Authors: Vishal S. Ngairangbam, Michael Spannowsky
Abstract: We explore the role of group symmetries in binary classification tasks,
presenting a novel framework that leverages the principles of Neyman-Pearson
optimality. Contrary to the common intuition that larger symmetry groups lead
to improved classification performance, our findings show that selecting the
appropriate group symmetries is crucial for optimising generalisation and
sample efficiency. We develop a theoretical foundation for designing group
equivariant neural networks that align the choice of symmetries with the
underlying probability distributions of the data. Our approach provides a
unified methodology for improving classification accuracy across a broad range
of applications by carefully tailoring the symmetry group to the specific
characteristics of the problem. Theoretical analysis and experimental results
demonstrate that optimal classification performance is not always associated
with the largest equivariant groups possible in the domain, even when the
likelihood ratio is invariant under one of its proper subgroups, but rather
with those subgroups themselves. This work offers insights and practical
guidelines for constructing more effective group equivariant architectures in
diverse machine-learning contexts.
Source: http://arxiv.org/abs/2408.08823v1
