Lipschitz constant estimation of Neural Networks via sparse polynomial optimizationDownload PDF

25 Sep 2019 (modified: 11 Mar 2020)ICLR 2020 Conference Blind SubmissionReaders: Everyone
  • Original Pdf: pdf
  • 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.
  • Code: https://drive.google.com/drive/folders/1bkj0H6Thgd9sjRloyq9NBP0uO0v704E9?usp=sharing
  • Keywords: robust networks, Lipschitz constant, polynomial optimization
  • TL;DR: LP-based upper bounds on the Lipschitz constant of Neural Networks
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