mlsanityData to 14 Oct 2026

Incidence Networks for Geometric Deep Learning

arXiv 1905.11460 ↗First posted 27 May 2019cs.LG stat.MLcited by 17

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Abstract (arXiv)

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors, analyze their structure, and present the family of equivariant networks that operate on them. We show that any incidence tensor decomposes into invariant subsets. This decomposition, in turn, leads to a decomposition of the corresponding equivariant linear maps, for which we prove an efficient pooling-and-broadcasting implementation.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 May 2019.

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Citing papers per year: 2021: 5; 2022: 5; 2023: 3; 2024: 3; 2025: 1.

17 papers.

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  1. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  2. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 122
  3. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  4. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 107
  5. 2021Reconstruction for Powerful Graph Representationscited by 65
  6. 2022Message passing all the way upcited by 47
  7. 2024Universal Neural Functionalscited by 26
  8. 2022Molecular Representation Learning via Heterogeneous Motif Graph Neural Networkscited by 23
  9. 2021Equivariant Networks for Pixelized Spherescited by 16
  10. 2022Equivariant Hypergraph Neural Networkscited by 14
  11. 2022Convergence of Invariant Graph Networkscited by 9
  12. 2024A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarseningcited by 8
5 more
  1. 2025GradMetaNet: An Equivariant Architecture for Learning on Gradientscited by 7
  2. 2024Towards Foundation Models on Graphs: An Analysis on Cross-Dataset Transfer of Pretrained GNNscited by 5
  3. 2021Subgraph Permutation Equivariant Networkscited by 2
  4. 2023Local-to-global Perspectives on Graph Neural Networkscited by 2
  5. 2023LoopTune: Optimizing Tensor Computations with Reinforcement Learningcited by 1