  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.
