{"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/provably-adversarially-robust-nearest","title":"Provably Adversarially Robust Nearest Prototype Classifiers","arxiv_id":"2207.07208","date":"2022-07-14","proceeding":null,"authors":["Václav Voráček","Matthias Hein"],"abstract":"Nearest prototype classifiers (NPCs) assign to each input point the label of the nearest prototype with respect to a chosen distance metric. A direct advantage of NPCs is that the decisions are interpretable. Previous work could provide lower bounds on the minimal adversarial perturbation in the $\\ell_p$-threat model when using the same $\\ell_p$-distance for the NPCs. In this paper we provide a complete discussion on the complexity when using $\\ell_p$-distances for decision and $\\ell_q$-threat models for certification for $p,q \\in \\{1,2,\\infty\\}$. In particular we provide scalable algorithms for the \\emph{exact} computation of the minimal adversarial perturbation when using $\\ell_2$-distance and improved lower bounds in other cases. Using efficient improved lower bounds we train our Provably adversarially robust NPC (PNPC), for MNIST which have better $\\ell_2$-robustness guarantees than neural networks. Additionally, we show up to our knowledge the first certification results w.r.t. to the LPIPS perceptual metric which has been argued to be a more realistic threat model for image classification than $\\ell_p$-balls. Our PNPC has on CIFAR10 higher certified robust accuracy than the empirical robust accuracy reported in (Laidlaw et al., 2021). The code is available in our repository.","url_abs":"https://arxiv.org/abs/2207.07208v1","url_pdf":"https://arxiv.org/pdf/2207.07208v1.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":"provably-adversarially-robust-nearest","repo_url":"https://github.com/vvoracek/provably-adversarially-robust-nearest-prototype-classifiers","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":{"status":"ok"}}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2207.07208","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}