mlsanityData to 7 Oct 2026

Autobahn: Automorphism-based Graph Neural Nets

arXiv 2103.01710 ↗First posted 2 Mar 2021cs.LGcited by 39

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Abstract (arXiv)

We introduce Automorphism-based graph neural networks (Autobahn), a new family of graph neural networks. In an Autobahn, we decompose the graph into a collection of subgraphs and apply local convolutions that are equivariant to each subgraph's automorphism group. Specific choices of local neighborhoods and subgraphs recover existing architectures such as message passing neural networks. Our formalism also encompasses novel architectures: as an example, we introduce a graph neural network that decomposes the graph into paths and cycles. The resulting convolutions reflect the natural way that parts of the graph can transform, preserving the intuitive meaning of convolution without sacrificing global permutation equivariance. We validate our approach by applying Autobahn to molecular graphs, where it achieves results competitive with state-of-the-art message passing algorithms.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 35 of its 54 references that are in the map. First posted on arXiv 2 Mar 2021.

Builds on

35 of 54 references.

References · 35

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  7. 2014DeepWalk: Online Learning of Social Representationscited by 1,543
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  10. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  11. 2019Strategies for Pre-training Graph Neural Networkscited by 964
  12. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
23 more
  1. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  2. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  3. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  4. 2019Provably Powerful Graph Networkscited by 385
  5. 2018Invariant and Equivariant Graph Networkscited by 339
  6. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  7. 2016Steerable CNNscited by 298
  8. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  9. 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
  10. 2020Can Graph Neural Networks Count Substructures?cited by 235
  11. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  12. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217
  13. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 168
  14. 2019On the Universality of Invariant Networkscited by 151
  15. 2020Directional Graph Networkscited by 132
  16. 2020Building powerful and equivariant graph neural networks with structural message-passingcited by 95
  17. 2020Subgraph Neural Networkscited by 73
  18. 2018On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Propertiescited by 63
  19. 2020Hierarchical Inter-Message Passing for Learning on Molecular Graphscited by 59
  20. 2020The expressive power of kth-order invariant graph networkscited by 34
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  23. 2020Neural Message Passing on High Order Pathscited by 17

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 7; 2023: 12; 2024: 10; 2025: 2; 2026: 2.

39 papers.

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  1. 2021Equivariant Subgraph Aggregation Networkscited by 154
  2. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 154
  3. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  4. 2023Rethinking the Expressive Power of GNNs via Graph Biconnectivitycited by 119
  5. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  6. 2022A Survey on Graph Representation Learning Methodscited by 66
  7. 2022Ordered Subgraph Aggregation Networkscited by 57
  8. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  9. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 38
  10. 2023Equivariant Polynomials for Graph Neural Networkscited by 38
  11. 2024Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressivenesscited by 38
  12. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
27 more
  1. 2023Cooperative Graph Neural Networkscited by 35
  2. 2023WL meet VCcited by 30
  3. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  4. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  5. 2023Approximately Equivariant Graph Networkscited by 16
  6. 2022Going Deeper into Permutation-Sensitive Graph Neural Networkscited by 15
  7. 2022Machine learning and invariant theorycited by 13
  8. 2024Weisfeiler-Leman at the margin: When more expressivity matterscited by 13
  9. 2024Towards Bridging Generalization and Expressivity of Graph Neural Networkscited by 12
  10. 2023PlanE: Representation Learning over Planar Graphscited by 11
  11. 2024Improving the Expressiveness of K-hop Message-Passing GNNs by Injecting Contextualized Substructure Informationcited by 9
  12. 2024Expressivity and Generalization: Fragment-Biases for Molecular GNNscited by 8
  13. 2023Union Subgraph Neural Networkscited by 6
  14. 2024MuGSI: Distilling GNNs with Multi-Granularity Structural Information for Graph Classificationcited by 5
  15. 2023Transformers are efficient hierarchical chemical graph learnerscited by 4
  16. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  17. 2024Foundations and Frontiers of Graph Learning Theorycited by 3
  18. 2021Beyond permutation equivariance in graph networkscited by 2
  19. 2021Subgraph Permutation Equivariant Networkscited by 2
  20. 2023P-Tensors: a General Formalism for Constructing Higher Order Message Passing Networkscited by 2
  21. 2024The Role of Fibration Symmetries in Geometric Deep Learningcited by 2
  22. 2025A Re-node Self-training Approach for Deep Graph-based Semi-supervised Classification on Multi-view Image Datacited by 1
  23. 2023A Geometric Insight into Equivariant Message Passing Neural Networks on Riemannian Manifoldscited by 0
  24. 2024Generalization of Graph Neural Networks through the Lens of Homomorphismcited by 0
  25. 2025Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectoriescited by 0
  26. 2026Any-Subgroup Equivariant Networks via Symmetry Breakingcited by 0
  27. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0