--- title: "Graph Neural Networks" aliases: ["GNN", "Graph networks"] tags: - deep-learning - graph - neural-networks --- # Graph Neural Networks ## Foundations - **The Graph Neural Network Model** - Learns node states from graph structure and attributes through recurrent updates; the original formulation uses a contraction condition to obtain a unique fixed point. [Scarselli et al. 2009]( "The Graph Neural Network Model; IEEE TNN"). - **Message Passing Neural Networks** - Separates local message computation and node updates from a graph-level readout. Unifies several molecular prediction architectures within one framework. [Gilmer et al. 2017]( "Neural Message Passing for Quantum Chemistry; ICML"). - **Graph networks** - Unifies computations on nodes, edges, and global graph attributes through shared update functions and permutation-invariant aggregation; connects graph structure to relational inductive biases. [Battaglia et al. 2018]( "Relational inductive biases, deep learning, and graph networks; arXiv"). ## Random-walk embedding baselines - **DeepWalk** - Treats short random walks as sequences and learns node vectors from their local contexts. Provides a graph-structure embedding baseline without a learned neighborhood feature aggregator. [Perozzi et al. 2014]( "DeepWalk: Online Learning of Social Representations; KDD"). - **node2vec** - Learns node vectors from biased random walks, with parameters controlling which neighborhoods are explored. Changes the context distribution used to train embeddings. [Grover and Leskovec 2016]( "node2vec: Scalable Feature Learning for Networks; KDD"). ## Neighborhood aggregation - **Spectral networks** - Extends convolution to graphs through filters in the graph Laplacian's eigenbasis; also studies locally connected architectures based on hierarchical clustering. [Bruna et al. 2013]( "Spectral Networks and Locally Connected Networks on Graphs; arXiv"). - **ChebNet** - Uses Chebyshev polynomials of the graph Laplacian to construct localized spectral filters, avoiding explicit eigendecomposition during filtering. [Defferrard et al. 2016]( "Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering; NeurIPS"). - **GCN** - Alternates learned feature transformations with degree-normalized neighborhood aggregation, including self-loops. Its semi-supervised setup uses graph structure and features beyond the labeled nodes. [Kipf and Welling 2017]( "Semi-Supervised Classification with Graph Convolutional Networks; ICLR"). - **GraphSAGE** - Samples neighborhoods and learns feature-aggregation functions that can embed unseen nodes or graphs sharing the input feature schema, instead of storing a separate learned vector for each node. [Hamilton et al. 2017]( "Inductive Representation Learning on Large Graphs; NeurIPS"). - **GAT** - Learns attention weights over graph neighborhoods to combine node features; multi-head attention provides several learned aggregations. The original attention is restricted to graph neighbors. [Veličković et al. 2018]( "Graph Attention Networks; ICLR"). - **GATv2** - Reorders attention operations so neighbor rankings can depend on the query node, addressing the original GAT's static attention ranking. [Brody et al. 2022]( "How Attentive are Graph Attention Networks?; ICLR"). - **Principal Neighbourhood Aggregation** - Combines multiple neighborhood statistics with degree-dependent scaling. Addresses information lost when a single aggregator summarizes continuous node features. [Corso et al. 2020]( "Principal Neighbourhood Aggregation for Graph Nets; NeurIPS"). ## Diffusion and propagation - **PPNP / APPNP** - Separates neural prediction from personalized PageRank propagation. APPNP approximates propagation iteratively, extending information flow without stacking more learned feature transformations. [Gasteiger et al. 2019]( "Predict then Propagate: Graph Neural Networks meet Personalized PageRank; ICLR"). - **Graph Diffusion Convolution** - Constructs a new graph by sparsifying generalized diffusion, including personalized PageRank or heat kernels. Subsequent message passing uses these diffusion-derived connections. [Gasteiger et al. 2019]( "Diffusion Improves Graph Learning; NeurIPS"). ## Expressivity and higher-order structure - **GIN and the 1-WL limit** - With enough layers and injective aggregation, updates and readout, can match 1-WL. The sum construction assumes countable features and bounded multisets; training need not find these functions, and 1-WL is not a complete isomorphism test. [Xu et al. 2019]( "How Powerful are Graph Neural Networks?; ICLR"). - **Higher-order GNNs** - Relates GNNs to Weisfeiler-Leman refinement and extends aggregation to sets of nodes. Higher-order representations distinguish structures that ordinary node-level message passing can miss. [Morris et al. 2019]( "Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks; AAAI"). - **Provably Powerful Graph Networks** - Uses matrix-valued representations, multilayer perceptrons, and matrix multiplication to exceed standard message-passing expressivity under the paper's graph-isomorphism analysis. [Maron et al. 2019]( "Provably Powerful Graph Networks; NeurIPS"). - **Equivariant Subgraph Aggregation Networks** - Represents a graph as a set of selected subgraphs and aggregates them equivariantly. Subgraph selection affects expressivity; sampling reduces the added computation. [Bevilacqua et al. 2022]( "Equivariant Subgraph Aggregation Networks; ICLR"). - **Graph Substructure Networks** - Augments message passing with structural features from subgraph-isomorphism counts. Expressivity depends on the chosen substructures; computing those counts adds preprocessing work. [Bouritsas et al. 2023]( "Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting; TPAMI"). ## Depth and normalization - **Different limits** - 1-WL concerns structural discrimination; oversquashing concerns information transport; oversmoothing concerns representation collapse. Stronger aggregation, rewiring and normalization address different limits. [Xu et al. 2019]( "How Powerful are Graph Neural Networks?; ICLR"), [Alon and Yahav 2021]( "On the Bottleneck of Graph Neural Networks and its Practical Implications; ICLR"), [Li et al. 2018]( "Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning; AAAI"). - **Oversmoothing** - Interprets GCN propagation as Laplacian smoothing; repeated smoothing can make node representations difficult to distinguish. Describes a depth-related failure mechanism, not a universal limit on GNN depth. [Li et al. 2018]( "Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning; AAAI"). - **Jumping Knowledge Networks** - Combines representations from different layer depths for each node, allowing the effective neighborhood range to vary instead of using only the final layer. [Xu et al. 2018]( "Representation Learning on Graphs with Jumping Knowledge Networks; ICML"). - **GCNII** - Adds initial residual connections and identity mappings to graph convolution, retaining input information through deep propagation. Studies these mechanisms as remedies for degradation with depth. [Chen et al. 2020]( "Simple and Deep Graph Convolutional Networks; ICML"). - **DropEdge** - Randomly removes graph edges at each training epoch to regularize graph convolution and alter propagation. Restores the input graph for evaluation; analyzes conditions that slow oversmoothing. [Rong et al. 2020]( "DropEdge: Towards Deep Graph Convolutional Networks on Node Classification; ICLR"). - **PairNorm** - Centers and rescales node features to keep their total pairwise squared distance fixed across layers. Counters representation collapse without preserving every individual pairwise distance. [Zhao and Akoglu 2020]( "PairNorm: Tackling Oversmoothing in GNNs; ICLR"). - **Oversquashing** - Studies bottlenecks when messages from expanding neighborhoods are compressed into fixed-size node vectors, hindering long-range signals even when a model can fit local dependencies. [Alon and Yahav 2021]( "On the Bottleneck of Graph Neural Networks and its Practical Implications; ICLR"). - **GraphNorm** - Normalizes features within each graph, with a learnable shift that controls how much mean information is removed. Addresses information loss from ordinary instance normalization on regular graphs. [Cai et al. 2021]( "GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training; ICML"). ## Learning and rewiring graph structure - **Learning Discrete Structures** - Jointly learns GCN parameters and a probability distribution over edges through bilevel optimization. Applies when the supplied graph is missing, incomplete, or corrupted. [Franceschi et al. 2019]( "Learning Discrete Structures for Graph Neural Networks; ICML"). - **Curvature and oversquashing** - Relates graph bottlenecks to message attenuation through an edge-curvature analysis. Proposes curvature-based rewiring to improve information flow across those bottlenecks. [Topping et al. 2022]( "Understanding over-squashing and bottlenecks on graphs via curvature; ICLR"). - **FoSR** - Selects added edges using a first-order approximation to spectral-gap improvement. Treats original and added edges as distinct relations so the model can retain information about the input graph. [Karhadkar et al. 2023]( "FoSR: First-order spectral rewiring for addressing oversquashing in GNNs; ICLR"). ## Global attention - **Graphormer** - Adds degree-based centrality, shortest-path distances, and path-edge encodings to Transformer attention, allowing graph-wide interactions to depend on graph structure. [Ying et al. 2021]( "Do Transformers Really Perform Bad for Graph Representation?; NeurIPS"). - **GraphGPS** - Combines positional or structural encodings, local message passing, and global attention. Scaling depends on the chosen attention mechanism; ordinary dense attention remains quadratic in node count. [Rampášek et al. 2022]( "Recipe for a General, Powerful, Scalable Graph Transformer; NeurIPS"). - **TokenGT** - Treats nodes and edges as tokens, augmenting them with orthonormal node identifiers and trainable type identifiers before a standard Transformer. Encodes graph connectivity through token representations. [Kim et al. 2022]( "Pure Transformers are Powerful Graph Learners; NeurIPS"). - **SignNet / BasisNet** - Encode spectral eigenvectors while respecting sign flips or basis changes within repeated-eigenvalue eigenspaces. Separate graph structure from arbitrary spectral coordinates. [Lim et al. 2023]( "Sign and Basis Invariant Networks for Spectral Graph Representation Learning; ICLR"). - **Exphormer** - Uses sparse attention with expander edges and virtual global nodes. Adds routes for graph-wide communication without requiring all-pairs attention. [Shirzad et al. 2023]( "Exphormer: Sparse Transformers for Graphs; ICML"). - **PRiSM** - Jointly canonicalizes spectral signs and node order. For every fixed k, its k-WL counterexamples are simple-spectrum multigraphs. Canonicalization is discontinuous; repeated-eigenvalue handling is heuristic. [Hordan et al. 2026]( "Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them; NeurIPS"). ## Graph pooling - **DiffPool** - Learns soft assignments of nodes to clusters, producing coarsened graphs for subsequent layers. Adds hierarchical representations for graph-level prediction. [Ying et al. 2018]( "Hierarchical Graph Representation Learning with Differentiable Pooling; NeurIPS"). - **Graph U-Nets** - Pools by selecting nodes using learned projection scores; unpooling restores their positions. Builds an encoder-decoder architecture for node- and graph-level prediction. [Gao and Ji 2019]( "Graph U-Nets; ICML"). - **MinCutPool** - Learns soft cluster assignments using a continuous relaxation of normalized min-cut. Produces differentiable graph pooling without recomputing a spectral decomposition for each graph. [Bianchi et al. 2020]( "Spectral Clustering with Graph Neural Networks for Graph Pooling; ICML"). ## Scaling to large graphs - **FastGCN** - Interprets graph convolution as an integral transform and uses Monte Carlo importance sampling to approximate it. Enables minibatch training without expanding every receptive field in full. [Chen et al. 2018]( "FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling; ICLR"). - **SGC** - Removes intermediate nonlinearities and collapses weight matrices, yielding fixed graph propagation followed by a linear classifier. A baseline for testing whether learned nonlinear propagation is needed. [Wu et al. 2019]( "Simplifying Graph Convolutional Networks; ICML"). - **Cluster-GCN** - Partitions the graph and trains on subgraphs formed from clusters, restricting neighborhood computation within each minibatch to reduce memory and repeated neighbor expansion. [Chiang et al. 2019]( "Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks; KDD"). - **LADIES** - Conditions layer-wise importance sampling on nodes sampled in the next layer. Restricts candidates to their neighbors to preserve connections between sampled layers. [Zou et al. 2019]( "Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks; NeurIPS"). - **GraphSAINT** - Samples subgraphs and reweights aggregation and loss by sampling probabilities. Its unbiasedness analysis treats layers independently; it does not establish unbiased gradients through the nonlinear stack. [Zeng et al. 2020]( "GraphSAINT: Graph Sampling Based Inductive Learning Method; ICLR"). - **SIGN** - Precomputes features using several graph filters and trains a feedforward model on them. Moves graph propagation out of the training loop, trading preprocessing and feature storage for simpler minibatches. [Frasca et al. 2020]( "SIGN: Scalable Inception Graph Neural Networks; arXiv"). ## Learning under heterophily - **MixHop** - Mixes feature representations from neighborhoods at different distances, enabling operators such as differences between neighborhood scales. Studies how useful mixing patterns vary across graphs. [Abu-El-Haija et al. 2019]( "MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing; ICML"). - **H2GCN** - Separates self and neighbor embeddings, includes higher-order neighborhoods, and combines intermediate representations to handle graphs whose adjacent nodes may have different labels or features. [Zhu et al. 2020]( "Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs; NeurIPS"). - **GPR-GNN** - Learns weights over propagation depths in generalized PageRank, adapting the graph filter to label and feature patterns. Evaluates both homophilous and heterophilous settings. [Chien et al. 2021]( "Adaptive Universal Generalized PageRank Graph Neural Network; ICLR"). - **FAGCN** - Uses self-gating to combine low- and high-frequency graph signals. Retains differences between neighboring nodes that low-pass smoothing can suppress. [Bo et al. 2021]( "Beyond Low-frequency Information in Graph Convolutional Networks; AAAI"). - **LINKX** - Embeds adjacency information and node features with separate networks before combining them with an MLP; a graph-learning baseline for weak homophily without repeated neighborhood propagation. [Lim et al. 2021]( "Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods; NeurIPS"). - **Reassessing heterophily benchmarks** - Finds duplicate-node leakage in Squirrel and Chameleon; introduces alternative benchmarks where standard GNNs are competitive. Low label homophily alone does not establish a need for a specialized model. [Platonov et al. 2023]( "A critical look at the evaluation of GNNs under heterophily: Are we really making progress?; ICLR"). ## Link prediction and recommendation [Evaluation](#benchmarks-and-evaluation): HeaRT compares endpoint-specific candidates. - **Variational Graph Auto-Encoders** - Uses a GCN encoder, Gaussian latent node variables, and an inner-product decoder to reconstruct adjacency. An unsupervised baseline for link prediction. [Kipf and Welling 2016]( "Variational Graph Auto-Encoders; NeurIPS BDL Workshop"). - **SEAL** - Predicts links from local enclosing subgraphs with labels marking nodes' positions relative to the candidate pair. Removes the target edge from positive training subgraphs to avoid exposing the answer. [Zhang and Chen 2018]( "Link Prediction Based on Graph Neural Networks; NeurIPS"). - **LightGCN** - Learns user and item embeddings through linear propagation on the interaction graph and combines layers. Removes feature transformations and nonlinearities from graph convolution for collaborative filtering. [He et al. 2020]( "LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation; arXiv"). - **Neural Bellman-Ford Networks** - Learns node-pair representations through generalized Bellman-Ford updates with neural initialization, message, and aggregation operators. Uses path information for link prediction. [Zhu et al. 2021]( "Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction; NeurIPS"). ## Directed graph structure - **MagNet** - Uses a complex Hermitian magnetic Laplacian: magnitudes encode undirected structure and phases encode edge direction. Supports spectral learning on directed graphs; symmetrizing adjacency would discard information that this construction retains. [Zhang et al. 2021]( "MagNet: A Neural Network for Directed Graphs; NeurIPS"). ## Typed graphs - **R-GCN** - Uses relation-specific transformations for multi-relational graphs, with parameter sharing to control model size. Applies the encoder to entity classification and link prediction. [Schlichtkrull et al. 2018]( "Modeling Relational Data with Graph Convolutional Networks; ESWC"). - **Heterogeneous Graph Attention Network** - Learns attention over neighbors connected by typed relation paths, then over path types. Separates node-level aggregation from weighting different semantic relationships. [Wang et al. 2019]( "Heterogeneous Graph Attention Network; WWW"). - **Heterogeneous Graph Transformer** - Conditions attention and message transformations on node and edge types; adds relative temporal encoding and heterogeneous graph sampling for large typed networks. [Hu et al. 2020]( "Heterogeneous Graph Transformer; WWW"). ## Temporal graphs - **TGAT** - Combines temporal neighborhood attention with continuous time encodings to produce time-dependent embeddings for observed and previously unseen nodes. [Da Xu et al. 2020]( "Inductive Representation Learning on Temporal Graphs; ICLR"). - **Temporal Graph Networks** - Represents dynamic graphs as timestamped events; combines node memory with graph-based embedding operators to track evolving interactions. [Rossi et al. 2020]( "Temporal Graph Networks for Deep Learning on Dynamic Graphs; arXiv"). - **DyGFormer / DyGLib** - Encodes historical first-hop interactions with neighbor co-occurrence features and sequence patches. Also supplies shared training and evaluation pipelines for comparing dynamic graph models. [Le Yu et al. 2023]( "Towards Better Dynamic Graph Learning: New Architecture and Unified Library; NeurIPS"). ## Higher-order relations and topology - **Hypergraph Neural Networks** - Incidence-based aggregation reduces to a normalized weighted clique-expansion operator with self-contributions. Encoding group relations alone does not guarantee higher-order expressivity. [Feng et al. 2019]( "Hypergraph Neural Networks; AAAI"). - **Simplicial message passing** - Passes messages over simplicial complexes, where edges, triangles and higher-dimensional simplices represent interactions; incorporates topology beyond ordinary node-edge connectivity. [Bodnar et al. 2021]( "Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks; ICML"). ## Geometric and molecular graphs - **Geometric graphs** - Positions add Euclidean symmetries beyond node relabeling. See [Geometric deep learning](https://mlpapers.org/geometric-deep-learning/#molecular-and-atomistic-representations) for DimeNet, NequIP and MACE; MeshGraphNets below connects message passing to adaptive-mesh simulation. - **SchNet** - Uses continuous-filter convolutions for atoms at continuous positions; learns rotation-invariant energies and a differentiable potential for interatomic forces. [Schütt et al. 2017]( "SchNet: A continuous-filter convolutional neural network for modeling quantum interactions; NeurIPS"). - **EGNN** - Builds graph layers equivariant to rotations, translations, reflections, and node permutations, using scalar features and coordinate updates without higher-order tensor representations. [Satorras et al. 2021]( "E(n) Equivariant Graph Neural Networks; ICML"). - **GemNet** - Combines directed edge embeddings with two-hop geometric message passing for molecular prediction. Develops the architecture from an analysis of GNNs with spherical representations. [Gasteiger et al. 2021]( "GemNet: Universal Directional Graph Neural Networks for Molecules; NeurIPS"). - **MeshGraphNets** - Learns physical dynamics through message passing on meshes, with adaptive discretization. Studies fluid, structural, and cloth simulations on irregular domains. [Pfaff et al. 2021]( "Learning Mesh-Based Simulation with Graph Networks; ICLR"). ## Self-supervised objectives - **Deep Graph Infomax** - Trains a discriminator to distinguish real node-graph-summary pairs from corrupted pairs, providing a mutual-information-inspired objective for unsupervised node representations. [Veličković et al. 2019]( "Deep Graph Infomax; ICLR"). - **GraphCL** - Learns graph representations by contrasting augmented views; studies node dropping, edge perturbation, attribute masking, and subgraph sampling as task-dependent augmentation choices. [You et al. 2020]( "Graph Contrastive Learning with Augmentations; NeurIPS"). - **GRACE** - Contrasts node representations across two graph views formed by corrupting structure and attributes. Encourages agreement for the same node while contrasting other nodes. [Zhu et al. 2020]( "Deep Graph Contrastive Representation Learning; arXiv"). - **GraphMAE** - Masks node features and reconstructs them with a graph autoencoder using scaled cosine error. The pretraining target is feature reconstruction rather than adjacency reconstruction. [Hou et al. 2022]( "GraphMAE: Self-Supervised Masked Graph Autoencoders; KDD"). - **GraphMAE2** - Extends masked feature reconstruction with multiple randomly re-masked decoding views and latent representation prediction. Regularizes reconstruction in both feature and embedding spaces. [Hou et al. 2023]( "GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner; WWW"). - **BGRL** - Learns node representations by predicting a target encoder's output across augmented graph views. Uses a bootstrap objective without explicit negative pairs. [Thakoor et al. 2022]( "Large-Scale Representation Learning on Graphs via Bootstrapping; ICLR"). ## Transfer across graphs - **Strategies for Pre-training GNNs** - Combines node- and graph-level pretraining to learn local and global representations. Shows cases where pretraining at only one level causes negative transfer. [Hu et al. 2020]( "Strategies for Pre-training Graph Neural Networks; ICLR"). - **ULTRA** - Conditions relation representations on relation interactions, enabling a pretrained link predictor to transfer across knowledge graphs with different entity and relation vocabularies. [Galkin et al. 2024]( "Towards Foundation Models for Knowledge Graph Reasoning; ICLR"). - **GraphAny** - Combines analytical linear graph predictors with learned attention across new feature and label spaces. Inference still uses a labeled subset of the target graph; no target gradient updates are required. [Zhao et al. 2025]( "Fully-inductive Node Classification on Arbitrary Graphs; ICLR"). ## Graph generation [Evaluation](#benchmarks-and-evaluation): graph-statistic and kernel choices affect generator rankings. - **GraphRNN** - Decomposes graph generation into autoregressive node and edge decisions conditioned on the graph built so far. Evaluates generated graph sets through distributions of structural statistics. [You et al. 2018]( "GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models; ICML"). - **GraphAF** - Uses an autoregressive normalizing flow to generate molecular graphs. Combines parallel likelihood training with sequential sampling that can check atom valence as atoms and bonds are added. [Shi et al. 2020]( "GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation; ICLR"). - **DiGress** - Learns to reverse discrete noise on categorical node and edge attributes with a graph Transformer. Generates molecular and other graphs through successive denoising steps. [Vignac et al. 2023]( "DiGress: Discrete Denoising diffusion for graph generation; ICLR"). - **DeFoG** - Applies discrete flow matching to graph generation. Separates the training objective from sampling choices, allowing generation procedures to be changed without retraining the predictor. [Qin et al. 2025]( "DeFoG: Discrete Flow Matching for Graph Generation; ICML"). ## Benchmarks and evaluation - **Evaluation pitfalls** - Shows that data splits, hyperparameter tuning, and early stopping can change GNN rankings. Compares architectures under shared protocols rather than inherited results on a single split. [Shchur et al. 2018]( "Pitfalls of Graph Neural Network Evaluation; NeurIPS R2L Workshop"). - **Open Graph Benchmark** - Provides node, link, and graph prediction tasks with application-specific splits and metrics. Includes large graphs and distribution shifts beyond small citation-network benchmarks. [Hu et al. 2020]( "Open Graph Benchmark: Datasets for Machine Learning on Graphs; NeurIPS"). - **Long Range Graph Benchmark** - Introduces five tasks intended to test long-range graph interactions across molecular and image-derived graphs, with message-passing and Transformer baselines. [Dwivedi et al. 2022]( "Long Range Graph Benchmark; NeurIPS"). - **Reassessing LRGB** - With roughly 500k parameters, tuned GCN/GINE/GatedGCN beat retuned GPS on both peptide tasks; a deeper prediction head explains much of the gain. GPS still leads these baselines on both superpixel tasks. [Tönshoff et al. 2023]( "Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark; arXiv"). - **LRGB protocol** - Input normalization improves the compared vision results. The 2023 audit found raw rather than specified filtered MRR in PCQM-Contact code. Filtering other positive tails and self-loops changes scores. [Tönshoff et al. 2023]( "Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark; arXiv"). - **Graph-generation evaluation** - MMD rankings can reverse with descriptor, kernel, bandwidth or histogram choices. Matching degree or clustering summaries does not establish matching graph distributions; record metric settings. [O'Bray et al. 2022]( "Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions; ICLR"). - **HeaRT** - Ranks links against 500 endpoint-specific negatives selected by heuristics with random fill. Changing validation/test negatives, not training, changes rankings across seven graphs and makes simple baselines more competitive; this is not full-catalog retrieval. [Li et al. 2023]( "Evaluating Graph Neural Networks for Link Prediction: Current Pitfalls and New Benchmarking; NeurIPS"). - **Temporal Graph Benchmark** - Moving averages beat TGN/DyRep on four node-affinity tasks (NDCG@10); persistence leads on trade. TGN leads mean link-prediction MRR on coin, comment and flight; CAWN, TCL and GraphMixer exhaust GPU memory. [Huang et al. 2023]( "Temporal Graph Benchmark for Machine Learning on Temporal Graphs; NeurIPS"). - **Classic GNNs as strong baselines** - Reassesses GCN, GAT, and GraphSAGE against graph Transformers; tuning normalization, dropout, residual connections, and depth changes the comparison on studied node-classification datasets. [Luo et al. 2024]( "Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classification; NeurIPS"). ## Software - **PyTorch Geometric** - Graph data containers, message-passing layers, pooling operators, sampling, and dataset utilities for PyTorch. [docs](). - **DGL** - Graph computation and message-passing APIs, heterogeneous graph support, sampling, and distributed graph-learning tools. [docs](). - **OGB tools** - Dataset loaders, prescribed splits, evaluators, and baseline implementations. Use each task's specified metric and candidate-set protocol when comparing link predictors. [docs](). ## Related topics - [Geometric deep learning](https://mlpapers.org/geometric-deep-learning/) - [Neural networks](https://mlpapers.org/neural-nets/) - [Bayesian networks](https://mlpapers.org/bayesian-nets/) - [Neurosymbolic learning and reasoning](https://mlpapers.org/neurosymbolic-learning/)