{"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/adaptive-smoothness-weighted-adversarial","title":"Adaptive Smoothness-weighted Adversarial Training for Multiple Perturbations with Its Stability Analysis","arxiv_id":"2210.00557","date":"2022-10-02","proceeding":null,"authors":["Jiancong Xiao","Zeyu Qin","Yanbo Fan","Baoyuan Wu","Jue Wang","Zhi-Quan Luo"],"abstract":"Adversarial Training (AT) has been demonstrated as one of the most effective methods against adversarial examples. While most existing works focus on AT with a single type of perturbation e.g., the $\\ell_\\infty$ attacks), DNNs are facing threats from different types of adversarial examples. Therefore, adversarial training for multiple perturbations (ATMP) is proposed to generalize the adversarial robustness over different perturbation types (in $\\ell_1$, $\\ell_2$, and $\\ell_\\infty$ norm-bounded perturbations). However, the resulting model exhibits trade-off between different attacks. Meanwhile, there is no theoretical analysis of ATMP, limiting its further development. In this paper, we first provide the smoothness analysis of ATMP and show that $\\ell_1$, $\\ell_2$, and $\\ell_\\infty$ adversaries give different contributions to the smoothness of the loss function of ATMP. Based on this, we develop the stability-based excess risk bounds and propose adaptive smoothness-weighted adversarial training for multiple perturbations. Theoretically, our algorithm yields better bounds. Empirically, our experiments on CIFAR10 and CIFAR100 achieve the state-of-the-art performance against the mixture of multiple perturbations attacks.","url_abs":"https://arxiv.org/abs/2210.00557v1","url_pdf":"https://arxiv.org/pdf/2210.00557v1.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":"adaptive-smoothness-weighted-adversarial","repo_url":"https://github.com/JiancongXiao/Adaptive-Smoothness-Weighted-AT","is_official":1,"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":{"atlas_url":"https://app.syntology.ai/?focus=2210.00557","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2210.00557"}},"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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