mlsanityData to 7 Oct 2026

Size-Invariant Graph Representations for Graph Classification Extrapolations

arXiv 2103.05045 ↗First posted 8 Mar 2021cs.LGcited by 82

Not on the map. Why?

Abstract (arXiv)

In general, graph representation learning methods assume that the train and test data come from the same distribution. In this work we consider an underexplored area of an otherwise rapidly developing field of graph representation learning: The task of out-of-distribution (OOD) graph classification, where train and test data have different distributions, with test data unavailable during training. Our work shows it is possible to use a causal model to learn approximately invariant representations that better extrapolate between train and test data. Finally, we conclude with synthetic and real-world dataset experiments showcasing the benefits of representations that are invariant to train/test distribution shifts.

Key facts. Cited by 82 papers in the map (data through 7 Oct 2026). Builds on 87 of its 156 references that are in the map. First posted on arXiv 8 Mar 2021.

Builds on

87 of 156 references.

References · 87

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  5. 2017Inductive Representation Learning on Large Graphscited by 6,284
  6. 2018How Powerful are Graph Neural Networks?cited by 4,355
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  8. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  9. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  10. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  11. 2020Shortcut Learning in Deep Neural Networkscited by 1,928
  12. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
38 more
  1. 2019Invariant Risk Minimizationcited by 1,832
  2. 2014DeepWalk: Online Learning of Social Representationscited by 1,543
  3. 2016Variational Graph Auto-Encoderscited by 1,373
  4. 2020WILDS: A Benchmark of in-the-Wild Distribution Shiftscited by 1,366
  5. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  6. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 929
  7. 2016Practical Black-Box Attacks against Machine Learningcited by 893
  8. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  9. 2018Link Prediction Based on Graph Neural Networkscited by 829
  10. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  11. 2020Out-of-Distribution Generalization via Risk Extrapolation (REx)cited by 737
  12. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  13. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  14. 2020Directional Message Passing for Molecular Graphscited by 556
  15. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  16. 2020Underspecification Presents Challenges for Credibility in Modern Machine Learningcited by 488
  17. 2020Principal Neighbourhood Aggregation for Graph Netscited by 477
  18. 2019Predicting Dynamic Embedding Trajectory in Temporal Interaction Networkscited by 443
  19. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  20. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  21. 2018Deep Learning on Graphs: A Surveycited by 393
  22. 2019Provably Powerful Graph Networkscited by 385
  23. 2018Invariant and Equivariant Graph Networkscited by 339
  24. 2019Analysing Mathematical Reasoning Abilities of Neural Modelscited by 331
  25. 2016Learning Representations for Counterfactual Inferencecited by 327
  26. 2016Learning Convolutional Neural Networks for Graphscited by 314
  27. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  28. 2015Diffusion-Convolutional Neural Networkscited by 268
  29. 2019Deep Learning for Symbolic Mathematicscited by 266
  30. 2020The Risks of Invariant Risk Minimizationcited by 262
  31. 2019Representation Learning for Dynamic Graphs: A Surveycited by 260
  32. 2019Hyperbolic Graph Neural Networkscited by 244
  33. 2018Graph networks as learnable physics engines for inference and controlcited by 242
  34. 2019Causality for Machine Learningcited by 242
  35. 2019Inductive Relation Prediction by Subgraph Reasoningcited by 237
  36. 2020Can Graph Neural Networks Count Substructures?cited by 235
  37. 2020How Neural Networks Extrapolate: From Feedforward to Graph Neural Networkscited by 218
  38. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217

50 most cited of 87 All 87 (JSON)

Built on by

Cited by year

Citing papers per year: 2021: 4; 2022: 24; 2023: 26; 2024: 18; 2025: 10.

82 papers.

Sort:

By area:

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2022Discovering Invariant Rationales for Graph Neural Networkscited by 186
  3. 2022Handling Distribution Shifts on Graphs: An Invariance Perspectivecited by 163
  4. 2022Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphscited by 144
  5. 2022GOOD: A Graph Out-of-Distribution Benchmarkcited by 140
  6. 2022The CLRS Algorithmic Reasoning Benchmarkcited by 103
  7. 2022Out-Of-Distribution Generalization on Graphs: A Surveycited by 97
  8. 2021OOD-GNN: Out-of-Distribution Generalized Graph Neural Networkcited by 78
  9. 2021Learning from Counterfactual Links for Link Predictioncited by 69
  10. 2023Energy-based Out-of-Distribution Detection for Graph Neural Networkscited by 67
  11. 2021Reconstruction for Powerful Graph Representationscited by 65
  12. 2022A Generalist Neural Algorithmic Learnercited by 58
38 more
  1. 2022Graph Neural Networks are Dynamic Programmerscited by 55
  2. 2023Does Invariant Graph Learning via Environment Augmentation Learn Invariance?cited by 42
  3. 2023Towards Understanding the Generalization of Graph Neural Networkscited by 41
  4. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  5. 2022SizeShiftReg: a Regularization Method for Improving Size-Generalization in Graph Neural Networkscited by 36
  6. 2022Reinforced Causal Explainer for Graph Neural Networkscited by 34
  7. 2023Mind the Label Shift of Augmentation-based Graph OOD Generalizationcited by 34
  8. 2023Contrastive Video Question Answering via Video Graph Transformercited by 32
  9. 2023Neural Algorithmic Reasoning with Causal Regularisationcited by 30
  10. 2024Graph Out-of-Distribution Generalization via Causal Interventioncited by 30
  11. 2022Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Taskscited by 29
  12. 2023Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalizationcited by 29
  13. 2023Learning on Graphs with Out-of-Distribution Nodescited by 29
  14. 2024Pairwise Alignment Improves Graph Domain Adaptationcited by 25
  15. 2022Evaluation Methods and Measures for Causal Learning Algorithmscited by 23
  16. 2022A Survey of Trustworthy Graph Learning: Reliability, Explainability, and Privacy Protectioncited by 20
  17. 2022FlowX: Towards Explainable Graph Neural Networks via Message Flowscited by 20
  18. 2023GraphMETRO: Mitigating Complex Graph Distribution Shifts via Mixture of Aligned Expertscited by 19
  19. 2023Graph Invariant Learning with Subgraph Co-mixup for Out-Of-Distribution Generalizationcited by 18
  20. 2023Limits, approximation and size transferability for GNNs on sparse graphs via graphopscited by 17
  21. 2023Approximately Equivariant Graph Networkscited by 16
  22. 2024A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptationcited by 16
  23. 2023Individual and Structural Graph Information Bottlenecks for Out-of-Distribution Generalizationcited by 15
  24. 2023Fused Gromov-Wasserstein Graph Mixup for Graph-level Classificationscited by 15
  25. 2022Domain Generalization -- A Causal Perspectivecited by 14
  26. 2023Explaining and Adapting Graph Conditional Shiftcited by 14
  27. 2024How Interpretable Are Interpretable Graph Neural Networks?cited by 13
  28. 2022FakeEdge: Alleviate Dataset Shift in Link Predictioncited by 12
  29. 2023GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networkscited by 12
  30. 2024Safety in Graph Machine Learning: Threats and Safeguardscited by 11
  31. 2022Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attackcited by 10
  32. 2023Graph Structure and Feature Extrapolation for Out-of-Distribution Generalizationcited by 10
  33. 2022Finding Diverse and Predictable Subgraphs for Graph Domain Generalizationcited by 9
  34. 2024Accurate and Scalable Estimation of Epistemic Uncertainty for Graph Neural Networkscited by 8
  35. 2023Towards out-of-distribution generalizable predictions of chemical kinetics propertiescited by 7
  36. 2024Distribution Consistency based Self-Training for Graph Neural Networks with Sparse Labelscited by 7
  37. 2024Cooperative Classification and Rationalization for Graph Generalizationcited by 7
  38. 2025Graph Data Selection for Domain Adaptation: A Model-Free Approachcited by 7

50 most cited of 82 All 82 (JSON)