{"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/mitigating-the-curse-of-dimensionality-for","title":"Mitigating the Curse of Dimensionality for Certified Robustness via Dual Randomized Smoothing","arxiv_id":"2404.09586","date":"2024-04-15","proceeding":null,"authors":["Song Xia","Yi Yu","Xudong Jiang","Henghui Ding"],"abstract":"Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of ${\\ell_2}$ certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension $d$, proportionally decreasing at a rate of $1/\\sqrt{d}$. This paper explores the feasibility of providing ${\\ell_2}$ certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight ${\\ell_2}$ certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the ${\\ell_2}$ robustness radius, which decreases proportionally at a rate of $(1/\\sqrt m + 1/\\sqrt n )$ with $m+n=d$. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and ${\\ell_2}$ certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.","url_abs":"https://arxiv.org/abs/2404.09586v4","url_pdf":"https://arxiv.org/pdf/2404.09586v4.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":"mitigating-the-curse-of-dimensionality-for","repo_url":"https://github.com/xiasong0501/drs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"randomized-smoothing","method_name":"Randomized Smoothing"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2404.09586","atlas_url":"https://app.syntology.ai/?focus=2404.09586","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2404.09586"}},"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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