Open- and Closed-Loop Neural Network Verification Using Polynomial Zonotopes

We present a novel approach to efficiently compute tight non-convex enclosures of the image through neural networks with ReLU, sigmoid, or hyperbolic tangent activation functions. In particular, we abstract input-output relation each neuron by polynomial approximation, which is evaluated in set-based manner using zonotopes. While our can also be beneficial for open-loop network verification, main application reachability analysis controlled systems, where zonotopes are able capture non-convexity caused as well system dynamics. This results superior performance compared other methods, demonstrate on various benchmarks.