title: 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.
  
authors: Fabian Latorre Paul Rolland Volkan Cevher
hIndex: Volkan Cevher 49