A PAC-Bayesian Link Between Generalisation and Flat Minima - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

A PAC-Bayesian Link Between Generalisation and Flat Minima

Résumé

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 flat minima (being minima with a neighbourhood nearly minimising the learning problem as well) on generalisation performances, involving directly the benefits of the optimisation phase.
Fichier principal
Vignette du fichier
PLS_inequalities_x_PAC_Bayes.pdf (431.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04455639 , version 1 (13-02-2024)

Licence

Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales

Identifiants

  • HAL Id : hal-04455639 , version 1

Citer

Maxime Haddouche, Paul Viallard, Umut Şimşekli, Benjamin Guedj. A PAC-Bayesian Link Between Generalisation and Flat Minima. 2024. ⟨hal-04455639⟩
34 Consultations
11 Téléchargements

Partager

Gmail Facebook X LinkedIn More