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Erfan Mirzaei · Italian Institute of Technology

Jul 19, 2026Session 1

Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime

By Andreas Maurer, Erfan Mirzaei, Massimiliano Pontil

Abstract

Overparameterized neural networks can fit both meaningful data and random labels, often achieving essentially zero training error in both cases. This makes the final training error a poor predictor of generalization in the interpolation regime. In this talk, I will present a data-dependent view of this problem based on Gibbs posteriors and Langevin Monte Carlo algorithms using the PAC-Bayes framework. The key idea is to look not only at the final interpolating model but also at the entire temperature path: how quickly the expected training loss decreases as the inverse temperature increases. We show that, for the Gibbs posterior, the PAC-Bayes complexity term admits an exact integral representation as an area under this mean training-loss curve. This area separates true-label learning from random-label memorization and leads to quantitative bounds that track the observed test error in overparameterized neural networks.

Materials

• paper
• slides
• video