2021/06/25 by Chao Huang, Huang, Chao, Jiameng Fan +8 · 3 citations
Computer Science · Physics and Astronomy · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Electrical engineering #Formal Methods in Verification #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2106.13867
openalex publication_date 2021/06/25 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28
We present POLAR, a polynomial arithmetic-based framework for efficient bounded-time reachability analysis of neural-network controlled systems (NNCSs). Existing approaches that leverage the standard Taylor Model (TM) arithmetic for approximating the neural-network controller cannot deal with non-differentiable activation functions and suffer from rapid explosion of the remainder when propagating the TMs. POLAR overcomes these shortcomings by integrating TM arithmetic with \textbfBernstein Bézier Form and symbolic remainder. The former enables TM propagation across non-differentiable activation functions and local refinement of TMs, and the latter reduces error accumulation in the TM remainder for linear mappings in the network. Experimental results show that POLAR significantly outperforms the current state-of-the-art tools in terms of both efficiency and tightness of the reachable set overapproximation. The source code can be found in https://github.com/ChaoHuang2018/POLARTool