MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem - ENAC - École nationale de l'aviation civile Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem

Résumé

It is well established that to ensure or certify the robustness of a neural network, its Lipschitz constant plays a prominent role. However, its calculation is NP-hard. In this note, by taking into account activation regions at each layer as new constraints, we propose new quadratically constrained MIP formulations for the neural network Lipschitz estimation problem. The solutions of these problems give lower bounds and upper bounds of the Lipschitz constant and we detail conditions when they coincide with the exact Lipschitz constant.
Fichier principal
Vignette du fichier
MIQCQP_Neural_Network_Lipschitz_Constant.pdf (136.65 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04431914 , version 1 (01-02-2024)

Licence

Domaine public

Identifiants

Citer

Mohammed Sbihi, Sophie Jan, Nicolas Couellan. MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem. 2024. ⟨hal-04431914⟩
40 Consultations
39 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More