mlsanityData to 7 Oct 2026

A Simple Proof of the Universality of Invariant/Equivariant Graph Neural Networks

arXiv 1910.03802 ↗First posted 9 Oct 2019cs.LG stat.MLcited by 19

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Abstract (arXiv)

We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed technique not only leads to simple proofs of the universality properties but also gives a natural explanation for the tensorization of the previously studied models. Finally, we give some remarks on the connection between our model and the continuous representation of graphs.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Oct 2019.

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Citing papers per year: 2021: 7; 2022: 4; 2023: 4; 2024: 2; 2025: 0; 2026: 2.

19 papers.

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  1. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  2. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  3. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  4. 2021Reconstruction for Powerful Graph Representationscited by 65
  5. 2022Ordered Subgraph Aggregation Networkscited by 57
  6. 2023Equivariant Polynomials for Graph Neural Networkscited by 38
  7. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
  8. 2023WL meet VCcited by 30
  9. 2022Weisfeiler and Leman Go Relationalcited by 28
  10. 2023Fine-grained Expressivity of Graph Neural Networkscited by 25
  11. 2021Neural Trees for Learning on Graphscited by 13
  12. 2024Weisfeiler-Leman at the margin: When more expressivity matterscited by 13
7 more
  1. 2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
  2. 2021Equivariant and Invariant Reynolds Networkscited by 4
  3. 2021Abelian Neural Networkscited by 2
  4. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  5. 2026Any-Dimensional Invariant Universalitycited by 1
  6. 2021Learning on Random Balls is Sufficient for Estimating (Some) Graph Parameterscited by 0
  7. 2026Learning to Approximate Uniform Facility Location via Graph Neural Networkscited by 0