{"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-fast-computation-of-certified","title":"Towards Fast Computation of Certified Robustness for ReLU Networks","arxiv_id":"1804.09699","date":"2018-04-25","proceeding":"ICML 2018 7","authors":["Tsui-Wei Weng","huan zhang","Hongge Chen","Zhao Song","Cho-Jui Hsieh","Duane Boning","Inderjit S. Dhillon","Luca Daniel"],"abstract":"Verifying the robustness property of a general Rectified Linear Unit (ReLU)\nnetwork is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer\nCAV17]. Although finding the exact minimum adversarial distortion is hard,\ngiving a certified lower bound of the minimum distortion is possible. Current\navailable methods of computing such a bound are either time-consuming or\ndelivering low quality bounds that are too loose to be useful. In this paper,\nwe exploit the special structure of ReLU networks and provide two\ncomputationally efficient algorithms Fast-Lin and Fast-Lip that are able to\ncertify non-trivial lower bounds of minimum distortions, by bounding the ReLU\nunits with appropriate linear functions Fast-Lin, or by bounding the local\nLipschitz constant Fast-Lip. Experiments show that (1) our proposed methods\ndeliver bounds close to (the gap is 2-3X) exact minimum distortion found by\nReluplex in small MNIST networks while our algorithms are more than 10,000\ntimes faster; (2) our methods deliver similar quality of bounds (the gap is\nwithin 35% and usually around 10%; sometimes our bounds are even better) for\nlarger networks compared to the methods based on solving linear programming\nproblems but our algorithms are 33-14,000 times faster; (3) our method is\ncapable of solving large MNIST and CIFAR networks up to 7 layers with more than\n10,000 neurons within tens of seconds on a single CPU core.\n  In addition, we show that, in fact, there is no polynomial time algorithm\nthat can approximately find the minimum $\\ell_1$ adversarial distortion of a\nReLU network with a $0.99\\ln n$ approximation ratio unless\n$\\mathsf{NP}$=$\\mathsf{P}$, where $n$ is the number of neurons in the network.","url_abs":"http://arxiv.org/abs/1804.09699v4","url_pdf":"http://arxiv.org/pdf/1804.09699v4.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-fast-computation-of-certified","repo_url":"https://github.com/huanzhang12/CertifiedReLURobustness","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"towards-fast-computation-of-certified","repo_url":"https://github.com/AkhilanB/CNN-Cert","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"towards-fast-computation-of-certified","repo_url":"https://github.com/huanzhang12/RecurJac","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"towards-fast-computation-of-certified","repo_url":"https://github.com/huanzhang12/RecurJac-Jacobian-Bounds","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"towards-fast-computation-of-certified","repo_url":"https://github.com/huanzhang12/RecurJac-and-CROWN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"towards-fast-computation-of-certified","repo_url":"https://github.com/lilyweng/PROVEN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":null,"task_name":"CPU"}],"methods":[{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.09699","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1804.09699"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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