mlsanityData to 14 Oct 2026

Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems

arXiv 2511.18417 ↗First posted 23 Nov 2025cs.LG cs.AI cs.CVcited by 4

Not on the map. Why?

Abstract (arXiv)

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a topological category with Radon measures. Formulating linear and nonlinear layers in the categorical setup, we prove the equivariant universal approximation theorem in the general setting: the class of finite-depth CENNs is dense in the space of continuous equivariant transformations. We instantiate the framework for groups/groupoids, posets/lattices, graphs and cellular sheaves, deriving universal approximation theorems for them in a systematic manner. Categorical equivariant deep learning thus allows us to expand the horizons of equivariant deep learning beyond group actions, encompassing not only geometric symmetries but also contextual and compositional symmetries.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 24 of its 44 references that are in the map. First posted on arXiv 23 Nov 2025.

Builds on

24 of 44 references.

References · 24

  1. 2018How Powerful are Graph Neural Networks?cited by 4,393
  2. 2017Deep Setscited by 1,421
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  4. 2016Group Equivariant Convolutional Networkscited by 1,165
  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  6. 2021E(n) Equivariant Graph Neural Networkscited by 965
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  8. 2018Spherical CNNscited by 456
  9. 2019General E(2)-Equivariant Steerable CNNscited by 446
  10. 2018Invariant and Equivariant Graph Networkscited by 346
  11. 2016Steerable CNNscited by 305
  12. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
12 more
  1. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 295
  2. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  3. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  4. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  5. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  6. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  7. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  8. 2018Universal approximations of invariant maps by neural networkscited by 127
  9. 2020Sheaf Neural Networkscited by 84
  10. 2022Sheaf Neural Networks with Connection Laplacianscited by 65
  11. 2025Learning with Category-Equivariant Architectures for Human Activity Recognitioncited by 3
  12. 2025Learning with Category-Equivariant Representations for Human Activity Recognitioncited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026What are the Right Symmetries for Formal Theorem Proving?cited by 1
  2. 2026Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networkscited by 1
  3. 2026Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networkscited by 1
  4. 2026Theory for groupoid equivariant neural networks: an approach for steerable CNNs on bounded domainscited by 0