mlsanityData to 14 Oct 2026

Weisfeiler and Leman go Machine Learning: The Story so far

arXiv 2112.09992 ↗First posted 18 Dec 2021cs.LG cs.DS cs.NEcited by 122

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Abstract (arXiv)

In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine-learning setting, focusing on the supervised regime. We discuss the theoretical background, show how to use it for supervised graph and node representation learning, discuss recent extensions, and outline the algorithm's connection to (permutation-)equivariant neural architectures. Moreover, we give an overview of current applications and future directions to stimulate further research.

Key facts. Cited by 122 papers in the map (data through 14 Oct 2026). Builds on 110 of its 251 references that are in the map. First posted on arXiv 18 Dec 2021.

Builds on

110 of 251 references.

References · 110

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  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
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  4. 2017Inductive Representation Learning on Large Graphscited by 6,320
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38 more
  1. 2016Group Equivariant Convolutional Networkscited by 1,165
  2. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
  3. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,051
  4. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 881
  5. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 754
  6. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 728
  7. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  8. 2020Directional Message Passing for Molecular Graphscited by 561
  9. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
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  14. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 310
  15. 2020Towards Deeper Graph Neural Networkscited by 296
  16. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  17. 2020Generalization and Representational Limits of Graph Neural Networkscited by 218
  18. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  19. 2019Graph Matching Networks for Learning the Similarity of Graph Structured Objectscited by 205
  20. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  21. 2020The Surprising Power of Graph Neural Networks with Random Node Initializationcited by 198
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  38. 2021DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networkscited by 118

50 most cited of 110 All 110 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 30; 2023: 21; 2024: 31; 2025: 22; 2026: 18.

122 papers.

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  1. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 179
  2. 2022Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphscited by 144
  3. 2023Rethinking the Expressive Power of GNNs via Graph Biconnectivitycited by 119
  4. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  5. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 107
  6. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  7. 2023Attending to Graph Transformerscited by 83
  8. 2024Understanding Transformer Reasoning Capabilities via Graph Algorithmscited by 67
  9. 2022Ordered Subgraph Aggregation Networkscited by 57
  10. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  11. 2022A Theoretical Comparison of Graph Neural Network Extensionscited by 48
  12. 2022Message passing all the way upcited by 47
38 more
  1. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 47
  2. 2022GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generationcited by 43
  3. 2024Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressivenesscited by 39
  4. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  5. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  6. 2023Equivariant Polynomials for Graph Neural Networkscited by 38
  7. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
  8. 2023WL meet VCcited by 31
  9. 2023Graph Positional Encoding via Random Feature Propagationcited by 31
  10. 2022Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Taskscited by 30
  11. 2022Graph Neural Networks with Adaptive Readoutscited by 29
  12. 2022Weisfeiler and Leman Go Relationalcited by 28
  13. 2023SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generationcited by 28
  14. 2023The Descriptive Complexity of Graph Neural Networkscited by 26
  15. 2023Probabilistically Rewired Message-Passing Neural Networkscited by 26
  16. 2023Fine-grained Expressivity of Graph Neural Networkscited by 25
  17. 2022Generalized Laplacian Positional Encoding for Graph Representation Learningcited by 21
  18. 2022Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networkscited by 21
  19. 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 19
  20. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 19
  21. 2025Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learningcited by 19
  22. 2024TopoTune : A Framework for Generalized Combinatorial Complex Neural Networkscited by 18
  23. 2023Efficient Subgraph GNNs by Learning Effective Selection Policiescited by 17
  24. 20221-WL Expressiveness Is (Almost) All You Needcited by 15
  25. 2024Probabilistic Graph Rewiring via Virtual Nodescited by 15
  26. 2024On the Expressive Power of Spectral Invariant Graph Neural Networkscited by 15
  27. 2025A Survey of Graph Transformers: Architectures, Theories and Applicationscited by 14
  28. 2024Weisfeiler-Leman at the margin: When more expressivity matterscited by 13
  29. 2022Graph neural networks for the prediction of molecular structure-property relationshipscited by 12
  30. 2022On the Ability of Graph Neural Networks to Model Interactions Between Verticescited by 12
  31. 2022A Simple and Universal Rotation Equivariant Point-cloud Networkcited by 11
  32. 2022From Local to Global: Spectral-Inspired Graph Neural Networkscited by 11
  33. 2024Towards Principled Graph Transformerscited by 11
  34. 2024Weisfeiler Leman for Euclidean Equivariant Machine Learningcited by 10
  35. 2025How simple can you go? An off-the-shelf transformer approach to molecular dynamicscited by 10
  36. 2022Weisfeiler and Leman Go Walking: Random Walk Kernels Revisitedcited by 9
  37. 2023Three iterations of (d-1)-WL test distinguish non isometric clouds of d-dimensional pointscited by 9
  38. 2024Improving the Expressiveness of K-hop Message-Passing GNNs by Injecting Contextualized Substructure Informationcited by 9

50 most cited of 122 All 122 (JSON)