Homogeneous vector bundles and G-equivariant convolutional neural networks

Journal article, 2022

G-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous G-space M. GCNNs are designed to respect the global symmetry in M, thereby facilitating learning. In this paper, we analyze GCNNs on homogeneous spaces M= G/ K in the case of unimodular Lie groups G and compact subgroups 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.