{"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-robustness-via-fisher-rao","title":"Adversarial Robustness via Fisher-Rao Regularization","arxiv_id":"2106.06685","date":"2021-06-12","proceeding":null,"authors":["Marine Picot","Francisco Messina","Malik Boudiaf","Fabrice Labeau","Ismail Ben Ayed","Pablo Piantanida"],"abstract":"Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce FIRE, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between the softmax outputs corresponding to natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some interesting properties as well as connections with standard regularization metrics. Furthermore, for a simple linear and Gaussian model, we show that all Pareto-optimal points in the accuracy-robustness region can be reached by FIRE while other state-of-the-art methods fail. Empirically, we evaluate the performance of various classifiers trained with the proposed loss on standard datasets, showing up to a simultaneous 1\\% of improvement in terms of clean and robust performances while reducing the training time by 20\\% over the best-performing methods.","url_abs":"https://arxiv.org/abs/2106.06685v3","url_pdf":"https://arxiv.org/pdf/2106.06685v3.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-robustness-via-fisher-rao","repo_url":"https://github.com/MarinePICOT/Adversarial-Robustness-via-Fisher-Rao-Regularization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"adversarial-defense","task_name":"Adversarial Defense"},{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2106.06685","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}