{"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/parseval-networks-improving-robustness-to","title":"Parseval Networks: Improving Robustness to Adversarial Examples","arxiv_id":"1704.08847","date":"2017-04-28","proceeding":"ICML 2017 8","authors":["Moustapha Cisse","Piotr Bojanowski","Edouard Grave","Yann Dauphin","Nicolas Usunier"],"abstract":"We introduce Parseval networks, a form of deep neural networks in which the\nLipschitz constant of linear, convolutional and aggregation layers is\nconstrained to be smaller than 1. Parseval networks are empirically and\ntheoretically motivated by an analysis of the robustness of the predictions\nmade by deep neural networks when their input is subject to an adversarial\nperturbation. The most important feature of Parseval networks is to maintain\nweight matrices of linear and convolutional layers to be (approximately)\nParseval tight frames, which are extensions of orthogonal matrices to\nnon-square matrices. We describe how these constraints can be maintained\nefficiently during SGD. We show that Parseval networks match the\nstate-of-the-art in terms of accuracy on CIFAR-10/100 and Street View House\nNumbers (SVHN) while being more robust than their vanilla counterpart against\nadversarial examples. Incidentally, Parseval networks also tend to train faster\nand make a better usage of the full capacity of the networks.","url_abs":"http://arxiv.org/abs/1704.08847v2","url_pdf":"http://arxiv.org/pdf/1704.08847v2.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":"parseval-networks-improving-robustness-to","repo_url":"https://github.com/mathialo/parsnet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1704.08847","atlas_url":"https://app.syntology.ai/?focus=1704.08847","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}