# Incidence Networks for Geometric Deep Learning

arXiv: https://arxiv.org/abs/1905.11460 · HTML: https://mlsanity.com/paper/1905.11460/

## Key facts

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

## Built on by (most cited first, 17 of 17)

- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries](https://mlsanity.com/paper/2206.11140/) (2022)
- [Equivariant Architectures for Learning in Deep Weight Spaces](https://mlsanity.com/paper/2301.12780/) (2023)
- [Reconstruction for Powerful Graph Representations](https://mlsanity.com/paper/2110.00577/) (2021)
- [Message passing all the way up](https://mlsanity.com/paper/2202.11097/) (2022)
- [Universal Neural Functionals](https://mlsanity.com/paper/2402.05232/) (2024)
- [Molecular Representation Learning via Heterogeneous Motif Graph Neural Networks](https://mlsanity.com/paper/2202.00529/) (2022)
- [Equivariant Networks for Pixelized Spheres](https://mlsanity.com/paper/2106.06662/) (2021)
- [Equivariant Hypergraph Neural Networks](https://mlsanity.com/paper/2208.10428/) (2022)
- [Convergence of Invariant Graph Networks](https://mlsanity.com/paper/2201.10129/) (2022)
- [A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarsening](https://mlsanity.com/paper/2406.09291/) (2024)
- [GradMetaNet: An Equivariant Architecture for Learning on Gradients](https://mlsanity.com/paper/2507.01649/) (2025)
- [Towards Foundation Models on Graphs: An Analysis on Cross-Dataset Transfer of Pretrained GNNs](https://mlsanity.com/paper/2412.17609/) (2024)
- [Subgraph Permutation Equivariant Networks](https://mlsanity.com/paper/2111.11840/) (2021)
- [Local-to-global Perspectives on Graph Neural Networks](https://mlsanity.com/paper/2306.06547/) (2023)
- [LoopTune: Optimizing Tensor Computations with Reinforcement Learning](https://mlsanity.com/paper/2309.01825/) (2023)

## 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.