Title: Symmetries in PAC-Bayesian Learning

Original: arXiv:2510.17303v2 Announce Type: replace Abstract: While it is well established that symmetries enhance the practical performance of machine learning models, theoretical frameworks that explain these improvements are still scarce. Previous research has predominantly concentrated on compact group symmetries and typically relies on the assumption that the underlying data distribution is invariant—a condition that is seldom met in practical scenarios. This study broadens generalization guarantees to encompass non-compact symmetries, such as translations, as well as data distributions that lack invariance. Utilizing the PAC-Bayes framework, we refine and strengthen existing bounds, illustrating this method using McAllester's PAC-Bayes bound and proving its applicability across a diverse spectrum of PAC-Bayes bounds. Our experimental validation on multiple datasets featuring non-uniform and non-compact transformations confirms that our derived guarantees are not only valid but also surpass previous results. These insights offer theoretical support for the preference of symmetric models over non-symmetric ones for symmetric data, extending beyond the restricted contexts of compact groups and invariant distributions, and paving the way for a more comprehensive understanding of symmetries in machine learning.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC