A PAC-Bayesian Link Between Generalisation and Flat Minima. Haddouche, M., Viallard, P., Şimşekli, U., & Guedj, B. 2024. Submitted.
A PAC-Bayesian Link Between Generalisation and Flat Minima [link]Paper  A PAC-Bayesian Link Between Generalisation and Flat Minima [pdf]Pdf  doi  abstract   bibtex   11 downloads  
Modern machine learning usually involves predictors in the overparametrised setting (number of trained parameters greater than dataset size), and their training yield not only good performances 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 dimension of the predictor space. Our results highlight the positive influence of \emphflat minima (being minima with a neighbourhood nearly minimising the learning problem as well) on generalisation performances, involving directly the benefits of the optimisation phase.

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