Lipschitz constant estimation of Neural Networks via sparse polynomial optimization

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.

Published as a conference paper in ICLR2020, originally submitted in September 25 2019 and available at https://openreview.net/forum?id=rJe4_xSFDB

Cited by in corpus (9)

• Communication-Efficient Robust Federated Learning Over Heterogeneous Datasets
• Markov-Lipschitz Deep Learning
• Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certification
• The Nonlinearity Coefficient - A Practical Guide to Neural Architecture Design
• What training reveals about neural network complexity
• Analytical bounds on the local Lipschitz constants of affine-ReLU functions
• Efficient Proximal Mapping of the 1-path-norm of Shallow Networks
• Building Compact and Robust Deep Neural Networks with Toeplitz Matrices
• Depthwise Separable Convolutions Allow for Fast and Memory-Efficient Spectral Normalization