{"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/computational-asymmetries-in-robust","title":"Computational Asymmetries in Robust Classification","arxiv_id":"2306.14326","date":"2023-06-25","proceeding":null,"authors":["Samuele Marro","Michele Lombardi"],"abstract":"In the context of adversarial robustness, we make three strongly related contributions. First, we prove that while attacking ReLU classifiers is $\\mathit{NP}$-hard, ensuring their robustness at training time is $\\Sigma^2_P$-hard (even on a single example). This asymmetry provides a rationale for the fact that robust classifications approaches are frequently fooled in the literature. Second, we show that inference-time robustness certificates are not affected by this asymmetry, by introducing a proof-of-concept approach named Counter-Attack (CA). Indeed, CA displays a reversed asymmetry: running the defense is $\\mathit{NP}$-hard, while attacking it is $\\Sigma_2^P$-hard. Finally, motivated by our previous result, we argue that adversarial attacks can be used in the context of robustness certification, and provide an empirical evaluation of their effectiveness. As a byproduct of this process, we also release UG100, a benchmark dataset for adversarial attacks.","url_abs":"https://arxiv.org/abs/2306.14326v1","url_pdf":"https://arxiv.org/pdf/2306.14326v1.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":"computational-asymmetries-in-robust","repo_url":"https://github.com/samuelemarro/counter-attack","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":"classification-1","task_name":"Classification"},{"task_slug":"robust-classification","task_name":"Robust classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}