{"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/certified-robustness-for-top-k-predictions-1","title":"Certified Robustness for Top-k Predictions against Adversarial Perturbations via Randomized Smoothing","arxiv_id":"1912.09899","date":"2019-12-20","proceeding":"ICLR 2020 1","authors":["Jinyuan Jia","Xiaoyu Cao","Binghui Wang","Neil Zhenqiang Gong"],"abstract":"It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to top-1 predictions. In many real-world applications, top-$k$ predictions are more relevant. In this work, we aim to derive certified robustness for top-$k$ predictions. In particular, our certified robustness is based on randomized smoothing, which turns any classifier to a new classifier via adding noise to an input example. We adopt randomized smoothing because it is scalable to large-scale neural networks and applicable to any classifier. We derive a tight robustness in $\\ell_2$ norm for top-$k$ predictions when using randomized smoothing with Gaussian noise. We find that generalizing the certified robustness from top-1 to top-$k$ predictions faces significant technical challenges. We also empirically evaluate our method on CIFAR10 and ImageNet. For example, our method can obtain an ImageNet classifier with a certified top-5 accuracy of 62.8\\% when the $\\ell_2$-norms of the adversarial perturbations are less than 0.5 (=127/255). Our code is publicly available at: \\url{https://github.com/jjy1994/Certify_Topk}.","url_abs":"https://arxiv.org/abs/1912.09899v1","url_pdf":"https://arxiv.org/pdf/1912.09899v1.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":"certified-robustness-for-top-k-predictions-1","repo_url":"https://github.com/jjy1994/Certify_Topk","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"randomized-smoothing","method_name":"Randomized Smoothing"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1912.09899","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}