POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems

We present POLAR (The source code can be found at https://github.com/ChaoHuang2018/POLAR_Tool . The full version of this paper https://arxiv.org/abs/2106.13867. ), a POLynomial ARithmetic-based framework for efficient time-bounded reachability analysis neural-network controlled systems. Existing approaches leveraging the standard Taylor Model (TM) arithmetic approximating controller cannot deal with non-differentiable activation functions and suffer from rapid explosion remainder when propagating TMs. overcomes these shortcomings by integrating TM Bernstein polynomial interpolation symbolic remainders. former enables propagation across local refinement TMs, latter reduces error accumulation in linear mappings neural network. Experimental results show significantly outperforms state-of-the-art tools on both efficiency tightness reachable set overapproximation.