Homogeneous vector bundles and G-equivariant convolutional neural networks

G-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous G-space M M . GCNNs are designed to respect the global symmetry in M M , thereby facilitating learning. In this paper, we analyze GCNNs on homogeneous spaces M = G/K M = G / K in the case of unimodular Lie groups G and compact subgroups K ≤ G K ≤ G . We demonstrate that homogeneous vector bundles are the natural setting for GCNNs. We also use reproducing kernel Hilbert spaces (RKHS) to obtain a sufficient criterion for expressing G-equivariant layers as convolutional layers. Finally, stronger results are obtained for some groups via a connection between RKHS and bandwidth.