Graph Automorphism Group Equivariant Neural Networks

07/15/2023

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by   Edward Pearce-Crump, et al.

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For any graph G having n vertices and its automorphism group Aut(G), we provide a full characterisation of all of the possible Aut(G)-equivariant neural networks whose layers are some tensor power of ℝ^n. In particular, we find a spanning set of matrices for the learnable, linear, Aut(G)-equivariant layer functions between such tensor power spaces in the standard basis of ℝ^n.