  Equivariant networks capture the inductive bias about the symmetry of the
learning task by building those symmetries into the model. In this paper, we
study how equivariance relates to generalization error utilizing PAC Bayesian
analysis for equivariant networks, where the transformation laws of feature
spaces are determined by group representations. By using perturbation analysis
of equivariant networks in Fourier domain for each layer, we derive norm-based
PAC-Bayesian generalization bounds. The bound characterizes the impact of group
size, and multiplicity and degree of irreducible representations on the
generalization error and thereby provide a guideline for selecting them. In
general, the bound indicates that using larger group size in the model improves
the generalization error substantiated by extensive numerical experiments.
