{"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/adversarial-training-and-robustness-for","title":"Adversarial Training and Robustness for Multiple Perturbations","arxiv_id":"1904.13000","date":"2019-04-30","proceeding":"NeurIPS 2019 12","authors":["Florian Tramèr","Dan Boneh"],"abstract":"Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\\ell_\\infty$-noise). For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple perturbation types. We prove that a trade-off in robustness to different types of $\\ell_p$-bounded and spatial perturbations must exist in a natural and simple statistical setting. We corroborate our formal analysis by demonstrating similar robustness trade-offs on MNIST and CIFAR10. Building upon new multi-perturbation adversarial training schemes, and a novel efficient attack for finding $\\ell_1$-bounded adversarial examples, we show that no model trained against multiple attacks achieves robustness competitive with that of models trained on each attack individually. In particular, we uncover a pernicious gradient-masking phenomenon on MNIST, which causes adversarial training with first-order $\\ell_\\infty, \\ell_1$ and $\\ell_2$ adversaries to achieve merely $50\\%$ accuracy. Our results question the viability and computational scalability of extending adversarial robustness, and adversarial training, to multiple perturbation types.","url_abs":"https://arxiv.org/abs/1904.13000v2","url_pdf":"https://arxiv.org/pdf/1904.13000v2.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":"adversarial-training-and-robustness-for","repo_url":"https://github.com/ftramer/MultiRobustness","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1904.13000","atlas_url":"https://app.syntology.ai/?focus=1904.13000","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1904.13000"}},"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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