How Jellyfish Characterise Alternating Group Equivariant Neural Networks

We provide a full characterisation of all of the possible alternating group (A_n) <PRE_TAG>equivariant neural networks</POST_TAG> 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 <PRE_TAG>tensor power spaces</POST_TAG> 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.