{"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/center-smoothing-for-certifiably-robust","title":"Center Smoothing: Certified Robustness for Networks with Structured Outputs","arxiv_id":"2102.09701","date":"2021-02-19","proceeding":"NeurIPS 2021 12","authors":["Aounon Kumar","Tom Goldstein"],"abstract":"The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured outputs like sets, images, language, etc. We model the output space as a metric space under a distance/similarity function, such as intersection-over-union, perceptual similarity, total variation distance, etc. Such models are used in many machine learning problems like image segmentation, object detection, generative models, image/audio-to-text systems, etc. Based on a robustness technique called randomized smoothing, our $\\textit{center smoothing}$ procedure can produce models with the guarantee that the change in the output, as measured by the distance metric, remains small for any norm-bounded adversarial perturbation of the input. We apply our method to create certifiably robust models with disparate output spaces - from sets to images - and show that it yields meaningful certificates without significantly degrading the performance of the base model. Code for our experiments is available at: https://github.com/aounon/center-smoothing.","url_abs":"https://arxiv.org/abs/2102.09701v3","url_pdf":"https://arxiv.org/pdf/2102.09701v3.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":"center-smoothing-for-certifiably-robust","repo_url":"https://github.com/aounon/center-smoothing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-reconstruction","task_name":"Image Reconstruction"},{"task_slug":"image-segmentation","task_name":"Image Segmentation"},{"task_slug":"object-detection","task_name":"Object Detection"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"},{"task_slug":"super-resolution","task_name":"Super-Resolution"},{"task_slug":"object-detection-1","task_name":"object-detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2102.09701","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2102.09701"}},"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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