How Jellyfish Characterise Alternating Group Equivariant Neural Networks

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 ${\mathbb{R}}^n$. 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 ${\mathbb{R}}^n$. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

arXiv commentICML 2023 Poster; 13 pages. arXiv admin note: text overlap with arXiv:2212.08648, arXiv:2212.08630