{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/polar-express-efficient-and-precise-formal","title":"POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systems","arxiv_id":"2304.01218","date":"2023-03-31","proceeding":null,"authors":["YiXuan Wang","Weichao Zhou","Jiameng Fan","Zhilu Wang","Jiajun Li","Xin Chen","Chao Huang","Wenchao Li","Qi Zhu"],"abstract":"Neural networks (NNs) playing the role of controllers have demonstrated impressive empirical performances on challenging control problems. However, the potential adoption of NN controllers in real-life applications also gives rise to a growing concern over the safety of these neural-network controlled systems (NNCSs), especially when used in safety-critical applications. In this work, we present POLAR-Express, an efficient and precise formal reachability analysis tool for verifying the safety of NNCSs. POLAR-Express uses Taylor model arithmetic to propagate Taylor models (TMs) across a neural network layer-by-layer to compute an overapproximation of the neural-network function. It can be applied to analyze any feed-forward neural network with continuous activation functions. We also present a novel approach to propagate TMs more efficiently and precisely across ReLU activation functions. In addition, POLAR-Express provides parallel computation support for the layer-by-layer propagation of TMs, thus significantly improving the efficiency and scalability over its earlier prototype POLAR. Across the comparison with six other state-of-the-art tools on a diverse set of benchmarks, POLAR-Express achieves the best verification efficiency and tightness in the reachable set analysis.","url_abs":"https://arxiv.org/abs/2304.01218v3","url_pdf":"https://arxiv.org/pdf/2304.01218v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"polar-express-efficient-and-precise-formal","repo_url":"https://github.com/chaohuang2018/polar_tool","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2304.01218","atlas_url":"https://app.syntology.ai/?focus=2304.01218","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}