXiv preprint arXiv:2603.30033, 2026 - arxiv.org",[],https://arxiv.org/abs/2603.30033,arxiv-completion,2026-09-26 (citations:OpenAlex),张量化Transformer,2603.30033,['https://arxiv.org/pdf/2603.30033'],tucker attention a generalization of approximate attention mechanisms,张量化Transformer / MPO/TT 压缩,1,,
PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decoding,"P Koromilas, A D Demou, J Oldfield, Y Panagakis, M Nicolaou",2026.0,,"Sparse autoencoders (SAEs) interpret neural network representations by decomposing activations into sparse combinations of dictionary atoms. However, SAEs assume features combine additively through linear reconstruction, an assumption that cannot capture compositional structure: linear models cannot distinguish whether ''Starbucks'' arises from the composition of ''star'' and ''coffee'' features or merely their co-occurrence. This forces SAEs to allocate monolithic features for compound concepts rather than decomposing them into interpretable constituents. We introduce PolySAE, which extends the SAE decoder with higher-order terms to model feature interactions while preserving the linear encoder essential for interpretability. Through low-rank tensor factorization on a shared projection subspace, PolySAE captures pairwise and triple feature interactions with small parameter overhead (3% on GPT2). Across four language models and three SAE variants, PolySAE achieves an average improvement of $\sim$8% in probing F1 while maintaining comparable reconstruction error, and produces 2--10$\times$ larger Wasserstein distances between class-conditional feature distributions. Critically, learned interaction weights exhibit negligible correlation with co-occurrence frequency ($r = 0.06$ vs $r = 0.82$ for SAE feature covariance), suggesting that polynomial terms capture compositional structure largely independent of surface statistics. Finally, the learned interaction directions causally steer model outputs toward the corresponding compositional semantics.",,"P Koromilas, A D Demou, J Oldfield, Y Panagakis, M Nicolaou - arXiv preprint arXiv:2602.01322, 2026 - arxiv.org",[],https://arxiv.org/abs/2602.01322,arxiv-completion,2026-09-26 (citations:OpenAlex),MPS 语言模型,2602.01322,['https://arxiv.org/pdf/2602.01322'],polysae modeling feature interactions in sparse autoencoders via polynomial decoding,MPS 语言模型 / MPO/TT 压缩,1,,
Self-Supervised Weight Templates for Scalable Vision Model Initialization,"Y Xie, F Feng, R Shi, J Wang, Y Rui, X Geng",2026.0,,"The increasing scale and complexity of modern model parameters underscore the importance of pre-trained models. However, deployment often demands architectures of varying sizes, exposing limitations of conventional pre-training and fine-tuning. To address this, we propose SWEET, a self-supervised framework that performs constraint-based pre-training to enable scalable initialization in vision tasks. Instead of pre-training a fixed-size model, we learn a shared weight template and size-specific weight scalers under Tucker-based factorization, which promotes modularity and supports flexible adaptation to architectures with varying depths and widths. Target models are subsequently initialized by composing and reweighting the template through lightweight weight scalers, whose parameters can be efficiently learned from minimal training data. To further enhance flexibility in width expansion, we introduce width-wise stochastic scaling, which regularizes the template along width-related dimensions and encourages robust, width-invariant representations for improved cross-width generalization. Extensive experiments on \textsc{classification}, \textsc{detection}, \textsc{segmentation} and \textsc{generation} tasks demonstrate the state-of-the-art performance of SWEET for initializing variable-sized vision models.",,"Y Xie, F Feng, R Shi, J Wang, Y Rui, X Geng - arXiv preprint arXiv:2601.19694, 2026 - arxiv.org",[],https://arxiv.org/abs/2601.19694,arxiv-completion,2026-09-26 (citations:OpenAlex),,2601.19694,['https://arxiv.org/pdf/2601.19694'],self supervised weight templates for scalable vision model initialization,,1,,
TN-SHAP-G: Graph-Structured Tensor Network Surrogates for Shapley Values and Interactions,"F Heidari, G Rabusseau",2026.0,,"Shapley values are a widely used tool for attributing importance and interactions among input variables in black-box models, but their computation involves a function defined over an exponentially large space of subsets. We propose TN-SHAP-G, a framework that exploits structure in graph-structured inputs to compute Shapley values and higher-order interaction indices efficiently. Given a predictor and a fixed masking scheme, TN-SHAP-G learns a compact, graph-aligned multilinear surrogate that approximates the masked-input behavior, represented as a tensor network whose topology mirrors the input graph. Once trained from a small number of oracle queries, the surrogate enables deterministic recovery of first- and higher-order Shapley indices via the multilinear extension, without additional model queries or Monte Carlo variance. Experiments on molecular benchmarks show that the learned factorization closely matches exact Shapley values on small graphs and scales efficiently to larger graphs where sampling-based methods become infeasible.",,"F Heidari, G Rabusseau - arXiv preprint arXiv:2606.01540, 2026 - arxiv.org",[],https://arxiv.org/abs/2606.01540,arxiv-completion,2026-09-26 (citations:OpenAlex),,2606.01540,['https://arxiv.org/pdf/2606.01540'],tn shap g graph structured tensor network surrogates for shapley values and interactions,,1,,
Renormalization Group Guided Tensor Network Structure Search,"M Wang, B Yu, S Zhang, L Mi, W Wang, Y Wang, P Jia, X Wei",2026.0,,"Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS methods face significant limitations in computational tractability, structure adaptivity, and optimization robustness across diverse tensor characteristics. They struggle with three key challenges: single-scale optimization missing multi-scale structures, discrete search spaces hindering smooth structure evolution, and separated structure-parameter optimization causing computational inefficiency. We propose RGTN (Renormalization Group guided Tensor Network search), a physics-inspired framework transforming TN-SS via multi-scale renormalization group flows. Unlike fixed-scale discrete search methods, RGTN uses dynamic scale-transformation for continuous structure evolution across resolutions. Its core innovation includes learnable edge gates for optimization-stage topology modification and intelligent proposals based on physical quantities like node tension measuring local stress, and edge information flow quantifying connectivity importance. Starting from low-complexity coarse scales and refining to finer ones, RGTN finds compact structures while escaping local minima via scale-induced perturbations. Extensive experiments on light field data, high-order synthetic tensors, and video completion tasks show RGTN achieves state-of-the-art compression ratios and runs 4-600 times faster than existing methods, validating the effectiveness of our physics-inspired approach.",,"M Wang, B Yu, S Zhang, L Mi, W Wang, Y Wang, P Jia, X Wei - Proceedings of the AAAI Conference on Artificial Intelligence, 2026",[],https://doi.org/10.1609/aaai.v40i31.39840,arxiv-completion,2026-09-26 (citations:OpenAlex),MPO/TT 压缩,,[],renormalization group guided tensor network structure search,MPO/TT 压缩,1,Proceedings of the AAAI Conference on Artificial Intelligence,
A Born Machine Approach to Controllable Text Generation with Language Models,"S Wang, D Luo",,0,… into a tractable Born-machine surrogate parameterized by a complex-valued Matrix Product State. Born machines are quantum-inspired probabilistic models that assign sequence …,rroOjRq4tNYJ,"S Wang, D Luo - … Probabilistic Inference {\&} Generative Modeling - openreview.net",['https://openreview.net/pdf?id=A6zrZmFpeQ'],https://openreview.net/forum?id=A6zrZmFpeQ,unknown,unknown,MPS 生成/Born机,,['https://openreview.net/pdf?id=A6zrZmFpeQ'],a born machine approach to controllable text generation with language models,MPS 生成/Born机,1,,
A Renormalization Framework for the Qualitative Theory of Entangled Systems,S Gluzman,,0,"… entangled operator is the renormalized form of the factorizable operator, and the coupling index α is the physical structural remnant of this renormalization … the geometric language of our …",kJr5-8MupP4J,S Gluzman - researchgate.net,['https://www.researchgate.net/profile/Simon-Gluzman/publication/399996445_A_Renormalization_Framework_for_the_QualitativeTheory_of_Entangled_Systems/links/6a427f172267bf198a6a190e/A-Renormalization-Framework-for-the-QualitativeTheory-of-Entangled-Systems.pdf'],https://www.researchgate.net/profile/Simon-Gluzman/publication/399996445_A_Renormalization_Framework_for_the_QualitativeTheory_of_Entangled_Systems/links/6a427f172267bf198a6a190e/A-Renormalization-Framework-for-the-QualitativeTheory-of-Entangled-Systems.pdf,unknown,unknown,互信息/标度,,['https://www.researchgate.net/profile/Simon-Gluzman/publication/399996445_A_Renormalization_Framework_for_the_QualitativeTheory_of_Entangled_Systems/links/6a427f172267bf198a6a190e/A-Renormalization-Framework-for-the-QualitativeTheory-of-Entangled-Systems.pdf'],a renormalization framework for the qualitative theory of entangled systems,互信息/标度,1,,
Supplemental Material to Tensor Networks for Probabilistic Sequence Modeling,"J Miller, G Rabusseau, J Terilla",,0,"In this section, we give definitions and known results concerning completely positive (CP) maps and regular expressions (regex), as well as further details regarding the assignment of …",pIiMCAF8SxIJ,"J Miller, G Rabusseau, J Terilla - proceedings.mlr.press",['http://proceedings.mlr.press/v130/miller21a/miller21a-supp.pdf'],http://proceedings.mlr.press/v130/miller21a/miller21a-supp.pdf,unknown,unknown,MPS/序列建模,,['http://proceedings.mlr.press/v130/miller21a/miller21a-supp.pdf'],supplemental material to tensor networks for probabilistic sequence modeling,MPS/序列建模,1,,
TensorSpike: Tractable Probabilistic Modeling for Neural Spike Trains with Tensor Networks,"Y Huang, F Wu, D Chen, X Gu, S Zhe, C Li",,0,… 2022) is a Transformer-based neural sequence model that uses attention to capture … represents a joint distribution over binary spike trains through tensor network contractions. …,XR3JY3vo2rwJ,"Y Huang, F Wu, D Chen, X Gu, S Zhe, C Li - ICML'26 workshop on … - openreview.net",['https://openreview.net/pdf?id=i37ukD43nT'],https://openreview.net/forum?id=i37ukD43nT,unknown,unknown,MPS/序列建模,,['https://openreview.net/pdf?id=i37ukD43nT'],tensorspike tractable probabilistic modeling for neural spike trains with tensor networks,MPS/序列建模,1,,
Variational Algorithms in Quantum Artificial Intelligence,A Circuit,,0,"… modeling, we explore the design of parameter-efficient quantum circuits for diffusion models, … For discriminative tasks, we examine the computational scaling of quantum kernel methods …",UHXkaNpHcfYJ,A Circuit - inspirehep.net,['https://inspirehep.net/files/9f18be0dd7295a8b9c34debc9474edbf'],https://inspirehep.net/files/9f18be0dd7295a8b9c34debc9474edbf,unknown,unknown,量子/混合LLM,,['https://inspirehep.net/files/9f18be0dd7295a8b9c34debc9474edbf'],variational algorithms in quantum artificial intelligence,量子/混合LLM,1,,
Variational Quantum Circuits for Efficient Transformer Attention,P Yadla,,0,"… [1], the transformer has become the backbone of state-of-the-art language models, demonstrating remarkable capabilities across diverse linguistic tasks. However, as these models …",YlRO1FvXwJwJ,P Yadla - openreview.net,['https://openreview.net/pdf?id=tdc6RrmUzh'],https://openreview.net/forum?id=tdc6RrmUzh,unknown,unknown,量子/混合LLM,,['https://openreview.net/pdf?id=tdc6RrmUzh'],variational quantum circuits for efficient transformer attention,量子/混合LLM,1,,
Language Modeling Using Tensor Trains,"Z Su, Y Zhou, F Mo, JG Simonsen",2024.0,0,"We propose a novel tensor network language model based on the simplest tensor network (i.e., tensor trains), called `Tensor Train Language Model' (TTLM). TTLM represents sentences in an exponential space constructed by the tensor product of words, but computing the probabilities of sentences in a low-dimensional fashion. We demonstrate that the architectures of Second-order RNNs, Recurrent Arithmetic Circuits (RACs), and Multiplicative Integration RNNs are, essentially, special cases of TTLM. Experimental evaluations on real language modeling tasks show that the proposed variants of TTLM (i.e., TTLM-Large and TTLM-Tiny) outperform the vanilla Recurrent Neural Networks (RNNs) with low-scale of hidden units. (The code is available at https://github.com/shuishen112/tensortrainlm.)",,"Z Su, Y Zhou, F Mo, JG Simonsen - arXiv preprint arXiv:2405.04590, 2024 - arxiv.org",['https://arxiv.org/pdf/2405.04590'],https://arxiv.org/abs/2405.04590,arxiv-completion,2026-10-03 (citations:OpenAlex),MPS 语言模型,2405.04590,['https://arxiv.org/pdf/2405.04590'],language modeling using tensor trains,MPS 语言模型,1,,
DisCoCLIP: A Distributional Compositional Tensor Network Encoder for Vision-Language Understanding,"KI Lo, H Hawashin, M Abbaszadeh, T Limback-Stokin, H Wazni, M Sadrzadeh",2025.0,3,"Recent vision-language models excel at large-scale image-text alignment but often neglect the compositional structure of language, leading to failures on tasks that hinge on word order and predicate-argument structure. We introduce DisCoCLIP, a multimodal encoder that combines a frozen CLIP vision transformer with a novel tensor network text encoder that explicitly encodes syntactic structure. Sentences are parsed with a Combinatory Categorial Grammar parser to yield distributional word tensors whose contractions mirror the sentence's grammatical derivation. To keep the model efficient, high-order tensors are factorized with tensor decompositions, reducing parameter count from tens of millions to under one million. Trained end-to-end with a self-supervised contrastive loss, DisCoCLIP markedly improves sensitivity to verb semantics and word order: it raises CLIP's SVO-Probes verb accuracy from 77.6% to 82.4%, boosts ARO attribution and relation scores by over 9% and 4%, and achieves 93.7% on a newly introduced SVO-Swap benchmark. These results demonstrate that embedding explicit linguistic structure via tensor networks yields interpretable, parameter-efficient representations that substantially improve compositional reasoning in vision-language tasks.",,"KI Lo, H Hawashin, M Abbaszadeh, T Limback-Stokin, H Wazni, M Sadrzadeh - arXiv preprint arXiv:2509.21287, 2025 - arxiv.org",['https://arxiv.org/pdf/2509.21287'],https://arxiv.org/abs/2509.21287,arxiv-completion,2026-10-03 (citations:SemanticScholar),MPO/TT 压缩,2509.21287,['https://arxiv.org/pdf/2509.21287'],discoclip a distributional compositional tensor network encoder for vision-language understanding,MPO/TT 压缩,1,,