How Jellyfish Characterise Alternating Group Equivariant Neural Networks

01/24/2023

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by   Edward Pearce-Crump, et al.

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We provide a full characterisation of all of the possible alternating group (A_n) equivariant neural networks whose layers are some tensor power of 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 ℝ^n. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.