Lipschitz constant estimation of Neural Networks via sparse polynomial optimization

TL;DR

This paper presents LiPopt, a polynomial optimization framework that efficiently estimates tighter upper bounds on neural network Lipschitz constants by exploiting network sparsity, with superior results on MNIST and random networks.

Contribution

LiPopt introduces a novel polynomial optimization method leveraging network sparsity to improve Lipschitz constant estimation for neural networks.

Findings

LiPopt provides tighter upper bounds on Lipschitz constants than existing methods.

The approach is effective for convolutional and pruned networks.

Experimental results show improved estimates on MNIST and random networks.

Abstract

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite (SDP) programming. We show how to use the sparse connectivity of a network, to significantly reduce the complexity of computation. This is specially useful for convolutional as well as pruned neural networks. We conduct experiments on networks with random weights as well as networks trained on MNIST, showing that in the particular case of the $\ell_\infty$-Lipschitz constant, our approach yields superior estimates, compared to baselines available in the literature.