CLIP: Cheap Lipschitz Training of Neural Networks

TL;DR

This paper introduces CLIP, a variational regularization method for neural networks that effectively controls their Lipschitz constant, enhancing stability against adversarial perturbations, with theoretical analysis and empirical validation on classification tasks.

Contribution

The paper proposes a novel variational regularization technique called CLIP for controlling neural network Lipschitz constants, improving stability and robustness.

Findings

CLIP effectively bounds the Lipschitz constant of neural networks.

Numerical experiments show improved stability over weight regularization.

Method performs well on MNIST and Fashion-MNIST datasets.

Abstract

Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so called adversarial examples, that can cause false predictions. This instability can have severe consequences in applications which influence the health and safety of humans, e.g., biomedical imaging or autonomous driving. While bounding the Lipschitz constant of a neural network improves stability, most methods rely on restricting the Lipschitz constants of each layer which gives a poor bound for the actual Lipschitz constant. In this paper we investigate a variational regularization method named CLIP for controlling the Lipschitz constant of a neural network, which can easily be integrated into the training procedure. We mathematically analyze the proposed model, in particular discussing the impact of the chosen regularization parameter on the output of the network. Finally, we numerically evaluate our method on both a nonlinear regression problem and the MNIST and Fashion-MNIST classification databases, and compare our results with a weight regularization approach.