Graph neural network

Overview

A graph neural network takes node features and the adjacency structure of a graph and returns an embedding for each node. An optional readout turns the node embeddings into one embedding for the whole graph 2103.00111 §3.1. The GNN is usually the encoder in graph self-supervised learning 2103.00111 §3.1.

Graphs differ from images and text because nodes are linked to each other, so samples are not independent 2103.00111 §1. A GNN handles this by letting each node's representation depend on its neighbours. Most variants below follow the same aggregate-and-combine form, which the general message-passing scheme describes 1911.06962 eq. 2 eq. 3.

Fifty-nine cards on wikillm list this concept. Forty-five of them have a variant below. Forty-three describe one GNN model used for a task. The other two are surveys whose GNN material is itself a variant: the graph self-supervision survey gives the first variant, and the scene graph survey names GNN-based methods as one model family. The remaining fourteen are nine surveys, four benchmarks and one graph-free baseline, summarised under Benchmarks and surveys. The surveys do not compare GNN architectures in depth. The graph-self-supervision survey names GCN and GAT only as baselines and does not give their equations 2103.00111 §8. The traffic survey writes out GCN, GAT and DCRNN equations, but its benchmark table mixes papers with different splits 2101.11174 eq. 1–6 2101.11174 tab. 11.

Variants

Pretext-trained encoder (graph self-supervised learning)

The encoder f_\theta maps node features \mathbf{X} and the adjacency matrix \mathbf{A} to node embeddings \mathbf{H}. A pretext decoder and a pretext loss are trained on unlabelled graphs 2103.00111 eq. 1. The pretext target can be a reconstruction of the graph, an auxiliary property, a contrast between two augmented views, or a mix of these 2103.00111 §3.2. Three training schemes then combine the encoder with labels: pre-train and fine-tune, joint learning with a trade-off weight \alpha, and unsupervised representation learning, where the encoder is frozen 2103.00111 §3.3 eq. 6–8.

The survey gives no training settings for any surveyed method, so learning rates, depths and widths must come from each method's original paper 2103.00111 §3.

Reported node-classification accuracy, compiled from the cited works: the self-supervised rows reach 84.7 on Cora and 74.2 on Citeseer, while the GCN and GAT baselines score 81.5 and 83.0 on Cora and 70.3 and 72.5 on Citeseer 2103.00111 tab. 5. The rows labelled PF or JL generally score higher than the URL rows 2103.00111 tab. 5.

Adaptive augmentation for graph contrastive learning (GCA)

Two random views of the same graph are encoded by one two-layer GCN. A projection head and a cosine critic with a temperature then pull each node's two embeddings together and push them away from every other node, in both directions 2010.14945 §3.2 eq. 1 eq. 2. The change from earlier graph contrastive methods is how the views are built. Each edge is kept with probability one minus a removal rate, and the rate is a capped, log-normalised function of the edge's centrality score, so central edges tend to survive 2010.14945 §3.3.1 eq. 3 eq. 4. The node score is degree, eigenvector centrality or PageRank, and the paper names the three choices GCA-DE, GCA-EV and GCA-PR §3.3.1 tab. 3.

Feature dimensions are masked the same way. One mask per view is shared by all nodes, and each dimension's weight sums the centrality of the nodes that have it 2010.14945 §3.3.2 eq. 6 eq. 7 eq. 8 eq. 9.

Author-reported linear-probe node classification on five datasets: a GCA variant is the best label-free row on all five, and above GCN and GAT on four of them. On Amazon-Photo, GAT is higher than all three GCA variants 2010.14945 tab. 3. The ablation on Amazon-Computers gives 87.85 for full adaptive augmentation and 86.25 for uniform edges and features, which the paper reports as a gain from each adaptive part 2010.14945 tab. 4 §4.3.

Card: Graph Contrastive Learning with Adaptive Augmentation.

Learned edge dropping for graph contrastive learning (AD-GCL)

AD-GCL replaces hand-picked graph augmentations with a learned one. A GIN encoder is trained to match each graph with an edge-dropped copy. A separate GNN augmenter gives every edge a drop probability and is trained to make the two copies as different as possible. A penalty on the mean drop probability, weighted by λ_reg, stops it from dropping almost every edge 2106.05819 §3.2 eq. 6–8. The two networks are updated in turn, one minibatch at a time 2106.05819 alg. 1. A Gumbel-max relaxation keeps the sampled edge mask differentiable 2106.05819 §3.2. The paper links the objective to the graph information bottleneck, under assumptions it states 2106.05819 §3.1 app. B.

Author-reported linear-probe accuracy on TU datasets, with λ_reg fixed at 5 (AD-GCL-FIX): on COLLAB it reaches 73.32 against 71.26 for GraphCL 2106.05819 tab. 1. The paper counts significant wins over InfoGraph and GraphCL on 5 and 6 of 8 TU datasets §5.1. The gains are not uniform. In the semi-supervised table GraphCL is higher on PROTEINS, 74.17 against 73.96 tab. 3, and the paper's mean rank across nine transfer datasets is 2.4 §5.3. The abstract's headline gains are up to 14%, 6% and 3% for the unsupervised, transfer and semi-supervised settings 2106.05819 abstract.

The paper's code differs from its text in ways that change the numbers. The dropout default is 0.0 in the code, against 0.5 in the paper's appendix. The code keeps every edge and weights its messages, where the paper removes edges gine_conv.py. The code's contrastive loss uses a temperature of 0.2 and averages the two directions, which eq. 9 does not ginfominmax.py. The original InfoGraph and GraphCL numbers used an SVM probe, while this paper uses a linear probe, so the two sets of numbers are not directly comparable §5.1.

Card: Adversarial Graph Augmentation to Improve Graph Contrastive Learning.

Relation-typed windowed graph over a sequence (DialogueGCN)

In a conversation, each utterance is a node, initialised with features from a bidirectional GRU that reads the utterances in order 1908.11540 §3.3.1. Each node is linked to the 10 utterances before it, the 10 after it, and itself 1908.11540 §3.3.2.

Edge weights are a softmax over bilinear scores of the two nodes, normalised over each node's incoming edges 1908.11540 eq. 1. Each edge also has a relation type: the speaker of the source, the speaker of the target, and whether the source comes first 1908.11540 §3.3.2 tab. 1.

The first graph layer uses one weight matrix per relation, with the edge weights and a self term 1908.11540 eq. 2. The second layer drops the relation types and uses one shared weight matrix over the window 1908.11540 eq. 3.

Ablations on IEMOCAP, weighted F1 1908.11540 §5.2–§5.3:

• Full model, window (10, 10): 64.18.
• Window (4, 4): 59.41. Window (0, 0), self-edges only: 55.80.
• Without the graph encoder: 55.30 1908.11540 tab. 5.
• Without speaker-pair relations, before/after kept: 61.03 1908.11540 tab. 6.
• Without before/after relations, speaker pairs kept: 62.52 1908.11540 tab. 6.

Card: DialogueGCN.

Feature-similarity graph added to a GCN (SimP-GCN)

A GCN layer averages each node with its neighbours. The authors argue that this pulls neighbouring features together and erases the original node similarity, and that the effect is strongest when linked nodes differ in label 2011.09643 §3. The share of edges shared by the original graph and a feature-similarity graph is 0.03% on Actor and 0.91% on Cornell, against 3.88% on Cora 2011.09643 tab. 1.

SimP-GCN extends a two-layer GCN. It builds a second graph that links each node to its 20 most cosine-similar nodes by features 2011.09643 §4.1. A learned sigmoid score per node sets how much each layer trusts the original graph and how much the feature graph 2011.09643 §4.1. A learned per-node count of self-loops scales the node's own term, with a fixed weight γ 2011.09643 §4.1. The loss adds a regression: for each node, its 5 most similar and 5 most dissimilar nodes are sampled, and the difference of their first-layer hidden states is fitted to their feature similarity, weighted by λ 2011.09643 §4.2 §4.3.

Results are author-reported on seven datasets. On assortative graphs the gain over GCN is small: 82.8 against 81.3 on Cora, 72.6 against 71.5 on Citeseer and 81.1 against 79.3 on Pubmed 2011.09643 tab. 3. On disassortative graphs it is large: 84.05 against 52.70 on Cornell, 81.62 against 52.16 on Texas and 85.49 against 45.88 on Wisconsin 2011.09643 tab. 4. The GCN and GAT numbers on those graphs are copied from the GCNII paper, not rerun 2011.09643 §5.2.

Ablation on Cornell 2011.09643 tab. 5:

• Full model: 84.05. Without the self-supervised term: 82.70.
• Without the self-loop term (γ = 0): 65.95.
• Without the self-loop term and without the self-supervised term: 64.59.

Under the Metattack poisoning attack, the authors report that SimP-GCN beats GCN at every perturbation rate on Cora, Citeseer and Pubmed. The curves are only in a figure, so no values are given here 2011.09643 §5.3 fig. 2.

Card: Node Similarity Preserving Graph Convolutional Networks.

Learned edge gates inside the GNN (PTDNet)

PTDNet keeps a small learned scorer for each GNN layer. It scores each edge from its two endpoint states, and a hard-concrete gate turns that score into a keep decision that is differentiable in training and can be exactly zero 2011.07057 §4.2 eq. 3 eq. 4. Two penalties push the kept graph toward fewer edges: the expected number of kept edges eq. 5, and the nuclear norm of each masked adjacency, approximated by its top-K singular values §4.3 alg. 2. The authors report GCN on Cora at 0.828 ± 0.026 against 0.811 ± 0.015 for the basic model. Those gaps sit inside one standard deviation, while the gains with injected noisy edges are larger 2011.07057 tab. 3 §5.3. The paper gives no values for the stretch parameters γ and ζ beyond their signs, and no combined loss §4.2.2. Card: Learning to Drop: Robust Graph Neural Network via Topological Denoising.

Learned graph with no predefined adjacency (GCNN-DDGF)

The usual GCN needs an adjacency matrix. This model is for stations or nodes that are linked by a graph the user cannot define well. The authors build the graph convolution on \tilde{A} = A + I, with the usual symmetric degree normalisation, and then treat the normalised filter \hat{A} as an unknown symmetric N \times N matrix learned with the weights 1712.04997 §3.1.1 eq. 6–7 §3.3.1 eq. 15. The paper calls this the data-driven graph filter (DDGF).

The task is next-hour bike demand at each of 272 stations, from the last 24 hourly vectors of all stations 1712.04997 §5 tab. 2. The baselines include four GCNs whose graph is fixed in advance: spatial distance, origin– destination demand, average trip duration and demand correlation. Each one sets the entries of \tilde{A} with a threshold 1712.04997 §3.2. The demand-correlation graph uses correlations computed from the training data only 1712.04997 §3.2.4 §5.

Two DDGF variants exist. The regular one stacks learned-filter layers with ReLU 1712.04997 §3.3.2 eq. 9. The recurrent one passes the filtered station vector at each step through an LSTM and predicts the next hour from the last hidden state 1712.04997 §3.3.2 fig. 1b.

Results are author-reported on one dataset, after selection on validation. Test RMSE: the recurrent variant 2.12, the regular variant 2.35, the best predefined-graph GCN (demand correlation) 2.50, and the historical average 3.44 1712.04997 tab. 3. The paper gives no run-to-run variance, so the gap between the two DDGF variants has no reported uncertainty §5.

The learned graph has 1,565 edges with weight at least 0.15 after normalising to [0, 1], and the authors read its edges as partly matching the predefined graphs 1712.04997 §5.3. This is a description of one trained model, not a test of which graph is correct.

Card: Predicting Station-level Hourly Demands in a Large-scale Bike-sharing Network.

Molecular message passing inside a drug-target encoder (MPNN)

DeepPurpose is a library that trains encoder-decoder models for drug-target interaction prediction. The user picks the compound encoder and the protein encoder by name 2004.08919 §2.1. One compound encoder is a message- passing neural network (MPNN) over the molecular graph. The other compound encoders use fingerprints, CNNs, RNNs or a Transformer over SMILES or substructure tokens 2004.08919 app. A. The protein encoders do not use a graph 2004.08919 app. A.

The paper says the MPNN readout is the mean or the sum over atoms 2004.08919 app. A. The compound and protein embeddings are concatenated and passed to an MLP decoder 2004.08919 §2.2.

Author-reported on DAVIS, with figure values read from a low-resolution raster: the MPNN+AAC pair reaches MSE 0.242 and concordance index 0.881, against 0.254 and 0.879 for the CNN+CNN pair, and against 0.262 and 0.870 for DeepDTA 2004.08919 fig. 1. The figure gives a parenthesised value next to each mean that the text does not define. The paper does not state the optimiser, learning rate, epochs or batch size for these results 2004.08919 §3.

Card: DeepPurpose.

Differentiable circular fingerprint for molecules (neural fingerprints)

A circular fingerprint hashes each local substructure into a fixed slot, so it must be long to avoid collisions and it cannot be tuned for the task 1509.09292 §1. The neural fingerprint keeps the same rounds of neighbourhood update but makes the hash and the slot lookup differentiable 1509.09292 §3 alg. 2. Each atom mixes its neighbours' states, using one weight matrix per number of bonds, and after every round a softmax over the fingerprint slots is summed over atoms 1509.09292 §3 alg. 2. The per-round vectors add up to one fingerprint.

The fingerprint is trained end-to-end with a small regression head on labelled molecules 1509.09292 §4.2. The paper's three regression sets are aqueous solubility, antimalarial drug efficacy and organic photovoltaic efficiency 1509.09292 §4.2. Author-reported results in tab. 1 compare against circular fingerprints under the same heads. On solubility the neural version with a one-hidden-layer head scores 0.52 against 1.40 for circular fingerprints with a one-hidden-layer head. On drug efficacy the circular fingerprint with a linear head is slightly better (1.13 against 1.15). On photovoltaic efficiency the neural version with the hidden layer scores 1.43 against 2.00. The metric is not named in the paper, so the values cannot be compared against other papers tab. 1.

The paper reports that neural and circular fingerprints correlate at r = 0.823 on the solubility set 1509.09292 §4 fig. 3. The learned features can be inspected by listing the fragments that most activate each one, which the authors show for solubility and toxicity 1509.09292 §4.1 fig. 4 fig. 5. Information moves only as far as the depth of the network, and the model does not distinguish stereoisomers 1509.09292 §5. The paper gives the cost as O(RNFL + RNF²) for N atoms, R rounds, F features and length L 1509.09292 §5. The card lists implementation details that the paper leaves out.

Card: Convolutional Networks on Graphs for Learning Molecular Fingerprints.

Message passing in scene graph generation

The scene graph survey lists GNN-based methods as one of five model families, which pass messages over the graph of objects and relations 2104.01111 §2.5. It gives no GNN equations and no hyperparameters. Its best SGCls R@100 row on VG150 is an RNN/LSTM method, BGT-Net at 47.1, not a GNN 2104.01111 tab. 2. Card: A Comprehensive Survey of Scene Graphs.

Direction-aware message passing for scene graphs (GPS-Net)

GPS-Net is a one-stage scene graph generator. Its message passing scores each ordered pair of objects with a tri-linear product of subject, object and union features, then sends each neighbour's features along both directions of the pair 2003.12962 §3.1 eq. 3 eq. 4. A node-priority loss gives each object a focusing parameter from the share of relation triplets that contain it, capped at 2 §3.2 eq. 6 eq. 7. A frequency prior is softened and gated per pair before relation classification §3.3 eq. 9 eq. 10. In the Visual Genome ablation, message passing gives the largest single gain: SGDET R@50 rises from 26.3 to 28.1 2003.12962 tab. 5. Author-reported mean recall is 45.9 with the MOTIFS detector, against 43.7 for MOTIFS tab. 1. The paper's best exponent is 4 §4.4, but the released code uses 5, and its detector build computes priority from proposal overlap rather than triplets. Do not treat the code as the paper's method; see the card's Paper vs code. Card: GPS-Net: Graph Property Sensing Network for Scene Graph Generation.

Enclosing-subgraph GNN for inductive link prediction (GraIL)

Knowledge-graph completion usually learns one vector per entity and assumes a fixed entity set, the transductive setting 1911.06962 §1. GraIL scores a candidate triple (u, r, v) from the subgraph that connects u and v. It keeps the nodes within k hops of both targets, labels each node by its distances to u and to v, and runs a relation-aware GNN with edge attention over that subgraph. The score reads the pooled subgraph and the two target states 1911.06962 §3.1 eq. 5. The model uses no entity embeddings, so it can be applied to inductive splits whose test graph shares the relation set but no entities 1911.06962 §4.1.

Author-reported: inductive AUC-PR is the best of all compared models on all 12 split–dataset columns, against RuleN, Neural-LP and DRUM. On WN18RR v1 the values are 94.32 for GraIL and 90.26 for RuleN 1911.06962 tab. 1. On transductive splits GraIL is not the strongest model alone. Ensembling it with each KGE model gives average gains of 1.5% on WN18RR and 0.62% on NELL-995, and none significant on FB15k-237. The paper gives no significance test 1911.06962 §4.2.

Ablation on the v3 splits 1911.06962 tab. 7: replacing the intersection of the two neighbourhoods with their union drops FB (v3) from 91.68 to 84.25. Removing the double-radius labels drops it to 82.07.

Card: Inductive Relation Prediction by Subgraph Reasoning.

Language model with a knowledge-graph GNN, joint scoring (QA-GNN)

For a multiple-choice question, the pretrained LM encodes the question joined to one answer choice 2104.06378 §3. The retrieved ConceptNet subgraph is capped at 200 nodes, and the LM scores each node's relevance to the QA context 2104.06378 §4.2 §3.2. The method then adds one QA-context node, linked to the question entities and the answer entities. Five attention-weighted GNN layers pass messages over this working graph. A head reads the LM vector, the context node and a pooled graph vector 2104.06378 §3.1 §3.3 §3.4.

Author-reported: on the CommonsenseQA in-house test, 73.41 for QA-GNN against 68.69 for RoBERTa-large and 71.11 for MHGRN 2104.06378 tab. 3. The relevance score is worth about one point on the in-house dev set, 76.54 against 75.56 without it 2104.06378 §4.6.1. The model has about 360M parameters and took about 20 hours on two RTX 2080 Ti for CommonsenseQA 2104.06378 §4.3 §4.5. The released code computes the relevance scores differently from the paper; see Contradictions.

Card: QA-GNN.

Interaction tokens between a language model and a knowledge-graph GNN (GreaseLM)

GreaseLM runs an LM and a GNN over the same question. It has a stack of unimodal LM layers, followed by M fusion layers. Each fusion layer runs one more LM block and one graph-attention layer. It then mixes only two bottleneck vectors, an interaction token and an interaction node, through a small MLP. All other tokens and nodes read these two vectors in the next layer 2201.08860 §4.2 §4.3. The subgraph retrieval follows QA-GNN 2201.08860 app. B.1.

Author-reported: on the CommonsenseQA in-house test, 74.2 for GreaseLM against 73.4 for QA-GNN and 71.1 for MHGRN 2201.08860 tab. 2. On OpenbookQA test it reaches 84.8 2201.08860 tab. 3, and on MedQA-USMLE 38.5 2201.08860 tab. 6. Removing the modality interaction drops the dev score from 78.5 to 76.5 2201.08860 tab. 8. Connecting the interaction node to all retrieved nodes, instead of only the linked ones, gives 77.6 2201.08860 app. C.1. On dev questions with negation, GreaseLM scores 69.9 against 66.2 for QA-GNN 2201.08860 tab. 5.

Card: GreaseLM.

Word-document graph with BERT node features (BertGCN)

The graph contains document nodes and word nodes. Each document node starts from a BERT or RoBERTa [CLS] embedding, and word nodes start at zero 2105.05727 §3.1. A two-layer GCN runs over the whole corpus. Its prediction is mixed with a BERT-only prediction, using a weight lambda 2105.05727 §3.2 eq. 6. BERT cannot process the whole graph at once, so the method keeps a memory bank with one embedding per document. The bank is refreshed each epoch and again for each minibatch. BERT starts from a copy fine-tuned on the target data 2105.05727 §3.3.

Author-reported test accuracy with BERT-base 2105.05727 tab. 1: 89.3 on 20NG, 98.1 on R8, 96.6 on R52, 72.8 on Ohsumed and 86.0 on MR. The BERT-only row gives 85.3, 97.8, 96.4, 70.5 and 85.7. The authors credit the graph with the largest gains on the long-document sets, 20NG and Ohsumed. On the short-document sets R52 and MR, pretrained models alone beat the GCN-only baselines 2105.05727 §4.2. Without the small BERT learning rate the 20NG dev run does not converge, at 10.3 accuracy 2105.05727 tab. 2. The lambda of 0.7 was chosen on that dev set 2105.05727 §4.3 fig. 1.

Card: BertGCN.

GNN as a flow predictor (GFlowNet)

GFlowNet trains a policy that builds a discrete object step by step, so that a finished object is sampled in proportion to its reward. The GNN here is a message-passing network that predicts the flow on each allowed action in the construction graph. Its convolution runs for 10 steps 2106.04399 app. A.4. Training matches log-flows with a squared-error loss over the construction DAG, and the training trajectories may come from another policy 2106.04399 §2.2.

Author-reported on a molecule task at 10^5 samples: the top-10 mean reward is 8.36 for GFlowNet, 8.06 for PPO and 8.05 for MARS 2106.04399 app. A.7. The mean pairwise Tanimoto similarity of the top-1000 molecules is 0.44 for GFlowNet, 0.62 for PPO and 0.59 for MARS 2106.04399 §4.2 app. A.7. Lower means more diverse. Card: Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation.

Graph transformer denoiser for discrete graph diffusion (DiGress)

DiGress generates whole graphs by discrete denoising diffusion. Each node and each edge is corrupted by a Markov chain over its categories, and a network predicts the clean categories from the noisy graph 2209.14734 §3.1 §3.2. The network is a graph transformer that carries node, edge and graph-level features 2209.14734 §3.2. It belongs under this concept because it works directly on the graph's nodes and edges. The paper also replaces the uniform noise of earlier graph diffusion with noise that moves toward training-set frequencies, which gives better results on QM9 2209.14734 §4.1 tab. 6.

Author-reported: 74% and 75% of generated graphs are valid, unique and novel on SBM and planar graphs 2209.14734 tab. 1. On QM9 the validity is 99.0 ± 0.1 2209.14734 tab. 2. On MOSES, the FCD is 1.19 against 1.22 for the autoregressive GraphINVENT 2209.14734 tab. 3. Sampling graphs larger than any training graph works on GuacaMol, at 85.6% valid and unique at n_max + 10, and fails on MOSES, at 2.2% 2209.14734 tab. 7.

Card: DiGress.

Encode-process-decode mesh GNN for weather (GraphCast)

GraphCast forecasts global weather 6 hours ahead, then feeds its own output back to reach 10 days 2212.12794 app. §3.1. The grid has 721 by 1440 points, each with 227 target values 2212.12794 app. §2.3. An encoder moves grid features onto a multi-mesh made from a refined icosahedron. The mesh has 40,962 nodes at the finest level, and its edges from all refinement levels are kept, so coarse edges give long-range links 2212.12794 app. §3.3. A processor of 16 message-passing layers, with unshared weights, runs on the mesh. A decoder returns to the grid, and the output is a scaled change added to the current state 2212.12794 app. §3.4 §3.5 §3.6 §3.7.

Training uses a latitude- and level-weighted squared error over rollouts of up to 12 steps, with backpropagation through time 2212.12794 app. §4.2 §4.3. The model has 36.7 million parameters 2212.12794 §GraphCast.

Author-reported: GraphCast has lower RMSE than the operational HRES forecast (HRES-fc0) on 90.3% of 1380 targets over 10 days [arxiv:2212.12794 §Forecast verification results]. The MSE objective blurs predictions at long lead times, and blurring HRES narrows the gap to 88.0% [arxiv:2212.12794 §Forecast verification results] app. §7.4. The repository holds the inference and loss code but not the training loop, so training cannot be checked against code 2212.12794 §Paper vs code.

Card: GraphCast.

Multiplex node embedding by high-order mutual information (HDMI)

Some networks link the same nodes in several ways, and each kind of link is a separate layer. HDMI gives each layer its own one-layer GCN encoder, then fuses the layer embeddings per node with a semantic attention step 2102.07810 §3.2 eq. 21–23. No labels are used. The training signal has three terms: each node against a global summary, each node against its own attributes, and each node against the attributes of another node. Corrupted inputs supply the negatives 2102.07810 §3.1.1 eq. 9–11.

Author-reported: HDMI has the highest Macro-F1 on all four datasets, at 0.901 on ACM, 0.650 on IMDB, 0.820 on DBLP and 0.808 on Amazon [arxiv:2102.07810 tab. 3]. On clustering and similarity search it is not best everywhere. On ACM, DMGI_attn scores higher NMI, 0.702 against 0.695 2102.07810 tab. 4. Card: HDMI.

Non-local graph block for occluded instances (BCNet)

BCNet is a mask head for detect-then-segment models. It treats the 14 × 14 region feature as a graph with one node per pixel, and it runs two non-local graph layers over it 2103.12340 §3.2 eq. 1–3. The first layer, for the occluder, predicts the front object's mask and boundary. Its output is added back to the region feature and guides the second layer, which predicts the partly hidden object 2103.12340 §3.1 eq. 4–6. Each adjacency is a softmax over pairwise dot products of two learned projections 2103.12340 eq. 2–3.

Author-reported: 39.8 mask AP on COCO test-dev with Faster R-CNN and ResNet-101, against 39.7 for HTC and 37.0 for Mask R-CNN 2103.12340 tab. 8. Modelling the occluder raises COCO-OCC AP from 29.04 to 30.37 2103.12340 tab. 1. The bilayer graph beats a single graph layer by 1.05 COCO-OCC AP, 30.68 against 29.63 2103.12340 tab. 3. The gains are larger on the overlap-heavy subset than on COCO 2103.12340 tab. 1. Card: BCNet.

Graph-nested language model for textual graphs (GraphFormers)

GraphFormers places a graph-attention step inside each layer of a BERT-style encoder (UniLM-base), so each node's text is encoded together with its neighbours' context at every layer 2105.02605 §3.1. Layer 0 encodes each node alone. In later layers, the [CLS] states of all nodes form one graph vector per node, with a learned position bias, and that vector joins the node's tokens in an asymmetric attention 2105.02605 §3.1 eq. 1 eq. 4. The unidirectional variant lets only the centre node query its neighbourhood, so neighbour states can be cached and reused 2105.02605 §3.2 eq. 5. Training is link prediction with in-batch negatives 2105.02605 §3.3 eq. 6.

Author-reported P@1 on three textual link-prediction sets: 0.7786 on Product, 0.7267 on DBLP and 0.3952 on Wiki, against 0.7570, 0.6934 and 0.3712 for the best cascaded baseline, PLM+Max 2105.02605 tab. 2. Removing the progressive warm-up costs 1.71 DBLP P@1 points 2105.02605 tab. 4. At 200 neighbours the time overhead is 3.5% 2105.02605 §4.5 tab. 5. Card: GraphFormers.

Lane-graph policy and trajectory decoder (PGP)

PGP predicts K = 10 future paths of a target vehicle from two seconds of history and a lane graph. GRU encoders, agent-to-node attention and GCN or GAT layers give each lane node a feature 2106.15004 §4.1 app. A.2–A.4. A policy scores the outgoing edges of each node with a softmax and rolls out routes through the lane graph 2106.15004 §4.2 eq. 1–2. Each route, together with a 5-dimensional latent sample, drives an attention decoder whose outputs are clustered into modes 2106.15004 §4.3 app. A.6. The policy is trained by behaviour cloning on ground-truth routes, and the decoder by winner-takes-all regression 2106.15004 eq. 3 eq. 5.

Author-reported on nuScenes: MinADE10 1.00 and MissRate10,2 0.37, against 1.16 and 0.46 for P2T 2106.15004 tab. 1. In the encoder ablation the graph layer changes MinADE10 by at most 0.01, whether it is absent, GCN or GAT 2106.15004 tab. 2. The decoder ablation spans MinADE10 from 1.01 to 1.12 2106.15004 tab. 3, so the decoder matters more on this benchmark. Card: PGP.

Graph network with gated recurrence for series imputation (GRIL)

GRIL fills missing values in a multivariate series whose channels are sensors on a fixed graph. It is a bidirectional recurrent network. Each step runs a GRU whose gates are message-passing networks, once forward and once backward 2108.00298 §4. Each step makes two guesses for every gap. The first comes from the hidden state. The second comes from neighbouring sensors, which send their filled values and masks, while the sensor's own input is excluded 2108.00298 §4 eq. 9–10. A final MLP combines the two directions 2108.00298 eq. 11.

Author-reported: MAE is 27.1% below BRITS on out-of-sample AQI and 54.4% and 54.7% below on point-missing PEMS-BAY and CER-E 2108.00298 tab. 1 tab. 2. The smallest real-data reduction is 13.2%, on METR-LA with block missingness 2108.00298 tab. 2. On METR-LA block missingness, a learned graph gives MAE 2.03, against 2.63 for a fully connected graph and 3.42 for no edges 2108.00298 tab. 9. Card: GRIL.

Edited graphs for out-of-distribution nodes (EERM)

When a node-level task has one graph and no environment labels, EERM builds virtual environments from that graph. K learned editors each flip a sampled set of node pairs in the adjacency matrix, adding missing edges and removing present ones 2202.02466 §3.2 app. A. The editors are trained with REINFORCE to maximise the variance of the GNN's risk across the edited graphs. The GNN then minimises that variance plus a weighted mean risk 2202.02466 §3.2 eq. 5.

Author-reported gains over ERM with the same backbone. On Facebook-100 the gaps run from −0.13 to +3.63 points. The largest is on Texas, 53.82 against 50.19 when trained on Bingham, Duke and Princeton 2202.02466 tab. 2. On OGB-Arxiv, GPRGNN improves from 47.25 to 49.88 on the 2014–2016 split 2202.02466 tab. 3. Several Facebook-100 gains lie within one standard deviation, so they are weak evidence 2202.02466 tab. 2. Each editor holds an n × n parameter matrix 2202.02466 app. A, so memory grows with the square of the node count, and the paper gives no sparse alternative. Card: EERM.

Graph attention over feature tracks for pose matching (OnePose)

OnePose estimates a 6D object pose from a short RGB scan, without a CAD model or per-object training 2205.12257 §1. The scan becomes a sparse 3D point map, and each point keeps the 2D features that observed it, its feature track 2205.12257 §3.1. For each query, a graph attention layer re-weights each track's descriptors. Stacked attention groups then let query features and 3D descriptors attend to each other, a dual softmax selects matches, and PnP with RANSAC gives the pose 2205.12257 §3.2 §4.2. The paper stacks N = 4 groups 2205.12257 §4.2.

Author-reported on the authors' dataset: for large objects, 0.471 at 1cm-1deg against 0.435 for HLoc with SuperPoint and SuperGlue, at 58 ms against 618 ms per frame 2205.12257 tab. 1. On medium objects HLoc is higher, 0.643 against 0.629 2205.12257 tab. 1. Replacing the attention in the aggregation with a plain average lowers large-object accuracy to 0.449 2205.12257 tab. 4. Card: OnePose.

Language model and knowledge graph pretrained jointly (DRAGON)

DRAGON pretrains one encoder on a text segment and a small knowledge-graph subgraph at the same time. An interaction token and an interaction node pass information between the two sides after each fusion layer 2210.09338 §2.2 eq. 5–7. The pretraining loss is masked language modelling plus link prediction on held-out edges, scored with DistMult 2210.09338 §2.3 eq. 8–10. The general model uses 19 unimodal language-model layers and 5 fusion layers 2210.09338 §3.1.

Author-reported: 76.0 on CommonsenseQA and 72.0 on OpenbookQA, against 74.2 and 66.9 for GreaseLM, which uses the graph only in fine-tuning [arxiv:2210.09338 tab. 1]. Feeding the graph as sentences instead of as a graph lowers CSQA to 74.7 2210.09338 tab. 5. On MedQA the reported score is 47.5 2210.09338 tab. 6. Card: DRAGON.

Equivariant interaction graph for motion prediction (EqMotion)

EqMotion predicts the future motion of interacting agents with a network that is equivariant to translation, rotation and reflection 2303.10876 §3.2 §4. Each agent has a geometric feature whose coordinates transform with the scene. It also has a pattern feature built from speed and turning angle, which is invariant 2303.10876 §4.1. Interaction categories come only from invariant inputs 2303.10876 §4.2 eq. 2. Each layer moves the coordinates by category-weighted differences to the other agents, and updates the pattern feature by message passing 2303.10876 §4.3 §4.4 eq. 3–4. The experiments use a fully connected graph 2303.10876 §4.3.

Author-reported: 55.0 mm mean joint error at 400 ms on H3.6M, against 58.3 for SPGSN 2303.10876 tab. 2. On charged particles, interaction recognition reaches 80.9% against 70.4% for dNRI 2303.10876 tab. 1. The equivariance result is a proof for the layers as written, not a test of the released code 2303.10876 §4.6. Card: EqMotion.

Higher-order neighbourhood mixing (MixHop)

MixHop replaces the one-hop propagation of a GCN layer with a concatenation over several adjacency powers, each with its own weights 1905.00067 §3.1 eq. 4. With the power set {1} the layer is the GCN layer §3.1. The authors argue that a stack of vanilla GCN layers cannot represent a two-hop delta operator, a difference between features at two distances, while MixHop with powers {0, 1, 2} can §3.3. Powers are applied by repeated sparse products, so no adjacency power is formed, and the cost per layer is stated as O(j_max · m · s) §3.2.

The width of each power is learned with a five-stage group-lasso procedure: a wide network is trained, whole columns are shrunk, columns are pruned to match the size of the {1} baseline, and the network is retrained with plain L2 §4.2. The default architecture splits the hidden width equally across powers §5.2.

Author-reported on the Planetoid splits, with 20 labelled nodes per class: the default architecture scores 71.4, 81.8 and 80.0 on Citeseer, Cora and Pubmed, and the learned architecture 71.4, 81.9 and 80.8 1905.00067 tab. 1. The vanilla GCN row is copied from Kipf and Welling, at 70.3, 81.5 and 79.0 tab. 1. The {1} baseline, which the authors ran themselves, scores 70.7, 81.1 and 79.9 tab. 1. On random splits with 100 labels per class, the learned architecture scores 77.0, 87.2 and 83.8, against 76.7, 86.1 and 82.2 for the vanilla GCN tab. 3. The paper does not say whether the random-split baselines were rerun tab. 3. At low homophily on the synthetic graphs, MixHop is significantly better than the strongest baseline §6.1.

Card: MixHop.

Learned propagation weights (GPR-GNN)

GPR-GNN separates feature extraction from propagation. A 2-layer MLP gives each node a representation H^(0). The representation is propagated K times with the symmetric normalised adjacency with self-loops, and the output is the sum of the K+1 terms, each weighted by a learned scalar γ_k 2006.07988 eq. 1 §3. Initialising γ to personalised-PageRank weights gives APPNP, and a one-hot γ at step K gives SGC §3. The paper does not restrict the learned γ_k to be positive §3. Because the output is a polynomial in the normalised adjacency, learning γ is learning a graph filter §4. The paper's low-pass result needs non-negative γ_k that sum to one, and with γ_k = (−α)^k and large K the filter acts as high-pass §4 app. A.3. The paper uses K = 10 §5.

Author-reported mean accuracy over 100 random splits, with 95% intervals. The paper gives the homophilic graphs a 2.5 / 2.5 / 95 split and the heterophilic graphs 60 / 20 / 20 §5 app. A.9. GPR-GNN has the best mean on seven of ten datasets tab. 2. On Texas it scores 92.92, against 92.26 for the MLP and 75.16 for GCN tab. 2. On Cornell APPNP is higher, 91.80 against 91.36 tab. 2. On the synthetic sparse split at φ = −1 it scores 97.19, against 55.24 for GCN and 49.57 for APPNP tab. 5. With a random initialisation of γ, the same setting drops to 88.39 tab. 5. The paper reports the per-epoch cost close to APPNP's, with 17.62 ms on Cora against 17.16 ms tab. 3.

Card: GPR-GNN.

Learned sensor graph for anomaly detection (GDN)

GDN learns the graph it needs. Each sensor has a learned embedding, and the top k sensors by cosine similarity of embeddings become its neighbours, giving a directed edge set 2106.06947 §3.4 eq. 2 eq. 3. A graph-attention layer forecasts each sensor's next value from its neighbours' windows. The attention uses both the embeddings and the projected windows §3.5 eq. 5–8. Each sensor's representation is multiplied element-wise by its embedding before a fully connected output layer §3.5 eq. 9. The model is trained on normal data with squared error §3.1 eq. 10. A time tick scores the largest per-sensor error, normalised by the sensor's median and IQR. The score is smoothed and compared with a threshold §3.6 eq. 11–13.

Author-reported F1 on SWaT is 0.81 and on WADI 0.57. The best baseline in the table, MAD-GAN, scores 0.77 and 0.37 2106.06947 tab. 2. Removing the learned top-k graph lowers WADI F1 to 0.51, removing the embedding from attention lowers it to 0.49, and uniform attention gives 0.48 tab. 3. The paper reports no standard deviations tab. 2.

Card: GDN.

Learned proposal graph for LiDAR detection (BADet)

BADet is a two-stage LiDAR 3D detector. The first stage proposes boxes. The second stage makes each proposal a node. Proposals whose centres lie closer than a cut-off r are linked, and each node is linked to itself 2104.10330 §3.3.1 eq. 2. The node state concatenates voxel, bird's-eye-view pixel and point features §3.2 eq. 1. The paper's node state has 120 dimensions §4.1.2. Each update step computes, for each neighbour, a message from the relative position minus a predicted alignment offset, concatenated with the neighbour's state. The messages are max-pooled over the neighbourhood, and the result is added to the node state §3.3.2 alg. 1 eq. 3. The paper runs T steps. It reports T = 3 for its test submission and T = 4 as best on validation §4.4.4. The cut-off r is not stated §3.3.1.

Author-reported. On the KITTI test split, Car at moderate difficulty scores 81.61 AP3D and 91.32 APBEV, against 81.62 AP3D for Voxel R-CNN and 90.65 APBEV for PV-RCNN 2104.10330 tab. 1. On the KITTI validation split, the moderate AP3D is 85.77, against 84.52 for Voxel R-CNN tab. 2. On validation, T = 0 gives 79.94, T = 3 gives 85.77, T = 4 gives 85.79 and T = 5 gives 79.87 tab. 7. The authors attribute the drop at T = 5 to gradient vanishing, which they do not test §4.4.4. The refiner takes 61.98 ms of a 140.36 ms frame on a GTX 1080 Ti §4.5 tab. 8.

Card: BADet.

Channel-wise topology for skeleton action recognition (CTR-GCN)

Skeleton graph convolutions usually share one adjacency matrix across all channels. CTR-GC keeps a shared matrix A and adds a correction for each sample and channel. The correction, scaled by a trainable α, comes from pairwise joint correlations of pooled features. Each channel then aggregates joints with its own refined matrix 2107.12213 §3.2 eq. 4–8. The correlation is a Tanh of the difference between two learned projections. An MLP form is an alternative §3.2 eq. 5. Three such branches are summed in each spatial module, and a multi-scale temporal module follows §3.4 fig. 3. The paper does not give the initial value of α §3.2.

Author-reported. On NTU RGB+D 120 the cross-subject and cross-setup top-1 are 88.9 and 90.6, against 87.3 and 88.6 for Dynamic GCN 2107.12213 tab. 5. On NTU RGB+D cross-subject it scores 92.4, against 91.5 for MS-G3D and Dynamic GCN tab. 6. On NW-UCLA it scores 96.5, against 95.3 tab. 7. In the ablation on NTU 120 cross-subject, removing the shared matrix gives 84.0 and removing the correction gives 83.7, against 84.9 for the full model tab. 2. The full model has 1.46M parameters, and the ST-GCN baseline has 1.22M tab. 2. The paper reports about 1.97 GFLOPs for CTR-GC against 1.65 for ST-GC tab. 4. The authors' repository is licensed CC BY-NC 4.0, which excludes commercial use. An implementation should therefore be written from the paper.

Card: CTR-GCN.

Bipartite graph convolution as a branching rule (learn2branch)

In branch-and-bound for a mixed-integer linear program, the solver splits on one fractional variable at each node. Strong branching picks the best variable but solves two LPs per candidate, so solvers fall back to cheaper hybrid rules 1906.01629 §3.2. This variant encodes the solver state as a bipartite graph, with one node per LP row, one per LP column, and one edge per non-zero coefficient 1906.01629 §4.2. A single graph convolution runs in two half-steps, from variables to constraints and back, with sum aggregation 1906.01629 §4.3 eq. 4. Training is behavioural cloning: cross-entropy over the candidate variables, with strong branching's choice as the label, and no reinforcement learning 1906.01629 §4.1 eq. 3.

Author-reported: the expert's variable is ranked first (acc@1) on 65.5% of set-covering test cases, against 57.6 for SVMrank, and on 56.5% of maximum-independent-set cases, against 48.9 for LambdaMART [arxiv:1906.01629 tab. 1]. Solve time is below SCIP's reliability pseudocost rule in most settings. The card counts 11 of 12 size settings from the table; the authors do not state that count 1906.01629 tab. 2. Models are trained on easy instances and the authors say they generalise to larger ones [arxiv:1906.01629 tab. 2] §5.2. Training took 3.8 to 18.2 hours per problem [arxiv:1906.01629 suppl. §5].

Card: Exact Combinatorial Optimization with Graph Convolutional Neural Networks.

Amortised explainer network (PGExplainer)

Explaining a GNN means finding a small set of edges whose presence keeps the prediction 2011.04573 §1 §4.1. Per-instance explainers such as GNNExplainer run a new optimisation for every node or graph, and do not carry over to unseen nodes 2011.04573 §1 §4.3. PGExplainer trains one MLP on the frozen GNN's embeddings. For an edge (i, j) it takes the embeddings of i and j, plus the explained node's embedding for node tasks, and outputs one logit for the edge 2011.04573 §4.3 eq. 8 eq. 10–11. Sampled edge masks use a binary concrete relaxation. The loss is a cross-entropy between the GNN's prediction on the full graph and on the masked graph, summed over instances 2011.04573 §4.2 eq. 4 eq. 9. Only the explainer's MLP is trained §4.3. The appendix anneals the temperature from 5.0 to 2.0 app. B.

Author-reported: on the synthetic motif benchmarks and MUTAG, explanation AUC is the highest of all methods in all six settings, for example 0.963 against 0.925 for GNNExplainer on BA-Shapes and 0.873 against 0.727 on MUTAG 2011.04573 tab. 2. Inference for one new instance takes about 6 to 80 ms, against 410 to 935 ms for GNNExplainer tab. 2. That comparison leaves out the explainer's own training time app. C.1. The AUC measures recovery of constructed motifs, not explanation quality in general §5.1. Feature-level explanations are out of scope app. D.

Card: Parameterized Explainer for Graph Neural Network.

Overlap-attention GNN for low-overlap point clouds (PREDATOR)

Two 3D scans taken from different places may share little surface. PREDATOR lets the two clouds exchange information before it chooses where to match 2011.13005 §3.3. Inside each cloud, superpoints are linked to their nearest neighbours, and a graph layer updates each one with a max over neighbours of a learned function of its feature and the offset to it 2011.13005 eq. 2–3. Cross-attention then links every superpoint of one cloud to every superpoint of the other, in both directions. A second within-cloud GNN refines the result §3.3. A linear head gives each superpoint an overlap logit, and the decoder adds a matchability score per point §3.3 §3.4. Interest points are sampled in proportion to overlap times matchability §4.1.

Author-reported: at 5000 samples, registration recall on 3DLoMatch (10–30% overlap) is 59.8% against 40.1% for FCGF, and 89.0% on 3DMatch [arxiv:2011.13005 tab. 2]. The sampling rule matters as much as the network. On 3DLoMatch at 5000 samples, probabilistic sampling by overlap times matchability gives 59.8%, top-k sampling 58.5% and random sampling 43.3% 2011.13005 tab. 1. Adding the overlap-attention block to FCGF lifts 3DLoMatch recall at 250 samples from 26.8 to 55.9 tab. 10. On 3DMatch the block takes 70 ms of a 271 ms pair, and the data loader takes 191 ms tab. 11. Cross-attention memory grows with the square of the superpoint count, which is why batch size is one app. A.3.

Card: PREDATOR: Registration of 3D Point Clouds with Low Overlap.

Graph ODE with restart term (STGODE)

STGODE writes graph propagation over a road sensor network as a tensor ODE with a restart term that keeps each node tied to its input state [arxiv:2106.12931 §4.2] eq. 8. It uses two adjacency matrices: a spatial one from road distances, and a semantic one from DTW similarity of sensor series §4.1 eq. 4–6. Each block is a dilated temporal convolution, an Euler solve of the ODE whose step count the paper does not state, and a second temporal convolution §4.3 §4.4 fig. 5. Blocks run in parallel for each adjacency, and their outputs are max-pooled before a two-layer MLP forecasts the next hour §4.4 §4.5. The paper argues that without the restart term, repeated propagation collapses the states onto the top eigenvector [arxiv:2106.12931 eq. 10]. The input is one hour of 5-minute steps, and the output is the next 60 minutes §5.3.

Author-reported: lowest RMSE, MAE and MAPE on all six PeMS datasets for the 60-minute horizon 2106.12931 tab. 2. Some margins are small: RMSE 32.82 against 33.65 for STSGCN on PeMS04, and 25.97 against 26.22 for ASTGCN(r) on PeMS08 tab. 2. No variance, repeated runs or significance tests are reported §5.4. The official code departs from the paper in ways that change the model, see Contradictions.

Card: Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting.

Mesh GNN with a stress-divergence penalty (P-DivGNN)

P-DivGNN predicts the stress at every node of a periodic micro-structure mesh, given the cell's mean stress 2507.05291 §2.2 §3. Each mesh node is a graph node carrying the mean stress, its position and a boundary label. Periodic edges join nodes on opposite sides of the square cell §3.1 fig. 2. The network is an encode-process-decode message-passing GNN with latent width 128 and ten steps that share one set of weights §3.2. The loss adds to the NMSE a penalty on the mean squared discrete stress divergence, weighted by λ, which pushes the prediction towards local equilibrium §3.3 eq. 41–42.

Author-reported: on the linear dataset the NMSE falls from 1.13e-2 for a periodic GNN without the penalty to 1.08e-2, and the mean divergence falls from 1.11e-3 to 3.23e-4 2507.05291 tab. 1. On the hyperelastic dataset the NMSE falls from 5.36e-2 to 2.18e-2 tab. 2. Inference is about 500 times faster than finite-element simulation on hyperelastic meshes §5.3.1. That figure compares GPU inference with CPU FE, and it excludes training §5.3.1. The penalty weight is tied to the stress scale, which is why the paper uses λ = 1e-2 for hyperelastic data §5.2.

Card: Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity.

Node-subgraph contrast for unsupervised anomaly scores (CoLA)

Each node is paired with a small subgraph sampled around it, and also with a subgraph sampled around another node. A one-layer GCN with a bilinear discriminator learns to tell these pairs apart 2103.00113 §4.1 §4.2 eq. 8. No anomaly labels are used. A node's score is the average, over R = 256 sampled rounds, of the negative-pair score minus the positive-pair score, so a higher score means more anomalous 2103.00113 §4.3 eq. 11–12 §5.2.3. Subgraphs have 4 nodes in the experiments 2103.00113 §5.2.3.

Author-reported ROC-AUC is the best of the compared methods in all seven benchmark columns, with 0.9512 on Pubmed 2103.00113 tab. 3. The benchmark anomalies are injected: dense cliques of unrelated nodes, and contextual copies of distant attributes. The scores therefore measure recovery of injected anomalies, not real anomaly rates 2103.00113 §5.1. The released code has no loader for the ogbn-arxiv row, so that row cannot be reproduced from the repository utils.py.

Card: Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning.

Transformer with graph structural biases (Graphormer)

Graphormer is an ordinary Transformer encoder with three additions that carry graph structure. Each node gets learned embeddings for its in-degree and its out-degree 2106.05234 §3.1 eq. 5. Each shortest-path distance between two nodes has one learned scalar, added to their attention score eq. 6. A third term averages learned weights over the edge features along one shortest path eq. 7. An extra graph token, linked to every node, carries the graph-level read-out 2106.05234 §3.2. The paper states that a Graphormer layer can represent the aggregate and combine steps of GIN, GCN and GraphSAGE, given suitable weights 2106.05234 §3.3 app. A.

Author-reported: validation MAE 0.1234 on PCQM4M-LSC against 0.1395 for GIN-VN 2106.05234 tab. 1, and MolHIV AUC 80.51 with FLAG augmentation 2106.05234 tab. 3. The paper names the cost of full attention, which grows with the square of the node count, as a main limitation and leaves large graphs to future work 2106.05234 §6. The text describes pre-layer-norm, but the PCQM4M and ZINC scripts train post-layer-norm unless a flag is set pcqv2.sh.

Card: Do Transformers Really Perform Bad for Graph Representation?.

Learnable positional stream (LSPE)

LSPE keeps a second vector per node, its positional features, next to its structural features. Both are updated at every layer. The positional update is a message-passing function of its own with a tanh output, so positions can be negative 2110.07875 §3.1 eq. 7–9. Starting positions come from random-walk return probabilities (RWPE) or from Laplacian eigenvectors (LapPE). The paper prefers RWPE, which avoids the sign ambiguity of eigenvectors 2110.07875 §2 §3.1. The same two-stream update is applied to GatedGCN and PNA, and to the Transformer GNNs SAN and GraphiT 2110.07875 app. C.

Author-reported: GatedGCN with LSPE and the optional Laplacian loss reaches test MAE 0.090 ± 0.001 on ZINC, against 0.251 ± 0.009 without positional encoding 2110.07875 tab. 1. The Laplacian loss moves the best ZINC score only from 0.093 to 0.090 2110.07875 §4.2. On the two OGB datasets the authors report results comparable to the baselines, not clear gains 2110.07875 §4.2 tab. 2.

Card: Graph Neural Networks with Learnable Structural and Positional Representations.

All-pair message passing with a learned sparse graph (NodeFormer)

NodeFormer lets every node exchange messages with every other node in each layer, without building the full N × N attention table. It writes softmax attention as an inner product of random feature maps, so the sums over nodes are computed once and shared by all queries, which gives cost linear in the number of nodes 2306.08385 §3.1 eq. 3–5. Gumbel noise on the logits, scaled by a temperature τ, turns the attention into a relaxed one-neighbour sample per node. The layer averages K such draws, so each layer has a sparse latent graph that differs from layer to layer §3.1 eq. 6–7 alg. 1. The paper's bound on the random-feature error depends on the number of features and on τ, not on N §3.2. If an input graph exists, the model adds a learned relational bias for observed edges and a likelihood term that rewards high probability on them §3.3 §3.4 eq. 8–10.

Author-reported: on OGB-Proteins, 77.45 ROC-AUC against 74.63 for GraphSAINT-GAT, with 3.2 GB against 5.2 GB of training memory [arxiv:2306.08385 tab. 2]. On Amazon2M it reaches 87.85 accuracy against 85.17 for GraphSAINT-GAT tab. 3. The ordinary-softmax rows at the same τ are 1.3 to 2.0 points lower on OGB-Proteins, which is the paper's evidence for the Gumbel operator tab. 2 §4.4. Relative to LDS, the paper reports up to 93.1% less training time and 97.9% less inference time §4.4. The model is not evaluated on graph classification §2.

The released code departs from the paper's formulas in several places. It scales queries and keys by d^(-1/4) on top of the τ scaling, draws Gumbel noise only in training, and concatenates the heads where the appendix says they are averaged 2306.08385 app. C.1 nodeformer.py nodeformer.py nodeformer.py. The repository has no license file, so implementers should work from the equations and not copy code 2306.08385 §Pitfalls.

Card: NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification.

Lane topology from endpoint gaps and query similarity (TopoLogic)

Lane detectors that predict connections with an MLP on each lane query encode every lane alone, so the endpoints of two connected lanes rarely coincide exactly 2405.14747 §1. TopoLogic adds two matrices. The first scores each lane pair by the gap between the end of one lane and the start of the other 2405.14747 §3.3 eq. 1–3. A learnable function of that gap, exp(−x^α / (λσ)), maps it to a score eq. 4. The authors argue that this form tolerates larger endpoint shifts than their Gaussian, sigmoid and tanh alternatives 2405.14747 §3.3 fig. 3. The second matrix is a sigmoid of the dot product of two three-layer MLP encodings of the lane queries 2405.14747 §3.4 eq. 7–9. Two learnable scalars combine the matrices eq. 10, and the result feeds a graph layer in each decoder layer. That layer mixes each lane's features with those of the lanes it connects to 2405.14747 §3.2 fig. 2. The paper gives no equation for this graph update. Only the similarity matrix receives a topology loss; the geometric matrix is trained only through the detection loss 2405.14747 §3.6.

Author-reported on OpenLane-V2 subset_A with a ResNet-50 backbone: TOP_ll 23.9 against 10.9 for TopoNet, and OLS 44.1 against 39.8 (v2.1.0) 2405.14747 tab. 1. Geometry alone reaches 20.1 of the 23.9, similarity alone 12.9, and an MLP on queries 10.8 tab. 4. Added after training, without retraining, the geometric step raises TopoNet's TOP_ll from 10.9 to 22.3 tab. 5. Every number comes from one benchmark, and the paper states that the work is for research only §5.

Card: TopoLogic.

Point-lane graph with endpoint queries (TopoPoint)

Lane queries are supervised together with the whole lane, so the two ends of connected lanes often do not coincide in the output 2505.17771 §1 fig. 1. TopoPoint adds one query per endpoint, separate from the lane queries §3.4. Both sets first pass through a merged self-attention, with geometric biases from the TopoLogic mapping added to the logits eq. 3–8 §3.4.

The point-lane graph convolution, PLGCN, passes messages between points and lanes. Its adjacency is built from the point-lane topology and the geometric matrix, with two learnable weights. Points receive messages from lanes through it, and lanes receive from points through its transpose [arxiv:2505.17771 eq. 11–12] §3.4. The lane branch adds a lane-lane graph convolution, with adjacency I + M_ll + M_llᵀ, and a traffic-to-lane convolution, and PLGCN runs once before and once after this step eq. 13–16 fig. 3. Three topology matrices, point-lane, lane-lane and lane-traffic, come from sigmoids of MLP dot products eq. 18–20 §3.5.

At inference, points and lanes scoring above 0.3 are kept. Each kept point is averaged with the kept lane ends within 1.5 m, and each matched lane takes that average as its endpoint 2505.17771 alg. 1 §3.7 §4.2. The algorithm does not say which end of a lane is matched. The released code does this differently, see Contradictions.

Author-reported on OpenLane-V2 subset_A, with ResNet-50 and 24 epochs 2505.17771 tab. 1: OLS 48.8 against 44.1 for TopoLogic, and DET_p 52.6 against 45.2. On subset_B, OLS is 49.2 against 42.3. DET_p is the authors' own endpoint metric §4.1 eq. 23, and TopoNet, TopoMLP and TopoLogic DET_p were computed by the authors, so only OLS is a shared benchmark number tab. 1. In the ablation, which starts from a re-run TopoLogic baseline tab. 2, the merged self-attention adds 5.0 DET_p on top of the front-view change. The point-lane graph convolutions add 0.7 OLS and 2.0 DET_p, and the matching step adds 0.5 OLS and 0.8 DET_p. The whole graph network, when removed, lowers subset_A OLS from 48.8 to 46.2 and DET_p from 52.6 to 48.6 tab. 3.

Card: TopoPoint.

Pre-trained long-history encoder feeding a sparse learned graph (STEP)

STEP adds a frozen time-series Transformer to a Graph WaveNet forecaster. The Transformer is pre-trained once per dataset by reconstructing masked patches of a long history 2206.09113 §3.1 §4.1. Its state for the last short patch is added to the backend's latent features, and its states build a kNN target that regularises a Gumbel-sampled sparse graph 2206.09113 eq. 3 eq. 5. The forecaster reads only 12 steps. Author-reported horizon-12 MAE is 3.37 on METR-LA against 3.53 for Graph WaveNet, and 1.79 against 1.95 on PEMS-BAY 2206.09113 tab. 2. The paper does not win every cell: on PEMS04 at horizon 12 its RMSE of 31.33 is behind GMAN's 30.21 and is not marked significant tab. 2. The released code drops the paper's dynamic term from the graph logits, so the learned graph is nearly static, and test-time predictions are random unless the sampler is seeded [arxiv:2206.09113 Paper vs code] [Pitfalls].

Card: STEP.

Signed and directed edges with a magnetic Laplacian (MSGNN)

MSGNN builds a Hermitian matrix in which an edge's sign sits in the real part and its direction in a phase, scaled by a charge parameter q [arxiv:2209.00546 §3.2]. Its normalised form has eigenvalues in [0, 2] §3.2. The network is two layers of first-order complex Chebyshev filters with real weights and a complex ReLU §3.3 §3.4. With positive weights it reduces to MagNet, and with no direction to the signed Laplacian §2 §3.2. Author-reported link-prediction accuracy is 73.0 on BitCoin-OTC sign prediction, against 70.1 for SSSNET, and 86.3 on Epinions direction prediction, against 73.9 for SSSNET [arxiv:2209.00546 tab. 1]. The paper claims the highest accuracy in all 25 link-prediction cells; on FiLL 5C it ties SNEA, so the claim holds outright in 24 §4.4.2 tab. 1. Node clustering is evaluated only on synthetic graphs §4.4.1. The main table's q is not stated. The card reads the released code as computing q0 once, from the first split, a reading it did not run 2209.00546 Paper vs code.

Card: MSGNN.

Adaptive mixing of low-pass, high-pass and identity channels (ACM-GCN)

Each ACM-GCN layer runs three channels: a low-pass average of neighbours, a high-pass neighbour difference and the node's own features. A learned, per-node softmax weights them 2210.07606 §4.2. A second option, ACMII, applies the ReLU before propagation instead §4.2. ACM+ and ACM++ add a structure channel and a residual app. B. The paper also proposes a label-free aggregation homophily that compares same-class and other-class similarity after aggregation, and reports that it tracks GNN accuracy better than the edge, node and class homophily measures §3.1 fig. 2. On random 60/20/20 splits, ACM-GCN reaches 94.75 on Cornell against 82.46 for GCN, and 90.66 on PubMed against 88.90 for GCN 2210.07606 app. A.1. On the Geom-GCN 48/32/20 splits its Cornell score of 85.14 is below GGCN (85.68) and GloGNN++ (85.95) app. A.2. Removing the mixing step costs about three points on Cornell, 91.64 against 94.75 tab. 1. Per-epoch time is about twice GCN's on Cornell tab. 1. The released code multiplies the mix by 3 and never applies the layer normalisation the appendix describes [arxiv:2210.07606 Paper vs code].

Card: Revisiting Heterophily For Graph Neural Networks.

Fully connected space-time graph in the Fourier domain (FourierGNN)

FourierGNN treats a window of N series over T steps as one fully connected graph with N·T nodes 2311.06190 §4.1. Each layer multiplies the spectrum by a complex d-by-d matrix that all frequencies share, and it sums the layer outputs over K = 3 orders §4.2 app. F.4. The shared matrix does not grow with the window: on ECG it has 0.18M parameters against 82.96M for a version with one matrix per frequency app. C.2. Author-reported horizon-12 results are a Traffic MAE of 0.011 against 0.013 for GraphWaveNet, and an Electricity MAE of 0.051 against 0.055 for FEDformer 2311.06190 tab. 1. Traffic uses 190,564 parameters against 280,860 for GraphWaveNet tab. 3. Its Traffic MAPE of 28.71 is above LSTNet's 25.77 tab. 1. The released code uses diagonal weights, builds no adjacency and compresses time to eight steps, so it is a different model from the paper's equations [arxiv:2311.06190 Paper vs code].

Card: FourierGNN.

Per-period learned graphs for multivariate forecasting (MSGNet)

MSGNet forecasts several series together by treating each strong period of the input as its own scale. An FFT picks the k strongest periods, and the series is reshaped for each one 2401.00423 §4.2 eq. 3 eq. 4. Each scale has its own learned adjacency, a softmax over a ReLU of two low-rank embeddings, and a Mixhop graph convolution over its powers §4.3 eq. 6 eq. 7. Self-attention then runs within each period §4.4 eq. 8, and the scales are summed with softmax weights over their amplitudes eq. 9. Author-reported: average rank 1.813 across eight datasets against 2.750 for TimesNet 2401.00423 tab. 1, and average MSE on Flight of 0.208 against 0.265 §5.4. The efficiency table shows lower time per epoch than TimesNet at every horizon, but higher GPU memory at horizons 96, 192 and 336 tab. 7. The released code differs from the equations in how scales are chained and how attention is masked, so check the card's Paper vs code before implementing. Card: MSGNet.

Benchmarks and surveys

These cards do not propose a GNN, but their numbers tell an implementer how GNN baselines behave under a fixed protocol.

Large-scale graph benchmark (OGB-LSC)

OGB-LSC has three large datasets, one per kind of graph question: node classification on MAG240M, link prediction on WikiKG90M and graph regression on PCQM4M 2103.09430 §2. It ships baselines and a summary of the KDD Cup 2021 winners §2 §3. Author-reported single-model test scores on the original datasets are 69.42% accuracy for R-GAT on MAG240M [arxiv:2103.09430 tab. 2], 0.8637 MRR for ComplEx-Concat on WikiKG90M tab. 5, and 0.1494 eV MAE for GIN-virtual on PCQM4M tab. 6. The winners' ensembles score higher, but they also use labels as inputs and ensembles, so compare them only with each other §2 tab. 2.

The WikiKG90M protocol ranks the true tail among 1,000 sampled negatives and scores only the top 10. Reciprocal rank is zero beyond rank 10, and a repeated id in any top-10 list sets the whole score to zero §2.2 wikikg90m.py. The v2 dataset removes the candidate tails, and the paper reports 0.1833 MRR for ComplEx-Concat there §3. The paper does not say which split that figure comes from app. C. Compare results only under the same protocol, since ranking by training frequency alone reaches 0.75 validation MRR on v1 §2.2 §3.

Card: OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs.

Spatio-temporal forecasting benchmark (BasicTS+)

BasicTS+ runs about 45 published models through one training and evaluation pipeline, with z-score scaling and masked MAE 2310.06119 §4.1. The paper's central claim is that reported results differ across papers because of data processing, training and evaluation choices. It reports that Graph WaveNet's MAE on PEMS04, reproduced in this pipeline, is up to 33% lower than the values other papers report 2310.06119 §4.1.

The paper sorts datasets by temporal pattern and by how indistinguishable their samples are 2310.06119 §5.1 §5.2. Its reported finding is that advanced networks beat linear models only on datasets with clear patterns, and that GCN-style spatial modelling helps only on datasets whose samples are hard to tell apart 2310.06119 §6.2 §6.3. In its STF table, D2STGNN has the lowest MAE on METR-LA at 2.88 and STEP has the lowest on PEMS-BAY at 1.48 2310.06119 §6.4. The paper reports seconds per epoch next to accuracy. STEP takes 497 s per epoch on METR-LA 2310.06119 §6.4.

Molecular property prediction under distribution shift (BOOM)

BOOM holds out, for each property, the molecules whose values have the lowest density in a kernel density estimate. It evaluates 15 models, averaged over 3 runs 2505.01912 §2 app. A.1. Its headline is that the top model's average OOD error is about three times its in-distribution error 2505.01912 abstract.

Among the GNNs, GotenNet has the lowest OOD RMSE on 7 of 10 properties and MACE on 2 2505.01912 §4.1 tab. 7. Averaged over models, the 3D models have lower OOD RMSE than the graph models on all 10 properties [arxiv:2505.01912 §4.4] tab. 1. Pretraining a transformer improves ID error by 12% to 35%, but OOD error does not change significantly 2505.01912 §4.2. The OOD and ID scores are only moderately correlated across tasks, with d = 0.4678 2505.01912 §4.7. Its released QM9 split, the paper's text, and the code disagree on the size of the test sets; see Contradictions.

Large models for time series and spatio-temporal data (survey)

This survey has no experiments and trains no model. It sorts the field into time series (LM4TS) and spatio-temporal data (LM4STD), and the spatio-temporal branch covers spatio-temporal graphs, temporal knowledge graphs and video 2310.10196 §3 §5. Read it as a map of the literature, not as evidence that a GNN performs well. Its coverage claims are the authors' own 2310.10196 tab. 1.

Traffic prediction benchmark (DL-Traff)

This paper reviews grid-based and graph-based traffic models and runs a subset of them under one protocol. The graph models predict 12 future speeds from the 12 past speeds 2108.09091 §2. Author-reported: Graph WaveNet has the lowest 12-step RMSE and MAE on METR-LA, 11.485 and 4.848, and MTGNN has the lowest 12-step MAE on PeMS-BAY, 1.950 2108.09091 tab. 5. The authors say DCRNN, Graph WaveNet and MTGNN rank in the top three across datasets 2108.09091 §5.2. The shared protocol is the point of the paper, but the released code departs from the stated settings in places (see Contradictions).

Graph transformer survey (Shehzad et al.)

The survey sorts how graph structure enters self-attention: node and edge positional encodings, message-passing placements, and attention biases 2407.09777 §3.1. It also sorts how attention is computed, as global quadratic, global linear or local §3.2. Its taxonomy has four types: shallow, deep, scalable and pre-trained §4. It runs no experiments. Its tables are the authors' own reading of the original papers, and some rows conflict with the text, for example the attention type of GAT §3.2.1 §4.1 table. Check each model against its own paper before relying on a row.

Card: Graph Transformers: A Survey.

Graph representation learning survey (Khoshraftar and An)

A survey of static and dynamic graph embedding, covering traditional methods and GNNs. It runs no experiments 2204.01855 §1 §6. For GNN limitations it lists the cause and the named fixes: expressive power, over-smoothing, scalability, long-range dependencies, catastrophic forgetting, homophily, substructures, over-squashing and design space 2204.01855 §4.6. The authors state that the survey covers more than 300 papers, which is their own count 2204.01855 §1.

Graph learning survey by method family (Xia et al.)

The survey sorts graph learning into four families: graph signal processing, matrix factorization, random walks, and deep learning on graphs 2105.00696 §1.3. The deep learning family covers graph convolutional networks, graph attention networks, graph auto-encoders and spatial-temporal networks 2105.00696 §2.4. It runs no experiments and reports no benchmark numbers, so it maps the field rather than ranking methods. It also gives no training settings for any method 2105.00696 §1.3. Its one summary table lists methods against neural components and applications, with repeated rows and two labels that look like typos 2105.00696 tab. 2. Check each cited original before quoting a name or a result.

Card: Graph Learning: A Survey.

Graph-free forecaster with learned identities (STID)

STID drops the graph. It embeds each series' history with one linear map, then adds three learned identities: one per series, one per time-of-day slot and one per day of the week 2208.05233 §3 eq. 2. Residual MLP blocks and a linear head predict the next steps eq. 3–4. The paper's argument is that two windows can look alike in their history but have different futures, and the identities separate them 2208.05233 §1.

Author-reported: the lowest average MAE on PEMS04, PEMS07, PEMS08, PEMS-BAY and Electricity among the methods in its table, which includes DCRNN, Graph WaveNet, AGCRN, MTGNN and GMAN 2208.05233 tab. 3. It also has the lowest seconds per epoch 2208.05233 tab. 2. The results come from single runs with no seeds or spread 2208.05233 §4. The paper's Electricity setting (168 input steps, 12 outputs) differs from the released configuration (336 and 336), so name the configuration you used 2208.05233 §4.1.

Card: Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting.

Graph neural networks for traffic forecasting (survey)

The survey reviews 212 papers from 2018 to 2020 on GNNs for traffic forecasting 2101.11174 §1. It sorts the problems into flow, speed, demand and others, sorts traffic graphs into road, region and station levels, and classifies adjacency matrices as road-based, distance-based, similarity-based or dynamic 2101.11174 §3 §4.1. It lists the GNN families used, with spectral and spatial convolutions, and a typical spatio-temporal stack of a 1D-CNN and a GCN §4.2 fig. 5. The benchmark table copies results from the surveyed papers, which the authors say are not directly comparable §5.3 tab. 11. Its TaxiNYC and BikeNYC rows are 30-minute results, while its stated default horizon is 60 minutes §5.3.

Card: Graph Neural Network for Traffic Forecasting: A Survey.

Spatio-temporal GNN survey for urban data (Jin et al.)

The survey maps spatio-temporal GNNs (STGNNs) for city data such as traffic, air quality and crime. It sorts graph construction into topology, distance, similarity and interaction rules 2303.14483 §2. It sorts the building blocks into graph convolution, recurrent units, temporal convolution and self-attention, and the fusion of space and time into factorised and coupled designs 2303.14483 §5. Recent variants include adaptive graphs, multi-scale and decomposition models, and neural ODEs 2303.14483 §6 §7.4. It runs no experiments. Its literature count puts transportation above 60% of the surveyed applications 2303.14483 §4 fig. 4.

Card: Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey.

Graph neural networks for time series (survey)

The survey covers GNNs for four time-series tasks: forecasting, classification, anomaly detection and imputation. It gives an objective for each task and a taxonomy by spatial, temporal and architecture choices 2307.03759 §3. It lists four ways to build the graph from data: inverse travel distance, a 0/1 link graph, similarity between series, and Granger causality [arxiv:2307.03759 §2]. It runs no experiments, and its appendix lists benchmark datasets without results 2307.03759 app. F.

Card: A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection.

Lane topology survey (Yao et al.)

This survey sorts lane topology reasoning for HD maps into procedural modeling, aerial imagery and onboard sensors, and calls the onboard group the current state of the art 2504.01989 §2.3. It proposes no method and has no code 2504.01989 Paper vs code. Its onboard pipeline ends in a topology decoder that may be a GNN, an MLP or a language model, and it gives no equations for any of them 2504.01989 §2.3 fig. 6.

The useful part for an implementer is the metric definitions. Lane-level metrics are DET_l, with Fréchet thresholds 1.0, 2.0 and 3.0, and TOP_ll 2504.01989 eq. 6–7. The survey's tables copy scores for Topo-Boundary and OpenLane-V2, and the text does not say, row by row, whether each was re-run or copied 2504.01989 tab. 2 tab. 3. On OpenLane-V2 subset A, its TopoNet TOP_ll is 4.1, against 10.9 in the TopoLogic and TopoPoint cards; see Contradictions.

Card: A Concise Survey on Lane Topology Reasoning for HD Mapping.

Power-system review of GNN families (survey)

The review sorts GNNs into six families: spectral and spatial GCNs, graph recurrent networks, graph attention, graph generative networks, spatio-temporal GNNs and hybrid forms 2101.10025 tab. I. It then maps applications to families, covering fault diagnosis, power forecasting, power-flow approximation and synthetic data generation tab. II §III. It has no method of its own and runs no experiments. Every number it copies comes from a cited work with different data and splits, so the tables should not be ranked against one another 2101.10025 §III [Pitfalls]. It gives the renormalised graph convolution eq. 9 and the single-head attention form eq. 16 eq. 17.

Card: A Review of Graph Neural Networks and Their Applications in Power Systems.

Graph representation learning in biomedicine (survey)

A review of graph representation learning for biomedical networks, such as protein interactions, drug interactions and co-occurring medical codes. It sorts methods into shallow node embeddings, graph neural networks and generative graph models, and applies them to molecules, genomics, therapeutics and healthcare 2104.04883 §1 §2 §4–§7. It runs no experiments and gives no metrics or training settings, so use it as a map of the families and read the cited papers for numbers 2104.04883 §1. Card: Graph Representation Learning in Biomedicine.

When to use which

Implementation sketch

Four patterns: pretraining a GNN encoder on a pretext loss, a relation-typed layer, a GCN layer with a feature-similarity graph, and a layer with a learned graph filter. The pseudocode is ours. Lines follow the cited equations. The other variants use the same aggregate-and-combine form, with the differences listed above.

# Step A: pretext pre-training of a GNN encoder  [arxiv:2103.00111 eq. 1]
# Input:  unlabelled graphs D = [(X, A), ...]; encoder f; pretext head p
def pretrain(D, f, p, ssl_loss, opt):
    for X, A in D:
        # Node embeddings from features and adjacency  [§3.1]
        H = f(X, A)
        # Pretext loss: reconstruction, property or view agreement  [§3.2]
        loss = ssl_loss(p(H), X, A)
        opt.step(loss)
    return f

# Step B: downstream training on labels  [arxiv:2103.00111 eq. 2]
# PF: keep training f. URL: freeze f, train only q  [§3.3]
def finetune(G, y, f, q, opt, frozen):
    H = f(G.X, G.A)
    loss = cross_entropy(q(H[G.labelled]), y)
    params = q.params if frozen else f.params + q.params
    opt.step(loss, params)

# Relation-typed windowed layer  [arxiv:1908.11540 eq. 1-2]
# Input:  g (N, d) sequence features; window[i] neighbour ids incl. i;
#         rel[i][j] relation id of edge j -> i
def relation_layer(g, window, rel, W_rel, W_root):
    # Edge weights: softmax of bilinear scores over each window  [eq. 1]
    alpha = window_softmax(g, window)
    out = []
    for i in range(N):
        # Self term, then relation-specific neighbour sum  [eq. 2]
        # c_{i,r} normalisation is fixed or learned; not stated [§3.3.2]
        h = alpha[i][i] * (W_root @ g[i])
        for j in window[i]:
            if j != i:
                h += alpha[i][j] * (W_rel[rel[i][j]] @ g[j])
        out.append(relu(h))
    return out

# One SimP-GCN layer, paper formula  [arxiv:2011.09643 §4.1]
# Input:  H (N, d); A_hat, K_hat normalised original and kNN graphs
# Output: (N, d')
def simp_gcn_layer(H, A_hat, K_hat, W, w_s, b_s, w_k, b_k, gamma, activate):
    HW = H @ W                                         # (N, d')
    # Per-node balance between the two graphs, in (0, 1)  [§4.1]
    s = sigmoid(H @ w_s + b_s)                         # (N, 1)
    # Per-node self-loop count  [§4.1]
    k = H @ w_k + b_k                                  # (N, 1)
    # One activation over the combined propagation  [§4.1]
    out = s * (A_hat @ HW) + (1 - s) * (K_hat @ HW) + gamma * k * HW
    return relu(out) if activate else out

# One learned-filter layer, paper formula  [arxiv:1712.04997 eq. 9] [eq. 15]
# Input:  X (N, C); A_hat (N, N) learned, trained with the other weights
# Output: (N, C')
def ddgf_layer(X, A_hat, W, b, activate):
    # Keep the learned matrix symmetric; the paper does not say how  [§3.3.1]
    filt = 0.5 * (A_hat + A_hat.T)                     # (N, N)
    # Symmetric degree normalisation  [eq. 15]
    d = filt.sum(axis=1) ** -0.5                        # (N,)
    norm = d[:, None] * filt * d[None, :]               # (N, N)
    # Mix stations, then transform features  [eq. 9]
    out = (norm @ X) @ W + b                            # (N, C')
    return relu(out) if activate else out

Contradictions

• Graph-free versus graph-based forecasting. STID reports the lowest average MAE on five sensor datasets without using any graph 2208.05233 tab. 3. BasicTS+ finds that GCN-style spatial modelling helps only on datasets whose samples are hard to tell apart 2310.06119 §6.3. STID names the same indistinguishability as the bottleneck, but argues that identities fix it 2208.05233 §1. The two cards do not report a shared protocol, so this disagreement is not settled here.

• Survey versus itself (anomaly scores). The GNN time-series survey sums absolute channel errors for its anomaly score 2307.03759 §5.1, but describes GDN as using the maximum channel error 2307.03759 §5.2. A sum and a maximum react differently to one large channel error. The survey does not say which one to use.

• Paper versus public code (LSPE). The paper treats the Laplacian orthogonality term as differentiable 2110.07875 eq. 12. The released code detaches that term before computing it, so it adds a constant to the loss value and no gradient gatedgcn_net.py. Only the trace term trains as written.

• Paper versus public code (Graphormer). The text describes pre-layer-norm 2106.05234 §3.2, but the PCQM4M and ZINC scripts train post-layer-norm unless a flag is set pcqv2.sh. An implementation that follows the text may behave differently from the released scripts.

• Paper versus public code (DialogueGCN). The paper writes a bilinear edge score and an activation σ in both graph layers 1908.11540 eq. 1–3. The public code scores edges with a learned vector per absolute position and applies no activation in the graph layers model.py model.py. Neither reproduces the other.

• Reported numbers may be optimistic (DialogueGCN). The public IEMOCAP script prints the maximum test F1 over all epochs train_IEMOCAP.py. The official README reports 64.67 and 64.44 with a different configuration from the paper's. The paper reports 64.18 1908.11540 tab. 3.

• Compiled numbers come from different protocols. The graph self-supervision survey says it runs an experimental comparison, but most rows of its tables are copied from the original papers, which use different protocols. The survey does not say which rows were re-run 2103.00111 §8.

• Paper versus public code (SimP-GCN). The paper applies one activation to the combined propagation 2011.09643 §4.1. The released code applies ReLU to each branch and then sums them models_simp.py layers.py. The self-supervised head takes the difference of hidden states in the paper and its absolute value in the code 2011.09643 §4.2 selfsl.py. The repository has no license file, so this page cites it and copies no code.

• Baseline GCN numbers differ between cards. The survey lists GCN at 81.5 on Cora and 70.3 on Citeseer 2103.00111 tab. 5. SimP-GCN lists GCN at 81.3 and 71.5 on the same datasets 2011.09643 tab. 3. The survey also lists SimP-GCN's own numbers, 82.8, 72.6 and 81.1 2103.00111 tab. 5. The cards do not say which GCN numbers were rerun.

• Learned filter: paper versus public code. The paper's output layer applies the graph filter 1712.04997 eq. 10, and eq. 15 has one filter for the whole network. The repository, as checked for the card, has no filter in the output layer and learns one filter per hidden layer. It also uses Adam, where the paper says classic SGD 1712.04997 §5.1, and a learning rate of 0.01 against 0.005 in Table 2 1712.04997 tab. 2. The public code implements only the regular variant. The recurrent variant behind the best reported RMSE cannot be checked against code. The card's Paper vs code section lists the details.

• Readout: paper versus public code (MPNN). The paper says the MPNN readout is the mean or the sum over atoms 2004.08919 app. A. The card's check of the public code finds the mean only.

• PPI scale. GAT scores 97.3 on PPI, far above every self-supervised row (51 to 74). The PPI metric is not named, so the column cannot be compared across rows without checking each original paper 2103.00111 tab. 5.

• QA-GNN: relevance score, paper versus code. The paper defines a node's relevance as the LM probability of the node text given the QA context 2104.06378 §3.2 eq. 1. The released code instead uses the summed token loss of a sentence built from the QA context and the node name, with no tokens masked, and it centres and rescales the result on the context node 2104.06378 §Paper vs code. The code also uses 4 attention heads where the paper describes one, and it multiplies attention weights by the source's out-degree 2104.06378 §Paper vs code. Follow the paper or the code, and state which one you reproduce.

• GraIL: label order, paper versus code. The paper's first label component is the distance to u, computed while avoiding v 1911.06962 §3.1. The code computes that component with u removed, so it holds the distance to v 1911.06962 §Paper vs code. Edge dropout is also scaled by PyTorch's rule, so a kept edge has weight 2 in training. The paper does not mention this 1911.06962 §Paper vs code. The repository has no license file.

• GreaseLM: initial interaction node and residuals, paper versus code. The paper says the interaction node is initialised randomly [arxiv:2201.08860 §4.3]. The code sets it to zero 2201.08860 §Paper vs code. The code's GNN layer also has no residual term, which the paper's equation includes 2201.08860 §Paper vs code. The text gives a gain of 0.9 over LM+KG models on CommonsenseQA test, while the table gives 0.8 [arxiv:2201.08860 tab. 2] §6.

• BertGCN: default encoder, paper versus code. The paper's headline model uses BERT-base 2105.05727 §4.1. The code's default encoder is RoBERTa-base, so running the defaults gives RoBERTaGCN, not BertGCN 2105.05727 §Paper vs code. The code also truncates BERT's input to 128 tokens, while the graph uses the full text 2105.05727 §Pitfalls.

• GFlowNet: epsilon and loss scale, paper versus code. The paper's epsilon is 2.5e-5 2106.04399 app. A.4. The molecule configuration in the code sets it to about 2.4e-8 2106.04399 §Paper vs code. The paper sums the loss over trajectory states, while the code averages each part over the batch 2106.04399 §Paper vs code. Learning rates do not transfer directly between the two.

• DiGress: edge weight and guidance, paper versus code. The paper leaves the edge weight lambda unset, while the code uses 5 in every experiment 2209.14734 §3.2 §Paper vs code. The regressor for guided generation is not in the repository, and its scale is not stated in the paper, so the guided QM9 results cannot be reproduced from the repository 2209.14734 §5 alg. 3.

• GraphCast: deployed model and training. The released weights include an operational model fine-tuned on HRES data, which the paper does not describe 2212.12794 §Paper vs code. The paper's training schedule has no counterpart in the repository 2212.12794 app. §4.5.

• BasicTS+: evaluation scale. The paper reports metrics on re-normalised data 2310.06119 §4.2. The released code leaves rescaling off by default, so its default metrics are on normalised values [arxiv:2310.06119 §Paper vs code]. The code's WAPE and MAPE also differ from the paper's formulas 2310.06119 §Paper vs code.

• BOOM: test-set sizes. The paper's text gives the OOD set as the lowest 10% of QM9 and the ID set as 10% of QM9 2505.01912 app. A.1. The released code uses 10,000 OOD molecules and 5% ID [arxiv:2505.01912 §Paper vs code]. The table labels Random Forest and MLP as SMILES models, though they use RDKit descriptors 2505.01912 tab. 7 §Paper vs code.

• BCNet: normalisation and boundary loss, paper versus code. The paper uses layer normalisation and ReLU in its graph layer 2103.12340 §3.2. The code uses batch normalisation and no ReLU mask_head.py. The boundary loss is summed twice before a weight of 0.5, so one boundary term has weight 1.0 where the paper gives 0.5 2103.12340 §3.3 fcos.py.

• GraphFormers: attention form and masking, paper versus code. The paper's asymmetric attention takes its queries from the plain tokens 2105.02605 eq. 4. The code uses standard self-attention over the augmented tokens modeling_graphformers.py. The paper masks the tokens of every input node 2105.02605 §3.3; the code masks only the centre node data_handler.py.

• GRIL: kernel width and validation split, paper versus code. The paper sets the kernel width to the standard deviation of distances 2108.00298 app. B.1. The code divides by that standard deviation squared air_quality.py. The paper's traffic and CER-E split is 70 / 10 / 20 2108.00298 app. B.2; the code gives 72 / 8 / 20.

• EERM: editor normalisation and resets, paper versus code. The paper normalises each editor row with a softmax 2202.02466 app. A. The code takes the softmax over the other dimension model.py. Algorithm 1 carries the editors across iterations 2202.02466 alg. 1; the code resets them every epoch main.py.

• OnePose: attention form, paper versus code. The paper says linear attention is used in all attention layers 2205.12257 §4.2. In the code only the self and cross layers use it; the aggregation layers use softmax attention GATs.py. The aggregation score is an inner product in the paper 2205.12257 §3.2 and an additive LeakyReLU score in the code GATs.py.

• DRAGON: negative term and pretraining recipe. Eq. 10 as printed gives the negative triples the same sign as the positive one, so the printed objective has no finite minimum. The code uses −log σ(−φ′) instead 2210.09338 eq. 10 modeling_gnn.py. The released pretraining script is a CommonsenseQA demo, not the recipe in the paper 2210.09338 §3.1 run_pretrain.sh.

• EqMotion: layers, paper versus code. The code adds a residual term in the inner-agent attention that eq. 6 does not have 2303.10876 eq. 6 gcl_t.py. It also passes the aggregated factors through an extra MLP that eq. 7 does not include 2303.10876 eq. 7 gcl_t.py. The equivariance theorem covers the layers as written, so it does not cover these additions 2303.10876 §4.6.

• DL-Traff: grid settings, paper versus code. The paper states MAE for every model and a learning rate of 0.001 2108.09091 §5.1. The grid code uses MSE Param_STDN.py and a learning rate of 0.0001 Param_STDN.py. It computes only the MSE, so the paper's grid MAE and MAPE cannot be reproduced from it predflowio_STDN_noflow.py.

• PGP: which encoder gives the headline row. Table 1's PGP row matches the encoder with no GNN layers, while the text describes two GAT layers 2106.15004 tab. 1 tab. 2 §5. The paper does not say which setting produced Table 1. The gap is 0.01 MinADE10, so the choice does not change the comparison's direction.

• Heterophilic GCN baselines differ between cards. SimP-GCN reports GCN at 52.16 on Texas and 52.70 on Cornell, copied from GCNII [arxiv:2011.09643 tab. 4] §5.2. GPR-GNN reports GCN at 75.16 on Texas and 66.72 on Cornell 2006.07988 tab. 2. GPR-GNN uses random 60 / 20 / 20 splits on heterophilic graphs §5. The cited sections do not say whether the two papers' splits and runs match, so the numbers are not reconciled here.

• Filter theory versus the training recipe (GPR-GNN). The over-smoothing argument assumes SGD with a decreasing learning rate 2006.07988 §4 app. A.4. The experiments use Adam app. A.9. The cited sections do not say how the argument applies to Adam.

• Threshold selection (GDN). The paper sets the threshold to the maximum validation score 2106.06947 §3.6 §4.3. The released script's default picks the threshold that maximises F1 on the test labels run.sh evaluate.py. Numbers from the default run may therefore be optimistic.

• Text versus table (CTR-GCN). The paper says its method is best under nearly all benchmarks 2107.12213 §4.6. On NTU RGB+D cross-view, DDGCN scores 97.1 against 96.8 for CTR-GCN tab. 6.

• learn2branch: GNN architecture, paper versus code. The paper has one constraint node per LP row 1906.01629 §4.2. The code makes one node per finite side of a row, so a ranged row gives two nodes with opposite-sign features 1906.01629 §Paper vs code. The code also adds a two-layer embedding for constraints and for variables, and an extra prenorm inside the message, neither of which the paper describes [arxiv:1906.01629 §Paper vs code]. Reproduce one of the two and say which.

• learn2branch: table counts disagree. For set covering, the GCNN node counts for medium and hard instances are 1450 and 29981 in tab. 2, but 1870 and 56348 in tab. 3. The times agree to rounding 1906.01629 tab. 2 tab. 3. The mapping of tab. 2's four blocks to problem families is inferred, because the titles sit outside the blocks in the source [arxiv:1906.01629 tab. 2].

• PGExplainer: relative gain. The printed 24.7% gain on BA-2motifs is measured against GNNExplainer (0.742). Against the best printed baseline, Gradient at 0.773, PGExplainer's 0.926 is about 19.8% higher, by the card's calculation from the table 2011.04573 tab. 2.

• PGExplainer: dataset size and layer sizes. The text describes 800 BA-2motifs graphs, while the table lists 1,000 2011.04573 §5.1 tab. 1. The appendix's explanation layers do not chain: the first outputs 64 values and the second takes 20 2011.04573 app. B.

• PREDATOR: headline numbers across versions. The arXiv abstract and the LaTeX source give different headline figures, "more than 20%" and "89%" against "more than 15 percent points" and "90.6%". The table gives 89.0 at 5000 samples and 90.6 at 1000 2011.13005 tab. 2. Cite the tables.

• PREDATOR: loss and training, paper versus code. The paper sums the matchability loss over all points 2011.13005 eq. 11; the code computes it only on ground-truth overlap points 2011.13005 §Paper vs code. The paper adds the matchability loss after a few epochs §3.5; the code keeps its weight at zero until validation feature-match recall passes 0.3 [§Paper vs code]. The paper gives no temperature for the soft assignment, and the code learns one 2011.13005 eq. 7 §Paper vs code.

• PREDATOR: split sizes. The text gives 46 training, 8 validation and 8 test scenes 2011.13005 §4.1. The appendix gives 54 training and 8 test scenes for the official benchmark 2011.13005 app. A.2.

• STGODE: model structure, paper versus code. The paper's temporal convolution is a dilated stack with a residual 2106.12931 §4.3. The code returns the ReLU of its input, and skips the dilated stack, whenever the input and output channel counts match. That is six of 24 temporal-convolution instances 2106.12931 §Paper vs code. The code scales the spatial term by a learnable factor that starts near 0.345, not the paper's fixed α = 0.8 2106.12931 §3.2 §Paper vs code. Its U and W matrices are not orthogonal as the paper requires, so the eigenvalue bound of §4.2 does not carry over 2106.12931 §4.2 §Paper vs code.

• STGODE: graphs, training and leakage. The code z-scores distances before the Gaussian kernel, while the paper uses raw distances [arxiv:2106.12931 eq. 4]. The code's semantic graph uses a daily profile and a z-score-based kernel. By the card's derivation from the code, not run, it keeps pairs whose DTW distance lies within about 0.07 standard deviations of the mean [§Paper vs code]. Z-score statistics and the daily profile use the full series, including validation and test periods §Paper vs code. The paper uses Adam at learning rate 0.01 with batch 32, while the code uses AdamW at 2e-3 with batch 16 2106.12931 §5.3 §Paper vs code.

• STGODE: names and sensor counts. The text says PeMSD3 and gives 288 sensors for PeMSD7(M), where the table and the code say PeMS03 and 228 2106.12931 §5.1 tab. 1.

• P-DivGNN: learning rate and penalty weight, paper versus code. The paper uses learning rate 1e-2 on both datasets 2507.05291 §4.2 §5.2. Both released training configs use 0.001 §Paper vs code. The paper sets λ = 1e-2 for hyperelastic data, and the hyperelastic config uses 10 §5.2 [§Paper vs code].

• P-DivGNN: stopping, edges and divergence values. The paper uses early stopping with patience 20 on validation NMSE §4.2. The released configs turn it off and keep the checkpoint with the lowest test loss §Paper vs code. The paper sets periodic edge features to zero §3.1; the code standardises them with the other edge features §Paper vs code. Section 4.3 gives a linear divergence of 4.56e-4 for P-DivGNN, and tab. 1 gives 3.23e-4 [arxiv:2507.05291 §4.3] tab. 1.

• Paper versus public code (TopoLogic). The paper's mapping has a learnable α, starting at 0.2, and a learnable λ, starting at 2, with σ in the exponent 2405.14747 §3.3 §4.2. The released code learns P and w instead, starting at 2 and 10, and computes σ without using it [arxiv:2405.14747 §Paper vs code]. Its inference path hard-codes P = 2, w = 11.5275 and both fusion scalars at 1, so reported results may not reflect the learned values §Paper vs code.

• Lane-topology numbers, survey versus other cards. On OpenLane-V2 subset A, the survey's table gives TopoNet TOP_ll 4.1, TopoMLP 7.2, and TopoLogic DET_l 34.4 and TOP_ll 23.4 2504.01989 tab. 3. TopoPoint's table gives 10.9, 21.6, 29.9 and 23.9 for the same rows 2505.17771 tab. 1, and the TopoLogic card gives 23.9 and 10.9 for TopoLogic and TopoNet [arxiv:2405.14747 tab. 1]. The survey does not say which source its rows were copied from, so the numbers are not reconciled here.

• Paper versus public code (TopoPoint). The paper's point-to-lane matching is commented out in the released code, and the active refinement matches lane ends to other lanes' starts with a similarity threshold, not the paper's 1.5 m distance 2505.17771 §Paper vs code. The code also builds no geometric attention mask and uses unnormalised graph adjacencies §Paper vs code. Its geometric matrices are detached, so the topology losses do not reach the endpoints through them 2505.17771 §Pitfalls. The ablation's matching gain is for the paper's version, not for the released code.

• Graph WaveNet numbers across papers. BasicTS+ reports that, in its own pipeline, Graph WaveNet's PEMS04 MAE is up to 33% lower than other papers report 2310.06119 §4.1. STEP's table gives Graph WaveNet an MAE of 20.69 at horizon 12 on PEMS04 2206.09113 tab. 2. The two cards use different protocols and horizons, so the figures are not directly comparable, and this card does not settle which is right.

Papers

• Predicting Station-level Hourly Demands in a Large-scale Bike-sharing Network: a GCN whose graph filter is learned from data, with a regular and an LSTM-based variant for hourly bike demand.
• DialogueGCN: A Graph Convolutional Neural Network for Emotion Recognition in Conversation: a windowed, relation-typed graph layer over a BiGRU encoder for text-only emotion recognition in conversation.
• Graph Self-Supervised Learning: A Survey: frames GNN pretraining as an encoder trained on a pretext loss, with three training schemes and compiled node- and graph-classification results.
• Graph Contrastive Learning with Adaptive Augmentation: GCA, two centrality-guided augmented views of a graph with a node-level contrastive loss, for label-free node embeddings.
• DeepPurpose: A Deep Learning Library for Drug-Target Interaction Prediction: a library of encoder-decoder models for drug-target interaction, with an MPNN compound encoder and several protein encoders.
• Convolutional Networks on Graphs for Learning Molecular Fingerprints: replaces the hashing and indexing steps of circular fingerprints with learnable, softmax-pooled ones, trained end-to-end on molecular regression.
• Node Similarity Preserving Graph Convolutional Networks: adds a feature-similarity kNN graph and a self-supervised pair regression to a two-layer GCN, for graphs where linked nodes differ and under structure attacks.
• A Comprehensive Survey of Scene Graphs: Generation and Application: a survey that names GNN-based scene graph generation as one model family, with no GNN equations of its own.
• Inductive Relation Prediction by Subgraph Reasoning: GraIL, which scores a knowledge-graph triple from its enclosing subgraph with double-radius labels and no entity embeddings.
• QA-GNN: Reasoning with Language Models and Knowledge Graphs for Question Answering: joins an LM with a retrieved ConceptNet subgraph, scores node relevance with the LM, and reasons with an attention GNN over a QA-context node.
• GreaseLM: Graph REASoning Enhanced Language Models for Question Answering: runs an LM and a graph network side by side and exchanges information through an interaction token and an interaction node in several fusion layers.
• BertGCN: Transductive Text Classification by Combining GCN and BERT: a word-document graph whose document nodes start from BERT embeddings, trained jointly with a memory bank and mixed with a BERT-only prediction.
• Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation: GFlowNet, which uses a message-passing network as the flow predictor to sample objects in proportion to their reward.
• DiGress: Discrete Denoising diffusion for graph generation: one-shot graph generation by discrete denoising diffusion with a graph transformer denoiser, with cycle and spectral features and property guidance.
• GraphCast: Learning skillful medium-range global weather forecasting: an encode-process-decode mesh GNN with 16 processor layers that forecasts global weather in six-hour steps.
• Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis: BasicTS+, a shared pipeline for forecasting benchmarks and a dataset split by temporal pattern and sample indistinguishability.
• Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlook: a survey of LLM and foundation-model work for time series and spatio-temporal graphs, with no experiments.
• BOOM: a benchmark that holds out low-density molecular property values, with 15 models including several GNNs.
• HDMI: High-order Deep Multiplex Infomax: a per-layer GCN with mutual-information training and attention fusion, for unlabelled multiplex networks.
• Deep Occlusion-Aware Instance Segmentation with Overlapping BiLayers: BCNet, two non-local graph layers in a mask head, the first modelling the occluder.
• GraphFormers: GNN-nested Transformers for Representation Learning on Textual Graph: a graph-attention step inside each layer of a BERT-style encoder, for textual graphs.
• Multimodal Trajectory Prediction Conditioned on Lane-Graph Traversals: PGP, a lane-graph policy and attention decoder that predicts several vehicle paths.
• GRIL: GRIL, a bidirectional GRU whose gates are message-passing networks, for sensor imputation.
• DL-Traff: Survey and Benchmark of Deep Learning Models for Urban Traffic Prediction: a survey and a shared-protocol benchmark of grid and graph traffic models.
• Handling Distribution Shifts on Graphs: An Invariance Perspective: EERM, learned graph editors that create virtual environments for node-level generalisation.
• A Survey on Graph Representation Learning Methods: a survey of static and dynamic graph embedding, with GNN limitations and named fixes.
• OnePose: One-Shot Object Pose Estimation without CAD Models: a graph attention matcher from 2D features to the 3D points of a scanned object.
• Deep Bidirectional Language-Knowledge Graph Pretraining: DRAGON, joint pretraining of one encoder on text and a local knowledge-graph subgraph.
• EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning: an equivariant interaction graph for predicting the motion of several agents.
• MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing: concatenates propagated features over several adjacency powers, each with its own weights.
• Adaptive Universal Generalized PageRank Graph Neural Network: GPR-GNN, learned weights on K+1 propagation steps of an MLP's output, which may be negative.
• BADet: Boundary-Aware 3D Object Detection from Point Clouds: graph refinement of LiDAR proposals with max-aggregated messages and learned alignment offsets.
• Graph Neural Network-Based Anomaly Detection in Multivariate Time Series: GDN, a sensor graph learned from embedding similarity, with graph-attention forecasting and deviation scoring.
• Channel-wise Topology Refinement Graph Convolution for Skeleton-Based Action Recognition: CTR-GC, a shared skeleton adjacency refined per channel and per sample from joint correlations.
• Exact Combinatorial Optimization with Graph Convolutional Neural Networks: a bipartite GCN that learns branch-and-bound variable selection by imitating strong branching.
• Parameterized Explainer for Graph Neural Network: PGExplainer, one shared edge-scoring MLP that explains a frozen GNN for many instances and unseen graphs.
• PREDATOR: Registration of 3D Point Clouds with Low Overlap: a GNN and cross-attention in the bottleneck that predict overlap and matchability for scans with little shared surface.
• Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting: STGODE, graph propagation written as a tensor ODE with a restart term, over distance and DTW graphs.
• Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity: P-DivGNN, a mesh GNN with periodic edges and a stress-divergence penalty for micro-structure stress.
• Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning: CoLA, a one-layer GCN that scores each node by how well it matches sampled local subgraphs, with no labels.
• Do Transformers Really Perform Bad for Graph Representation?: Graphormer, a Transformer with degree, shortest-path and path-edge attention terms and a graph token.
• Graph Neural Networks with Learnable Structural and Positional Representations: LSPE, a learned per-node positional stream updated in every layer, started from random-walk return probabilities.
• Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting: STID, an MLP forecaster with learned series and time identities and no graph.
• Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey: a survey of spatio-temporal GNNs for city data, covering graph construction and model variants, with no experiments.
• A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection: a survey of GNNs for four time-series tasks, with task objectives and graph-construction rules, and no experiments.
• TopoLogic: An Interpretable Pipeline for Lane Topology Reasoning on Driving Scenes: a lane-topology GNN layer fed by an endpoint-gap matrix with a learnable distance mapping and a query-similarity matrix.
• TopoPoint: Enhance Topology Reasoning via Endpoint Detection in Autonomous Driving: separate endpoint queries and a point-lane graph network, with a matching step that pulls lane ends to detected points at inference.
• A Concise Survey on Lane Topology Reasoning for HD Mapping: a survey of lane topology methods, their metrics and their OpenLane-V2 and Topo-Boundary scores, with no method of its own.
• Graph Learning: A Survey: a survey that sorts graph learning into four families, graph deep learning among them, with no experiments.
• Adversarial Graph Augmentation to Improve Graph Contrastive Learning: AD-GCL, a learned edge-drop augmenter trained against a GIN encoder, with a penalty on the drop ratio.
• NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification: all-pair attention in linear time through random features and a sparse latent graph per layer.
• OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs: three large graph datasets with baselines, and a summary of the KDD Cup 2021 winners.
• Graph Transformers: A Survey: a survey of how graph structure enters attention and how attention is computed, with no experiments.
• Graph Neural Network for Traffic Forecasting: A Survey: a survey of GNNs for traffic forecasting from 2018 to 2020, with a benchmark table copied from the surveyed papers.
• STEP: Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting: a frozen masked-patch Transformer pre-trained on long history, feeding a Graph WaveNet backend and a Gumbel-sampled sparse graph.
• MSGNN: a two-layer complex spectral GNN on a magnetic signed Laplacian, for signed and directed graphs.
• Revisiting Heterophily For Graph Neural Networks: ACM-GCN, per-node adaptive mixing of low-pass, high-pass and identity channels, plus a post-aggregation homophily measure.
• FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective: a fully connected space-time graph of series and steps, with shared complex Fourier-domain layers.
• A Review of Graph Neural Networks and Their Applications in Power Systems: a survey of GNN families and their power-system applications, with no experiments of its own.
• Learning to Drop: Robust Graph Neural Network via Topological Denoising: PTDNet, a per-layer edge scorer trained with the GNN, with a hard-concrete gate, an expected-edge penalty and a low-rank penalty.
• GPS-Net: Graph Property Sensing Network for Scene Graph Generation: direction-aware message passing, a node-priority focal loss and a gated frequency prior for one-stage scene graph generation.
• MSGNet: FFT-selected periods, a learned adjacency and Mixhop convolution per period, then within-period attention and an amplitude-weighted sum.
• Graph Representation Learning in Biomedicine: a review of shallow, GNN and generative graph methods for molecules, genomics, drugs and patient records, with no experiments.