Brauer's Group Equivariant Neural Networks

2022/12/16 by Edward Pearce-Crump, Pearce-Crump, Edward · 2 citations
Computer Science · Mathematics · #Advanced Graph Neural Networks #Basis (linear algebra) #Combinatorics #Combinatorics (math.CO) #Equivariant map #FOS: Computer and information sciences #FOS: Mathematics #Geometry #Group (periodic table) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Neural Networks and Applications #Orthogonal group #Physics #Pure mathematics #Quantum mechanics #Representation Theory (math.RT) #Symmetry (geometry) #Symmetry group #Symplectic geometry #Symplectic group #Tensor (intrinsic definition) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2212.08630

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

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).

Cited by

• Learning Group Actions In Disentangled Latent Image Representations
• Constructing 3D Rotational Invariance and Equivariance with Symmetric Tensor Networks

Related

• An Algorithm for Computing with Brauer's Group Equivariant Neural Network Layers
• How Jellyfish Characterise Alternating Group Equivariant Neural Networks
• Graph Automorphism Group Equivariant Neural Networks
• A Practical Method for Constructing Equivariant Multilayer Perceptrons\n for Arbitrary Matrix Groups
• Categorification of Group Equivariant Neural Networks