{"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/robustness-via-curvature-regularization-and","title":"Robustness via curvature regularization, and vice versa","arxiv_id":"1811.09716","date":"2018-11-23","proceeding":"CVPR 2019 6","authors":["Seyed-Mohsen Moosavi-Dezfooli","Alhussein Fawzi","Jonathan Uesato","Pascal Frossard"],"abstract":"State-of-the-art classifiers have been shown to be largely vulnerable to\nadversarial perturbations. One of the most effective strategies to improve\nrobustness is adversarial training. In this paper, we investigate the effect of\nadversarial training on the geometry of the classification landscape and\ndecision boundaries. We show in particular that adversarial training leads to a\nsignificant decrease in the curvature of the loss surface with respect to\ninputs, leading to a drastically more \"linear\" behaviour of the network. Using\na locally quadratic approximation, we provide theoretical evidence on the\nexistence of a strong relation between large robustness and small curvature. To\nfurther show the importance of reduced curvature for improving the robustness,\nwe propose a new regularizer that directly minimizes curvature of the loss\nsurface, and leads to adversarial robustness that is on par with adversarial\ntraining. Besides being a more efficient and principled alternative to\nadversarial training, the proposed regularizer confirms our claims on the\nimportance of exhibiting quasi-linear behavior in the vicinity of data points\nin order to achieve robustness.","url_abs":"http://arxiv.org/abs/1811.09716v1","url_pdf":"http://arxiv.org/pdf/1811.09716v1.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":"robustness-via-curvature-regularization-and","repo_url":"https://github.com/F-Salehi/CURE_robustness","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"robustness-via-curvature-regularization-and","repo_url":"https://github.com/alirezaabdollahpour/CURE_fast_adversarial","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1811.09716","atlas_url":"https://app.syntology.ai/?focus=1811.09716","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1811.09716"}},"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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