Lipschitz constant estimation of Neural Networks via sparse polynomial optimization
This work addresses the need for efficient Lipschitz constant estimation in neural networks, particularly for convolutional and pruned architectures, though it is incremental as it builds on existing optimization methods.
The authors tackled the problem of estimating Lipschitz constants for neural networks by introducing LiPopt, a polynomial optimization framework that reduces computational complexity using network sparsity, and demonstrated superior estimates for the ℓ∞-Lipschitz constant compared to baselines on MNIST-trained networks.
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.