Exactly Computing the Local Lipschitz Constant of ReLU Networks
This work addresses the need for precise Lipschitz constant estimation in neural networks for applications like robustness and fairness, though it is incremental in improving computational methods.
The authors tackled the problem of exactly computing the local Lipschitz constant for ReLU neural networks, which is important for robustness and fairness, by developing an algorithm that provides exact values and evaluating its tightness against other estimators.
The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of nonsmooth vector-valued functions to a maximization over the norm of the generalized Jacobian. We present a sufficient condition for which backpropagation always returns an element of the generalized Jacobian, and reframe the problem over this broad class of functions. We show strong inapproximability results for estimating Lipschitz constants of ReLU networks, and then formulate an algorithm to compute these quantities exactly. We leverage this algorithm to evaluate the tightness of competing Lipschitz estimators and the effects of regularized training on the Lipschitz constant.