{"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/characterizing-the-optimal-0-1-loss-for-multi","title":"Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attacker","arxiv_id":"2302.10722","date":"2023-02-21","proceeding":null,"authors":["Sihui Dai","Wenxin Ding","Arjun Nitin Bhagoji","Daniel Cullina","Ben Y. Zhao","Haitao Zheng","Prateek Mittal"],"abstract":"Finding classifiers robust to adversarial examples is critical for their safe deployment. Determining the robustness of the best possible classifier under a given threat model for a given data distribution and comparing it to that achieved by state-of-the-art training methods is thus an important diagnostic tool. In this paper, we find achievable information-theoretic lower bounds on loss in the presence of a test-time attacker for multi-class classifiers on any discrete dataset. We provide a general framework for finding the optimal 0-1 loss that revolves around the construction of a conflict hypergraph from the data and adversarial constraints. We further define other variants of the attacker-classifier game that determine the range of the optimal loss more efficiently than the full-fledged hypergraph construction. Our evaluation shows, for the first time, an analysis of the gap to optimal robustness for classifiers in the multi-class setting on benchmark datasets.","url_abs":"https://arxiv.org/abs/2302.10722v2","url_pdf":"https://arxiv.org/pdf/2302.10722v2.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":[],"tasks":[{"task_slug":"diagnostic","task_name":"Diagnostic"},{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2302.10722","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.10722"}},"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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/inspire-group/multiclass_robust_lb","reach":null}],"summary":{"ran_draft_wrong":2},"by_repo_kind":{"found_in_text":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":2,"samples":[{"code_sha256_prefix":"f59b7d631a61fe4d","entry":"get_dist_mat_name","repo":"inspire-group/multiclass_robust_lb","repo_kind":"found_in_text","path":"optimal_log_loss_lp_hyper.py","file_url":"https://github.com/inspire-group/multiclass_robust_lb/blob/HEAD/optimal_log_loss_lp_hyper.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f59b7d631a61fe4d"}},{"code_sha256_prefix":"d435ec59bdd55f3a","entry":"get_save_filename","repo":"inspire-group/multiclass_robust_lb","repo_kind":"found_in_text","path":"optimal_log_loss_lp_hyper.py","file_url":"https://github.com/inspire-group/multiclass_robust_lb/blob/HEAD/optimal_log_loss_lp_hyper.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d435ec59bdd55f3a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}