Group Cross-Correlations with Faintly Constrained Filters

ArXi:2601.00045v2 Announce Type: replace-cross Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained filters and $G$ a non-abelian group, any hidden layer of such a network requires as many nodes as vertices in a fine enough discretization of $G$. In order to reduce the necessary number of nodes, certain constraints on filters were proposed in the literature.