{"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/semidefinite-relaxations-for-certifying","title":"Semidefinite relaxations for certifying robustness to adversarial examples","arxiv_id":"1811.01057","date":"2018-11-02","proceeding":"NeurIPS 2018 12","authors":["Aditi Raghunathan","Jacob Steinhardt","Percy Liang"],"abstract":"Despite their impressive performance on diverse tasks, neural networks fail\ncatastrophically in the presence of adversarial inputs---imperceptibly but\nadversarially perturbed versions of natural inputs. We have witnessed an arms\nrace between defenders who attempt to train robust networks and attackers who\ntry to construct adversarial examples. One promise of ending the arms race is\ndeveloping certified defenses, ones which are provably robust against all\nattackers in some family. These certified defenses are based on convex\nrelaxations which construct an upper bound on the worst case loss over all\nattackers in the family. Previous relaxations are loose on networks that are\nnot trained against the respective relaxation. In this paper, we propose a new\nsemidefinite relaxation for certifying robustness that applies to arbitrary\nReLU networks. We show that our proposed relaxation is tighter than previous\nrelaxations and produces meaningful robustness guarantees on three different\n\"foreign networks\" whose training objectives are agnostic to our proposed\nrelaxation.","url_abs":"http://arxiv.org/abs/1811.01057v1","url_pdf":"http://arxiv.org/pdf/1811.01057v1.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":"semidefinite-relaxations-for-certifying","repo_url":"https://github.com/GuanZihan/verification","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"semidefinite-relaxations-for-certifying","repo_url":"https://github.com/TongCHEN779/MultiMomOpt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"semidefinite-relaxations-for-certifying","repo_url":"https://github.com/soc-ucsd/verification","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.01057","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}