{"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/verification-of-geometric-robustness-of","title":"Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation","arxiv_id":"2408.13140","date":"2024-08-23","proceeding":null,"authors":["Ben Batten","Yang Zheng","Alessandro De Palma","Panagiotis Kouvaros","Alessio Lomuscio"],"abstract":"We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz optimisation. The method obtains provably tighter over-approximations of the perturbation region than the present state-of-the-art. We report results from experiments on a comprehensive set of verification benchmarks on MNIST and CIFAR10. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.","url_abs":"https://arxiv.org/abs/2408.13140v3","url_pdf":"https://arxiv.org/pdf/2408.13140v3.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":"verification-of-geometric-robustness-of","repo_url":"https://github.com/benbatten/pwl-geometric-verification","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}