{"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/provable-robustness-against-all-adversarial","title":"Provable robustness against all adversarial $l_p$-perturbations for $p\\geq 1$","arxiv_id":"1905.11213","date":"2019-05-27","proceeding":"ICLR 2020 1","authors":["Francesco Croce","Matthias Hein"],"abstract":"In recent years several adversarial attacks and defenses have been proposed. Often seemingly robust models turn out to be non-robust when more sophisticated attacks are used. One way out of this dilemma are provable robustness guarantees. While provably robust models for specific $l_p$-perturbation models have been developed, we show that they do not come with any guarantee against other $l_q$-perturbations. We propose a new regularization scheme, MMR-Universal, for ReLU networks which enforces robustness wrt $l_1$- and $l_\\infty$-perturbations and show how that leads to the first provably robust models wrt any $l_p$-norm for $p\\geq 1$.","url_abs":"https://arxiv.org/abs/1905.11213v2","url_pdf":"https://arxiv.org/pdf/1905.11213v2.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":"provable-robustness-against-all-adversarial","repo_url":"https://github.com/fra31/mmr-universal","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"all","task_name":"All"}],"methods":[{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.11213","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}