[edit]

# How Jellyfish Characterise Alternating Group Equivariant Neural Networks

*Proceedings of the 40th International Conference on Machine Learning*, PMLR 202:27483-27495, 2023.

#### 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.