mlsanityData to 14 Oct 2026

Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning

arXiv 2403.13749 ↗First posted 20 Mar 2024cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

We introduce r-loopy Weisfeiler-Leman (r-ℓWL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, r-ℓMPNN, that can count cycles up to length r + 2. Most notably, we show that r-ℓWL can count homomorphisms of cactus graphs. This strictly extends classical 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to k-WL for any fixed k. We empirically validate the expressive and counting power of the proposed r-ℓMPNN on several synthetic datasets and present state-of-the-art predictive performance on various real-world datasets. The code is available at https://github.com/RPaolino/loopy

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 60 of its 93 references that are in the map. First posted on arXiv 20 Mar 2024.

Builds on

60 of 93 references.

References · 60

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  4. 2017Graph Attention Networkscited by 8,923
  5. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  6. 2018How Powerful are Graph Neural Networks?cited by 4,393
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  8. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  9. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,051
  10. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  11. 2019Strategies for Pre-training Graph Neural Networkscited by 971
  12. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 881
38 more
  1. 2019Graph Neural Networks for Social Recommendationcited by 714
  2. 2020Benchmarking Graph Neural Networkscited by 680
  3. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  4. 2019Provably Powerful Graph Networkscited by 389
  5. 2017Residual Gated Graph ConvNetscited by 346
  6. 2018Invariant and Equivariant Graph Networkscited by 346
  7. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 313
  8. 2022Long Range Graph Benchmarkcited by 263
  9. 2020Can Graph Neural Networks Count Substructures?cited by 236
  10. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  11. 2020The Surprising Power of Graph Neural Networks with Random Node Initializationcited by 198
  12. 2021Identity-aware Graph Neural Networkscited by 198
  13. 2020Random Features Strengthen Graph Neural Networkscited by 186
  14. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  15. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 179
  16. 2019On the equivalence between graph isomorphism testing and function approximation with GNNscited by 172
  17. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 155
  18. 2021Equivariant Subgraph Aggregation Networkscited by 154
  19. 2019On the Universality of Invariant Networkscited by 152
  20. 2019Relational Pooling for Graph Representationscited by 150
  21. 2021Nested Graph Neural Networkscited by 137
  22. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 122
  23. 2019Fake News Detection on Social Media using Geometric Deep Learningcited by 118
  24. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  25. 2021Breaking the Limits of Message Passing Graph Neural Networkscited by 101
  26. 2020Building powerful and equivariant graph neural networks with structural message-passingcited by 97
  27. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  28. 2022Expressiveness and Approximation Properties of Graph Neural Networkscited by 64
  29. 2018On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Propertiescited by 63
  30. 2020Hierarchical Inter-Message Passing for Learning on Molecular Graphscited by 59
  31. 2022Ordered Subgraph Aggregation Networkscited by 57
  32. 2022Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNscited by 56
  33. 2019Coloring graph neural networks for node disambiguationcited by 52
  34. 2021Graph Neural Networks with Local Graph Parameterscited by 52
  35. 2022Shortest Path Networks for Graph Property Predictioncited by 46
  36. 2024Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressivenesscited by 39
  37. 2023An Empirical Study of Realized GNN Expressivenesscited by 33
  38. 2023Path Neural Networks: Expressive and Accurate Graph Neural Networkscited by 32

50 most cited of 60 All 60 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Message Passing on the Edge: Towards Scalable and Expressive GNNscited by 0
  2. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0