Lipschitz Constant Estimation of Neural Networks via Sparse Polynomial Optimization
Abstract
We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bound 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 as compared to other baselines available in the literature.
Cite
Text
Latorre et al. "Lipschitz Constant Estimation of Neural Networks via Sparse Polynomial Optimization." International Conference on Learning Representations, 2020.Markdown
[Latorre et al. "Lipschitz Constant Estimation of Neural Networks via Sparse Polynomial Optimization." International Conference on Learning Representations, 2020.](https://mlanthology.org/iclr/2020/latorre2020iclr-lipschitz/)BibTeX
@inproceedings{latorre2020iclr-lipschitz,
title = {{Lipschitz Constant Estimation of Neural Networks via Sparse Polynomial Optimization}},
author = {Latorre, Fabian and Rolland, Paul and Cevher, Volkan},
booktitle = {International Conference on Learning Representations},
year = {2020},
url = {https://mlanthology.org/iclr/2020/latorre2020iclr-lipschitz/}
}