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How good is PAC-Bayes at explaining generalisation?
Antoine Picard-Weibel, Eugenio Clerico, Roman Moscoviz, Benjamin · 2025-03-11 · via stat.ML updates on arXiv.org

We discuss necessary conditions for a PAC-Bayes bound to provide a meaningful generalisation guarantee. Our analysis reveals that the optimal generalisation guarantee depends solely on the distribution of the risk induced by the prior distribution. In particular, achieving a target generalisation level is only achievable if the prior places sufficient mass on high-performing predictors. We relate these requirements to the prevalent practice of using data-dependent priors in deep learning PAC-Bayes applications, and discuss the implications for the claim that PAC-Bayes ``explains'' generalisation.

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