How Jellyfish Characterise Alternating Group Equivariant Neural Networks

2023/01/24 by Pearce-Crump, Edward
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2301.10152

Abstract

We provide a full characterisation of all of the possible alternating group (A_n) equivariant neural networks whose layers are some tensor power of ℝⁿ. In particular, we find a basis of matrices for the learnable, linear, A_n-equivariant layer functions between such tensor power spaces in the standard basis of ℝⁿ. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

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• In Search of Projectively Equivariant Networks