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arXiv · 2207.02715

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

Niklas Kochdumper·Christian Schilling·Matthias Althoff·Stanley Bak
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Abstract

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 the input-output relation of each neuron by a polynomial approximation, which is evaluated in a set-based manner using polynomial zonotopes. While our approach can also can be beneficial for open-loop neural network verification, our main application is reachability analysis of neural network controlled systems, where polynomial zonotopes are able to capture the non-convexity caused by the neural network as well as the system dynamics. This results in a superior performance compared to other methods, as we demonstrate on various benchmarks.

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Niklas Kochdumper, Christian Schilling, Matthias Althoff, Stanley Bak. 2022-07-06. Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes. https://doi.org/10.1007/978-3-031-33170-1_2

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