Graph Automorphism Group Equivariant Neural Networks
Edward Pearce-Crump
For any graph $G$ having $n$ vertices and its automorphism group
$\textrm{Aut}(G)$, we provide a full characterisation of all of the possible
$\textrm{Aut}(G)$-equivariant neural networks whose layers are some tensor
power of $\mathbb{R}^{n}$. In particular, we find a spanning set of matrices
for the learnable, linear, $\textrm{Aut}(G)$-equivariant layer functions
between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$.