{"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/evaluating-robustness-of-neural-networks-with","title":"Evaluating Robustness of Neural Networks with Mixed Integer Programming","arxiv_id":"1711.07356","date":"2017-11-20","proceeding":"ICLR 2019 5","authors":["Vincent Tjeng","Kai Xiao","Russ Tedrake"],"abstract":"Neural networks have demonstrated considerable success on a wide variety of\nreal-world problems. However, networks trained only to optimize for training\naccuracy can often be fooled by adversarial examples - slightly perturbed\ninputs that are misclassified with high confidence. Verification of networks\nenables us to gauge their vulnerability to such adversarial examples. We\nformulate verification of piecewise-linear neural networks as a mixed integer\nprogram. On a representative task of finding minimum adversarial distortions,\nour verifier is two to three orders of magnitude quicker than the\nstate-of-the-art. We achieve this computational speedup via tight formulations\nfor non-linearities, as well as a novel presolve algorithm that makes full use\nof all information available. The computational speedup allows us to verify\nproperties on convolutional networks with an order of magnitude more ReLUs than\nnetworks previously verified by any complete verifier. In particular, we\ndetermine for the first time the exact adversarial accuracy of an MNIST\nclassifier to perturbations with bounded $l_\\infty$ norm $\\epsilon=0.1$: for\nthis classifier, we find an adversarial example for 4.38% of samples, and a\ncertificate of robustness (to perturbations with bounded norm) for the\nremainder. Across all robust training procedures and network architectures\nconsidered, we are able to certify more samples than the state-of-the-art and\nfind more adversarial examples than a strong first-order attack.","url_abs":"http://arxiv.org/abs/1711.07356v3","url_pdf":"http://arxiv.org/pdf/1711.07356v3.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":"evaluating-robustness-of-neural-networks-with","repo_url":"https://github.com/vtjeng/MIPVerify.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"evaluating-robustness-of-neural-networks-with","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/MIPVerify.jl-e5e5f8be-2a6a-5994-adbb-5afbd0e30425","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"evaluating-robustness-of-neural-networks-with","repo_url":"https://github.com/fra31/mmr-universal","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"evaluating-robustness-of-neural-networks-with","repo_url":"https://github.com/rtoth11/NNAdversary-MIPVerify","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"evaluating-robustness-of-neural-networks-with","repo_url":"https://github.com/sisl/OVERTVerify.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"evaluating-robustness-of-neural-networks-with","repo_url":"https://github.com/yycdavid/TilerVerify","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1711.07356","atlas_url":"https://app.syntology.ai/?focus=1711.07356","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1711.07356"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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