{"paper":{"title":"Breaking the Finite-Sample Barrier in Entropy Coupling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Dependence among fixed-marginal observations can drive conditional entropy to zero after finitely many samples.","cross_cats":["math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.IT","authors_text":"Jun Chen, Shahab Asoodeh","submitted_at":"2026-05-15T17:39:57Z","abstract_excerpt":"Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \\emph{minimum list entropy coupling} $H(P\\|Q_1,\\dots,Q_m)$, the minimum conditional entropy $H(X|Y_1,\\dots,Y_m)$ over all joint distributions with prescribed discrete marginals $X\\sim P$ and $Y_i\\sim Q_i$. Unlike classical formulations based on independent observations, our model allows $Y_1,\\dots,Y_m$ to be arbitrarily dependent while keeping each marginal fixed. This enlarged coupling space reveals a sharp dichotomy: independent observations reduce residual u"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under mild support assumptions, zero entropy is achieved with O(log(1/P_min)) observations, where P_min is the minimum nonzero mass of P; dependent observations can eliminate residual uncertainty exactly after finitely many samples.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The characterization of the zero-entropy regime relies on mild support assumptions for the discrete marginals and the enlarged coupling space allowing arbitrary dependence among the Y_i while preserving each marginal exactly.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Minimum list entropy coupling shows dependent observations can achieve zero residual entropy with O(log(1/P_min)) samples under mild support assumptions, with applications to exact recovery in representation learning and randomness extraction.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Dependence among fixed-marginal observations can drive conditional entropy to zero after finitely many samples.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fe9760352267eac6ecaa9a153b44ff6100559cca3ba8a0dc4df9216f7b5fc8d7"},"source":{"id":"2605.16229","kind":"arxiv","version":1},"verdict":{"id":"30b52f20-f82e-4be7-ba88-2948ce34f30b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:26:47.782679Z","strongest_claim":"Under mild support assumptions, zero entropy is achieved with O(log(1/P_min)) observations, where P_min is the minimum nonzero mass of P; dependent observations can eliminate residual uncertainty exactly after finitely many samples.","one_line_summary":"Minimum list entropy coupling shows dependent observations can achieve zero residual entropy with O(log(1/P_min)) samples under mild support assumptions, with applications to exact recovery in representation learning and randomness extraction.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The characterization of the zero-entropy regime relies on mild support assumptions for the discrete marginals and the enlarged coupling space allowing arbitrary dependence among the Y_i while preserving each marginal exactly.","pith_extraction_headline":"Dependence among fixed-marginal observations can drive conditional entropy to zero after finitely many samples."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16229/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T18:40:53.042585Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:31:18.716848Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T17:49:42.204199Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:41.822110Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:23.131710Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:28.241353Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.626898Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T16:51:58.429621Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fcfe921065bdac1a591c3108396ee5e423d383d91ec1f1aeb13d3338a5fc23ab"},"references":{"count":35,"sample":[{"doi":"","year":2002,"title":"Lindvall,Lectures on the Coupling Method","work_id":"91e8411b-4973-4732-9281-c770fda8688b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"A metric between probability distributions on finite sets of different cardinalities,","work_id":"fda6f999-c369-43a8-8910-f981712d8a66","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"How to find a joint probability distribution of minimum entropy (almost) given the marginals,","work_id":"d9e71efb-bd07-4e13-97d9-0e38ff9b1adc","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Minimum-entropy couplings and their applications,","work_id":"cd868c17-d035-4b1e-b197-63fdad504d9c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Computing low-entropy couplings for large-support distributions,","work_id":"6a45e4ab-fc84-4c16-aadf-2568312b2b19","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"71acd7fc3ac32b7666c3af05b7b37dd6acb6d406d7f194386e636e10f8a69b71","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"}