A PAC-Bayesian Link Between Generalisation and Flat Minima
Abstract
Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good generalisation capacity. This phenomenon challenges many theoretical results, and remains an open problem. To reach a better understanding, we provide novel generalisation bounds involving gradient terms. To do so, we combine the PAC-Bayes toolbox with Poincaré and Log-Sobolev inequalities, avoiding an explicit dependency on the dimension of the predictor space. Our results highlight the positive influence of flat minima (being minima with a neighbourhood nearly minimising the learning problem as well) on generalisation performance, involving directly the benefits of the optimisation phase.
Cite
Text
Haddouche et al. "A PAC-Bayesian Link Between Generalisation and Flat Minima." Proceedings of The 36th International Conference on Algorithmic Learning Theory, 2025.Markdown
[Haddouche et al. "A PAC-Bayesian Link Between Generalisation and Flat Minima." Proceedings of The 36th International Conference on Algorithmic Learning Theory, 2025.](https://mlanthology.org/alt/2025/haddouche2025alt-pacbayesian/)BibTeX
@inproceedings{haddouche2025alt-pacbayesian,
title = {{A PAC-Bayesian Link Between Generalisation and Flat Minima}},
author = {Haddouche, Maxime and Viallard, Paul and Simsekli, Umut and Guedj, Benjamin},
booktitle = {Proceedings of The 36th International Conference on Algorithmic Learning Theory},
year = {2025},
pages = {481-511},
volume = {272},
url = {https://mlanthology.org/alt/2025/haddouche2025alt-pacbayesian/}
}