LipBaB: Computing exact Lipschitz constant of ReLU networks

TL;DR

LipBaB is a branch and bound method that computes exact local Lipschitz constants of ReLU neural networks, aiding robustness and stability analysis with guaranteed precision.

Contribution

It introduces LipBaB, a novel framework capable of exactly computing Lipschitz constants for ReLU networks using Jacobian bounds and branch and bound techniques.

Findings

Provides provably exact Lipschitz constant computation.

Applicable to any p-norm with guaranteed precision.

Enhances robustness certification and stability analysis.

Abstract

The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining tight bounds of the Lipschitz constant is therefore important. We introduce LipBaB, a branch and bound framework to compute certified bounds of the local Lipschitz constant of deep neural networks with ReLU activation functions up to any desired precision. We achieve this by bounding the norm of the Jacobians, corresponding to different activation patterns of the network caused within the input domain. Our algorithm can provide provably exact computation of the Lipschitz constant for any p-norm.