Lipschitz Constants of Hybrid Zonotope Representations of Feedforward Neural Networks

Verifying the robustness of neural network outputs to perturbations in inputs is a key criterion for integrating them as part of any commercial or safety-critical application. The Lipschitz constant–a measure of the steepness of the surface–has been the standard statistic used to quantify input sensitivity. Recent work has established that hybrid zonotopes can exactly represent ReLU feedfoward networks. Here we expand this exactness to neural networks with any piecewise affine activation function and discuss tight approximations of neural networks with smooth activation functions. We leverage the hybrid zonotope representation to efficiently calculate exact Lipschitz constants and further present the opportunity to develop novel, more informative statistics for neural network verification.