{"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/gaussian-universality-of-linear-classifiers","title":"Gaussian Universality of Perceptrons with Random Labels","arxiv_id":"2205.13303","date":"2022-05-26","proceeding":null,"authors":["Federica Gerace","Florent Krzakala","Bruno Loureiro","Ludovic Stephan","Lenka Zdeborová"],"abstract":"While classical in many theoretical settings - and in particular in statistical physics-inspired works - the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we redeem this line of work in the case of generalized linear classification, a.k.a. the perceptron model, with random labels. We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance. In the limit of vanishing regularization, we further demonstrate that the training loss is independent of the data covariance. On the theoretical side, we prove this universality for an arbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that the universality holds also for a broad range of real datasets.","url_abs":"https://arxiv.org/abs/2205.13303v2","url_pdf":"https://arxiv.org/pdf/2205.13303v2.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":"gaussian-universality-of-linear-classifiers","repo_url":"https://github.com/idephics/randomlabelsuniversality","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"gaussian-universality-of-linear-classifiers","repo_url":"https://github.com/lucpoisson/gaussianmixtureuniversality","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2205.13303","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2205.13303"}},"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":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lucpoisson/gaussianmixtureuniversality","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/idephics/randomlabelsuniversality","reach":null}],"summary":{"ran_violates":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"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":3,"samples":[{"code_sha256_prefix":"7723a1c3edf47e98","entry":"dmh_m_Gs","repo":"idephics/randomlabelsuniversality","repo_kind":"official","path":"Theory/gaussian_mixture.py","file_url":"https://github.com/idephics/randomlabelsuniversality/blob/HEAD/Theory/gaussian_mixture.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"7723a1c3edf47e98"}},{"code_sha256_prefix":"f43239e3595bbc8e","entry":"dmh_p_Gs","repo":"idephics/randomlabelsuniversality","repo_kind":"official","path":"Theory/gaussian_mixture.py","file_url":"https://github.com/idephics/randomlabelsuniversality/blob/HEAD/Theory/gaussian_mixture.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f43239e3595bbc8e"}},{"code_sha256_prefix":"39f4390af2c89f52","entry":"dqh_p_Gs","repo":"idephics/randomlabelsuniversality","repo_kind":"official","path":"Theory/gaussian_mixture.py","file_url":"https://github.com/idephics/randomlabelsuniversality/blob/HEAD/Theory/gaussian_mixture.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"39f4390af2c89f52"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}