A dual number abstraction for static analysis of Clarke Jacobians

We present a novel abstraction for bounding the Clarke Jacobian of Lipschitz continuous, but not necessarily differentiable function over local input region. To do so, we leverage abstract domain built upon dual numbers, adapted to soundly over-approximate all first derivatives needed compute Jacobian. formally prove that our forward-mode interval evaluation produces sound, domain-based over-approximation true given Due generality formalism, can and analyze Jacobians broader class functions than previous works supported – specifically, arbitrary compositions neural networks with Lipschitz, non-differentiable perturbations. implement technique in tool called DeepJ evaluate it on multiple deep perturbations showcase both scalability analysis. Concretely, obtain robustness optimization landscapes fully-connected convolutional rotational, contrast variation, haze perturbations, as well their compositions.