{"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/towards-universal-certified-robustness-with","title":"Towards Universal Certified Robustness with Multi-Norm Training","arxiv_id":"2410.03000","date":"2024-10-03","proceeding":null,"authors":["Enyi Jiang","David S. Cheung","Gagandeep Singh"],"abstract":"Existing certified training methods can only train models to be robust against a certain perturbation type (e.g. $l_\\infty$ or $l_2$). However, an $l_\\infty$ certifiably robust model may not be certifiably robust against $l_2$ perturbation (and vice versa) and also has low robustness against other perturbations (e.g. geometric and patch transformation). By constructing a theoretical framework to analyze and mitigate the tradeoff, we propose the first multi-norm certified training framework \\textbf{CURE}, consisting of several multi-norm certified training methods, to attain better \\emph{union robustness} when training from scratch or fine-tuning a pre-trained certified model. Inspired by our theoretical findings, we devise bound alignment and connect natural training with certified training for better union robustness. Compared with SOTA-certified training, \\textbf{CURE} improves union robustness to $32.0\\%$ on MNIST, $25.8\\%$ on CIFAR-10, and $10.6\\%$ on TinyImagenet across different epsilon values. It leads to better generalization on a diverse set of challenging unseen geometric and patch perturbations to $6.8\\%$ and $16.0\\%$ on CIFAR-10. Overall, our contributions pave a path towards \\textit{universal certified robustness}.","url_abs":"https://arxiv.org/abs/2410.03000v2","url_pdf":"https://arxiv.org/pdf/2410.03000v2.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":"towards-universal-certified-robustness-with","repo_url":"https://github.com/uiuc-focal-lab/CURE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}