{"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/efficient-neural-network-robustness","title":"Efficient Neural Network Robustness Certification with General Activation Functions","arxiv_id":"1811.00866","date":"2018-11-02","proceeding":"NeurIPS 2018 12","authors":["Huan Zhang","Tsui-Wei Weng","Pin-Yu Chen","Cho-Jui Hsieh","Luca Daniel"],"abstract":"Finding minimum distortion of adversarial examples and thus certifying\nrobustness in neural network classifiers for given data points is known to be a\nchallenging problem. Nevertheless, recently it has been shown to be possible to\ngive a non-trivial certified lower bound of minimum adversarial distortion, and\nsome recent progress has been made towards this direction by exploiting the\npiece-wise linear nature of ReLU activations. However, a generic robustness\ncertification for general activation functions still remains largely\nunexplored. To address this issue, in this paper we introduce CROWN, a general\nframework to certify robustness of neural networks with general activation\nfunctions for given input data points. The novelty in our algorithm consists of\nbounding a given activation function with linear and quadratic functions, hence\nallowing it to tackle general activation functions including but not limited to\nfour popular choices: ReLU, tanh, sigmoid and arctan. In addition, we\nfacilitate the search for a tighter certified lower bound by adaptively\nselecting appropriate surrogates for each neuron activation. Experimental\nresults show that CROWN on ReLU networks can notably improve the certified\nlower bounds compared to the current state-of-the-art algorithm Fast-Lin, while\nhaving comparable computational efficiency. Furthermore, CROWN also\ndemonstrates its effectiveness and flexibility on networks with general\nactivation functions, including tanh, sigmoid and arctan.","url_abs":"http://arxiv.org/abs/1811.00866v1","url_pdf":"http://arxiv.org/pdf/1811.00866v1.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":"efficient-neural-network-robustness","repo_url":"https://github.com/huanzhang12/CROWN-Robustness-Certification","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"efficient-neural-network-robustness","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":"efficient-neural-network-robustness","repo_url":"https://github.com/CROWN-Robustness/Crown","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/IBM/CROWN-Robustness-Certification","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/Verified-Intelligence/alpha-beta-CROWN_vnncomp2024","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/ZhaoyangLyu/FROWN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/aria-systems-group/formal-deep-kernel-synthesis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/avrahamraviv/formal-verification-of-object-detection","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/huanzhang12/CROWN-IBP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/huanzhang12/CertifiedReLURobustness","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-2-Clause"}},{"paper_slug":"efficient-neural-network-robustness","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":"efficient-neural-network-robustness","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":"efficient-neural-network-robustness","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":"efficient-neural-network-robustness","repo_url":"https://github.com/huanzhang12/alpha-beta-CROWN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/huanzhang12/sa_ppo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"efficient-neural-network-robustness","repo_url":"https://github.com/verified-intelligence/alpha-beta-crown","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"efficient-neural-network","task_name":"Efficient Neural Network"}],"methods":[{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.00866","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1811.00866"}},"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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