A PAC-Bayesian Generalization Bound for Equivariant Networks
This provides theoretical insights for researchers designing equivariant networks to improve generalization in tasks with symmetries, though it is incremental as it builds on existing PAC-Bayesian analysis.
The paper tackles the problem of understanding how equivariance in neural networks relates to generalization error by deriving norm-based PAC-Bayesian generalization bounds for equivariant networks, showing that larger group sizes improve generalization error, as supported by numerical experiments.
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.