[
 {
  "key": "ext-exm",
  "t": "Exponential Machines",
  "a": "Alexander Novikov, Mikhail Trofimov, Ivan Oseledets",
  "y": 2016,
  "c": null,
  "v": "arXiv 预印本（2016）；ICLR 2017 workshop",
  "u": "https://arxiv.org/abs/1605.03795",
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/1605.03795"
   ]
  ],
  "abs": "以 Tensor Train 参数化各阶特征交互的预测器。",
  "absn": "题录及方法摘要据作者 arXiv／期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "key": "ext-vtnn",
  "t": "Variational tensor neural networks for deep learning",
  "a": "Saeed S. Jahromi, Román Orús",
  "y": 2024,
  "c": null,
  "v": "Scientific Reports 14（2024）；预印本 2022",
  "u": "https://www.nature.com/articles/s41598-024-69366-8",
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/2211.14657"
   ],
   [
    "Nature",
    "https://doi.org/10.1038/s41598-024-69366-8"
   ]
  ],
  "abs": "将张量层与稠密层结合，采用 DMRG 启发的局部训练并在回归、分类和 MNIST 上验证。",
  "absn": "题录及方法摘要据作者 arXiv／期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "MPO/TT 压缩",
  "pdf": null
 },
 {
  "key": "ext-patch",
  "t": "Patch-based Medical Image Segmentation using Matrix Product State Tensor Networks",
  "a": "Raghavendra Selvan, Erik B. Dam, Søren Alexander Flensborg, Jens Petersen",
  "y": 2022,
  "c": null,
  "v": "Machine Learning for Biomedical Imaging 1（2022）；预印本 2021",
  "u": "https://arxiv.org/abs/2109.07138",
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/2109.07138"
   ],
   [
    "MELBA",
    "https://doi.org/10.59275/j.melba.2022-d1f5"
   ]
  ],
  "abs": "用局部图像块上的 MPS 张量网络学习医疗图像分割映射。",
  "absn": "题录及方法摘要据作者 arXiv／期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "key": "ext-peps",
  "t": "Multi-Layered Projected Entangled Pair States for Image Classification",
  "a": "L. Li, H. Lai",
  "y": 2023,
  "c": null,
  "v": "Sustainability 15(6), 5120（2023）",
  "u": "https://www.mdpi.com/2071-1050/15/6/5120",
  "lk": [
   [
    "MDPI",
    "https://doi.org/10.3390/su15065120"
   ]
  ],
  "abs": "以多层 PEPS 做 Fashion-MNIST 与 COVID-19 胸部 X 光图像分类。",
  "absn": "题录及方法摘要据作者 arXiv／期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "TTN/MERA/PEPS",
  "pdf": null
 },
 {
  "key": "ext-tt",
  "t": "Tensor-Train Decomposition",
  "a": "I. V. Oseledets",
  "y": 2011,
  "c": null,
  "v": "SIAM Journal on Scientific Computing 33(5), 2295–2317",
  "u": "https://epubs.siam.org/doi/10.1137/090752286",
  "lk": [
   [
    "SIAM",
    "https://doi.org/10.1137/090752286"
   ]
  ],
  "abs": "提出 Tensor Train 分解、构造与截断算法，是 TT/MPS 数值方法的基础文献。",
  "absn": "题录及方法摘要据作者 arXiv／期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "MPO/TT 压缩",
  "pdf": null
 },
 {
  "key": "ext-cft",
  "t": "Entanglement entropy and conformal field theory",
  "a": "Pasquale Calabrese, John Cardy",
  "y": 2009,
  "c": null,
  "v": "Journal of Physics A 42, 504005",
  "u": "https://arxiv.org/abs/0905.4013",
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/0905.4013"
   ],
   [
    "IOP",
    "https://doi.org/10.1088/1751-8113/42/50/504005"
   ]
  ],
  "abs": "综述共形场论方法描述临界系统的纠缠熵及有限尺寸、边界等情形。",
  "absn": "题录及方法摘要据作者 arXiv／期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "互信息/标度",
  "pdf": null
 },
 {
  "key": "ext-orus",
  "t": "Tensor networks for complex quantum systems",
  "a": "Román Orús",
  "y": 2019,
  "c": null,
  "v": "Nature Reviews Physics 1, 538–550（2019）",
  "u": "https://arxiv.org/abs/1812.04011",
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/1812.04011"
   ],
   [
    "Nature",
    "https://doi.org/10.1038/s42254-019-0086-7"
   ]
  ],
  "abs": "综述张量网络的基本概念、主要结构和算法及其在复杂量子系统等方向的应用。",
  "absn": "题录与方法摘要据作者预印本及期刊页面核对；被引数未查询",
  "vk": 1,
  "cl": "量子启发综述",
  "pdf": null
 },
 {
  "key": "ext-ttlm",
  "t": "Language Modeling Using Tensor Trains",
  "a": "Zhan Su, Yuqin Zhou, Fengran Mo, Jakob Grue Simonsen",
  "y": 2024,
  "c": null,
  "v": "arXiv 预印本",
  "u": "https://arxiv.org/abs/2405.04590",
  "lk": [
   [
    "论文",
    "https://arxiv.org/abs/2405.04590"
   ],
   [
    "GitHub",
    "https://github.com/shuishen112/tensortrainlm"
   ],
   [
    "作者主页",
    "https://shuishen112.github.io/zhansu/"
   ]
  ],
  "abs": "TTLM-Large 在 PTB／WikiText-2 上 PPL 99.3／82.3；比较小 RNN，Transformer 基线较弱。",
  "absn": "题录与分数按原论文核对，2026-10-01；被引 0（OpenAlex，2026-10-03；论文为 2024 年 arXiv 预印本）；代码核查（2026-10-01）：作者仓库可访问，含数据、模型和训练入口；未运行复现。",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "key": "ext-m2rnn",
  "t": "M²RNN: Non-Linear RNNs with Matrix-Valued States for Scalable Language Modeling",
  "a": "Mayank Mishra, Shawn Tan, Ion Stoica, Joseph E. Gonzalez, Tri Dao",
  "y": 2026,
  "c": null,
  "v": "arXiv 预印本（v2）",
  "u": "https://arxiv.org/abs/2603.14360",
  "lk": [
   [
    "论文",
    "https://arxiv.org/abs/2603.14360"
   ],
   [
    "训练代码",
    "https://github.com/open-lm-engine/lm-engine"
   ],
   [
    "内核",
    "https://github.com/open-lm-engine/accelerated-model-architectures"
   ],
   [
    "模型权重",
    "https://huggingface.co/collections/open-lm-engine/m2rnn"
   ]
  ],
  "abs": "矩阵状态非线性 RNN，410M／7B MoE 使用 100B 词元；直接对标 Mamba-2。",
  "absn": "题录与分数按原论文核对，2026-10-01；被引数未查询；代码核查（2026-10-01）：作者训练框架、内核仓库与模型权重集合均可访问。",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "key": "ext-saten",
  "t": "Saten: Sparse Augmented Tensor Networks for Post-Training Compression of Large Language Models",
  "a": "Ryan Solgi, Kai Zhen, Rupak Vignesh Swaminathan, Nathan Susanj, Athanasios Mouchtaris, Siegfried Kunzmann, Zheng Zhang",
  "y": 2025,
  "c": null,
  "v": "Findings of EMNLP 2025",
  "u": "https://arxiv.org/abs/2505.14871",
  "lk": [
   [
    "论文",
    "https://arxiv.org/abs/2505.14871"
   ],
   [
    "发表版",
    "https://aclanthology.org/2025.findings-emnlp.1287/"
   ],
   [
    "GitHub",
    "https://github.com/rmsolgi/saten"
   ]
  ],
  "abs": "TT 加稀疏误差项；在 BERT GLUE、Llama-3.2-1B 下游任务报告压缩质量权衡。",
  "absn": "题录与分数按原论文核对，2026-10-01；被引数未查询；代码核查（2026-10-01）：论文所列仓库可访问，README 给出 Llama-3.2-3B 实验入口；不代表每项论文实验均已复现。",
  "vk": 1,
  "cl": "MPO/TT 压缩",
  "pdf": null
 },
 {
  "key": "ext-enhanced-ttlm",
  "t": "Language Modeling Using Entanglement Enhanced Tensor Trains",
  "a": "Ellis Reyes, Yi-Shin Chen",
  "y": 2025,
  "c": null,
  "v": "ROCLING 2025, pp. 258–265",
  "u": "https://aclanthology.org/2025.rocling-main.27/",
  "lk": [
   [
    "论文",
    "https://aclanthology.org/2025.rocling-main.27/"
   ],
   [
    "论文 PDF",
    "https://aclanthology.org/2025.rocling-main.27.pdf"
   ]
  ],
  "abs": "模块化 TTLM 加残差、权重共享与分块低秩注意力／Hadamard 池化。rank 60 时 PTB PPL 83.7、WT2 PPL 73.5；WT2 上下文 256、约 117M 参数的注意力变体 PPL 65.38。",
  "absn": "题录与分数按原论文核对，2026-10-01；被引数未查询；代码核查（2026-10-01）：检查原文、ACL 页面并定向检索，尚未定位作者代码链接；不等于确认未开源。",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "key": "ext-tslm",
  "t": "A Generalized Language Model in Tensor Space",
  "a": "Lipeng Zhang, Peng Zhang, Xindian Ma, Shuqin Gu, Zhan Su, Dawei Song",
  "y": 2019,
  "c": null,
  "v": "AAAI 33(01), 7450–7458（2019）",
  "u": "https://arxiv.org/abs/1901.11167",
  "lk": [
   [
    "论文",
    "https://arxiv.org/abs/1901.11167"
   ],
   [
    "发表版",
    "https://ojs.aaai.org/index.php/AAAI/article/view/4735"
   ],
   [
    "GitHub（作者主页所列）",
    "https://github.com/shuishen112/AAAI19-TSLM"
   ],
   [
    "作者主页",
    "https://shuishen112.github.io/zhansu/"
   ]
  ],
  "abs": "张量空间语言模型以递归张量分解计算 next-token 条件概率。PTB／WT2 的 TSLM PPL 为 108.1／100.4，自实现 LSTM 为 110.3／101.4；MoS 变体为 83.6／81.0，对照 RNN+MoS 为 84.3／81.8。",
  "absn": "题录与分数按原论文核对，2026-10-01；被引数未查询；代码核查（2026-10-01）：作者主页列有代码链接；本轮无法读取 GitHub/API/README，当前可访问性与许可证未确认。",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "key": "ext-qttn",
  "t": "Sequence processing with quantum-inspired tensor networks",
  "a": "Carys Harvey, Richie Yeung, Konstantinos Meichanetzidis",
  "y": 2025,
  "c": null,
  "v": "Scientific Reports 15, 7155（2025）",
  "u": "https://www.nature.com/articles/s41598-024-84295-2",
  "lk": [
   [
    "论文",
    "https://www.nature.com/articles/s41598-024-84295-2"
   ],
   [
    "arXiv",
    "https://arxiv.org/abs/2308.07865"
   ],
   [
    "GitHub",
    "https://github.com/Quantinuum/classification-with-qttn"
   ]
  ],
  "abs": "比较量子启发链、树、语法和卷积网络做真实序列分类；50,000 条 IMDb 评论上卷积模型准确率 88%。",
  "absn": "题录与分数按原论文核对，2026-10-01；被引数未查询；代码核查（2026-10-01）：作者仓库可访问；CQCL 旧地址现重定向至 Quantinuum。",
  "vk": 1,
  "cl": "MPS/序列建模",
  "pdf": null
 },
 {
  "t": "Tensor networks for probabilistic sequence modeling",
  "a": "J Miller, G Rabusseau, J Terilla",
  "y": 2021,
  "c": 59,
  "v": "arXiv (Cornell University)",
  "abs": "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.",
  "absn": "与 arXiv 摘要逐字一致；代码核查（2026-10-01）：作者 MIT 代码可访问；README 明确未包含完整 regex sampler。",
  "vk": 1,
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/2003.01039"
   ],
   [
    "开放获取 PDF",
    "https://arxiv.org/pdf/2003.01039"
   ],
   [
    "GitHub",
    "https://github.com/jemisjoky/umps_code"
   ]
  ],
  "u": "https://proceedings.mlr.press/v130/miller21a.html",
  "cl": "MPS/序列建模",
  "pdf": "../lit/papers/2021_Tensor_networks_for_probabilistic_sequence_modelin.pdf",
  "key": "ext-code-0"
 },
 {
  "t": "Tensorized Embedding Layers for Efficient Model Compression",
  "a": "O Hrinchuk, V Khrulkov, L Mirvakhabova, E Orlova, I Oseledets",
  "y": 2019,
  "c": 50,
  "v": "arXiv preprint arXiv:1901.10787, 2019",
  "abs": "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.",
  "absn": "与 arXiv 摘要逐字一致；代码核查（2026-10-01）：原文所列 TT-embedding 实验仓库可访问；另有作者 TT-PyTorch 实现。",
  "vk": 1,
  "lk": [
   [
    "arXiv 预印本",
    "https://arxiv.org/abs/1901.10787"
   ],
   [
    "开放获取 PDF",
    "https://arxiv.org/pdf/1901.10787"
   ],
   [
    "GitHub",
    "https://github.com/tt-embedding/tt-embeddings"
   ],
   [
    "作者 TT-PyTorch",
    "https://github.com/KhrulkovV/tt-pytorch"
   ],
   [
    "发表版",
    "https://aclanthology.org/2020.findings-emnlp.436/"
   ]
  ],
  "u": "https://arxiv.org/abs/1901.10787",
  "cl": "MPS 语言模型 / 张量化Transformer / MPO/TT 压缩",
  "pdf": "../lit/papers/2019_Tensorized_Embedding_Layers_for_Efficient_Model_Co.pdf",
  "key": "ext-code-1"
 }
]