{"paper":{"title":"Statistical Consistency and Generalization of Contrastive Representation Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Contrastive loss is statistically consistent with optimal ranking in retrieval tasks","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Tianbao Yang, Xiyuan Wei, Yiming Ying, Yuanfan Li","submitted_at":"2026-05-04T00:38:29Z","abstract_excerpt":"Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood; (ii) available generalization bounds deteriorate as the number of negative samples increases, contradicting the empirical benefits of large negative sets; and (iii) the retrieval performance of CRL has received limited theoretical attention. In this paper, we develop a unified statistical learning theory for CRL. For downstream tasks, we evaluate retrieval "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the contrastive loss is statistically consistent with optimal ranking and derive generalization bounds of order O(1/m + 1/sqrt(n)) and O(1/sqrt(m) + 1/sqrt(n)) for supervised and self-supervised CRL respectively.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The paper does not state the weakest assumption explicitly in the abstract; the bounds and consistency results are likely to rest on standard statistical-learning assumptions such as i.i.d. sampling, bounded loss functions, and appropriate regularity conditions on the data distribution that are not detailed here.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Contrastive representation learning is statistically consistent for optimal retrieval and admits generalization bounds of order O(1/m + 1/sqrt(n)) supervised and O(1/sqrt(m) + 1/sqrt(n)) self-supervised that benefit from large negative-sample counts m.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Contrastive loss is statistically consistent with optimal ranking in retrieval tasks","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5ba978c8ed98c321c22678001f012980c211e13824edf06855ec4830aefe9c32"},"source":{"id":"2605.02116","kind":"arxiv","version":2},"verdict":{"id":"0264c3e4-f5dc-4e19-b5d2-3e99d21d7892","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T16:52:33.174189Z","strongest_claim":"We show that the contrastive loss is statistically consistent with optimal ranking and derive generalization bounds of order O(1/m + 1/sqrt(n)) and O(1/sqrt(m) + 1/sqrt(n)) for supervised and self-supervised CRL respectively.","one_line_summary":"Contrastive representation learning is statistically consistent for optimal retrieval and admits generalization bounds of order O(1/m + 1/sqrt(n)) supervised and O(1/sqrt(m) + 1/sqrt(n)) self-supervised that benefit from large negative-sample counts m.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The paper does not state the weakest assumption explicitly in the abstract; the bounds and consistency results are likely to rest on standard statistical-learning assumptions such as i.i.d. sampling, bounded loss functions, and appropriate regularity conditions on the data distribution that are not detailed here.","pith_extraction_headline":"Contrastive loss is statistically consistent with optimal ranking in retrieval tasks"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02116/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T16:37:40.598294Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T04:01:22.646763Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T16:39:39.227981Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7e055980203754714e3434be3efad1e3797fd7a368fa4093da582dcb5f288c56"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}