Lipschitz constant estimation for general neural network architectures using control tools

TL;DR

This paper introduces a novel method for estimating the Lipschitz constant of various neural network architectures by modeling them as dynamical systems and using control theory tools, improving scalability and generality.

Contribution

It proposes a new approach that interprets neural networks as dynamical systems and employs semidefinite programming with integral quadratic constraints for Lipschitz estimation.

Findings

Effective estimation of Lipschitz constants for diverse architectures.

Demonstrated scalability on large neural networks.

Applied to MNIST and CIFAR-10 datasets with promising results.

Abstract

This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th layer corresponds to the dynamics at time $k$. A key novelty with respect to prior work is that we use this interpretation to exploit the series interconnection structure of feedforward neural networks with a dynamic programming recursion. Nonlinearities, such as activation functions and nonlinear pooling layers, are handled with integral quadratic constraints. If the neural network contains signal processing layers (convolutional or state space model layers), we realize them as 1-D/2-D/N-D systems and exploit this structure as well. We distinguish ourselves from related work on Lipschitz constant estimation by more extensive structure exploitation (scalability) and a generalization to a large class of common neural network architectures. To show the versatility and computational advantages of our method, we apply it to different neural network architectures trained on MNIST and CIFAR-10.