mlsanityData to 7 Oct 2026

Natural Graph Networks

arXiv 2007.08349 ↗First posted 16 Jul 2020cs.LG cs.CV stat.MLcited by 35

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Abstract (arXiv)

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Jul 2020.

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Citing papers per year: 2021: 4; 2022: 7; 2023: 12; 2024: 7; 2025: 4; 2026: 1.

35 papers.

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  1. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  2. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  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. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  6. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 38
  7. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
  8. 2023The Expressive Power of Graph Neural Networks: A Surveycited by 27
  9. 2023Probabilistically Rewired Message-Passing Neural Networkscited by 26
  10. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  11. 2023Deep Generative Models for Detector Signature Simulation: A Taxonomic Reviewcited by 18
  12. 2021Zero-shot Node Classification with Decomposed Graph Prototype Networkcited by 15
23 more
  1. 2023Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexescited by 15
  2. 2024Probabilistic Graph Rewiring via Virtual Nodescited by 15
  3. 2023CIN++: Enhancing Topological Message Passingcited by 14
  4. 2023Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexescited by 10
  5. 2022Towards a Grounded Theory of Causation for Embodied AIcited by 9
  6. 2024Improving the Expressiveness of K-hop Message-Passing GNNs by Injecting Contextualized Substructure Informationcited by 9
  7. 2023Physics and Chemistry from Parsimonious Representations: Image Analysis via Invariant Variational Autoencoderscited by 7
  8. 2021K"ahler Geometry of Quiver Varieties and Machine Learningcited by 3
  9. 2023A Category-theoretical Meta-analysis of Definitions of Disentanglementcited by 3
  10. 2023Equivariant Matrix Function Neural Networkscited by 3
  11. 2021Subgraph Permutation Equivariant Networkscited by 2
  12. 2023Enriching Disentanglement: From Logical Definitions to Quantitative Metricscited by 2
  13. 2023P-Tensors: a General Formalism for Constructing Higher Order Message Passing Networkscited by 2
  14. 2024The Role of Fibration Symmetries in Geometric Deep Learningcited by 2
  15. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  16. 2025CanonNet: Canonical Ordering and Curvature Learning for Point Cloud Analysiscited by 2
  17. 2024The Topos of Transformer Networkscited by 1
  18. 2022Graph-level Neural Networks: Current Progress and Future Directionscited by 0
  19. 2024Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactionscited by 0
  20. 2025Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passingcited by 0
  21. 2025The power of dynamic causality in observer-based design for soft sensor applicationscited by 0
  22. 2025Disentangling Hyperedges through the Lens of Category Theorycited by 0
  23. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0