mlsanityData to 14 Oct 2026

Brauer's Group Equivariant Neural Networks

arXiv 2212.08630 ↗First posted 16 Dec 2022cs.LG math.CO math.RTcited by 17

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Abstract (arXiv)

We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of ℝn for three symmetry groups that are missing from the machine learning literature: O(n), the orthogonal group; SO(n), the special orthogonal group; and Sp(n), the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of ℝn when the group is O(n) or SO(n), and in the symplectic basis of ℝn when the group is Sp(n).

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 14 of its 40 references that are in the map. First posted on arXiv 16 Dec 2022.

Builds on

14 of 40 references.

References · 14

  1. 2017Deep Setscited by 1,421
  2. 2016Group Equivariant Convolutional Networkscited by 1,165
  3. 2019Hamiltonian Neural Networkscited by 712
  4. 2018Spherical CNNscited by 456
  5. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  6. 2018Invariant and Equivariant Graph Networkscited by 346
  7. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  8. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
  9. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  10. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 121
  11. 2018Deep Models of Interactions Across Setscited by 69
  12. 2022What is an equivariant neural network?cited by 21
2 more
  1. 2020Universal Approximation Theorem for Equivariant Maps by Group CNNscited by 12
  2. 2022A Simple and Universal Rotation Equivariant Point-cloud Networkcited by 11

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Cited by year

Citing papers per year: 2023: 7; 2024: 6; 2025: 4.

17 papers.

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  1. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 23
  2. 2024Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Modelscited by 22
  3. 2023Expressive Sign Equivariant Networks for Spectral Geometric Learningcited by 15
  4. 2023Fast computation of permutation equivariant layers with the partition algebracited by 7
  5. 2024Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networkscited by 7
  6. 2024High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spacescited by 6
  7. 2023How Jellyfish Characterise Alternating Group Equivariant Neural Networkscited by 5
  8. 2023Graph Automorphism Group Equivariant Neural Networkscited by 4
  9. 2024Tensor learning with orthogonal, Lorentz, and symplectic symmetriescited by 3
  10. 2023Categorification of Group Equivariant Neural Networkscited by 2
  11. 2024Revisiting Multi-Permutation Equivariance through the Lens of Irreducible Representationscited by 2
  12. 2023An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layerscited by 1
5 more
  1. 2023Compact Matrix Quantum Group Equivariant Neural Networkscited by 0
  2. 2025Precoder Learning for Weighted Sum Rate Maximizationcited by 0
  3. 2025Permutation Equivariant Neural Networks for Symmetric Tensorscited by 0
  4. 2025Constructing 3D Rotational Invariance and Equivariance with Symmetric Tensor Networkscited by 0
  5. 2025Learning Group Actions In Disentangled Latent Image Representationscited by 0