{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LTBNUH7KFYQYQQLNASOGZPTWTB","short_pith_number":"pith:LTBNUH7K","schema_version":"1.0","canonical_sha256":"5cc2da1fea2e2188416d049c6cbe76987005b302bfd99dee4a01d2792054c282","source":{"kind":"arxiv","id":"2408.13115","version":2},"attestation_state":"computed","paper":{"title":"Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.CO"],"primary_cat":"stat.ML","authors_text":"Jonathan Niles-Weed, Jonathan Weare, Xiaoou Cheng, Yifan Chen","submitted_at":"2024-08-20T01:24:54Z","abstract_excerpt":"The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension $d$ of the problem increases, the number of iterations required to ensure convergence within a desired error in the $W_2$ metric scales in proportion to $d$ or $\\sqrt{d}$. In this paper, we argue that, despite this poor scaling of the $W_2$ error for the full set of variables, the behavior for a small number of variables can be significantly better: a numbe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.13115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-08-20T01:24:54Z","cross_cats_sorted":["cs.LG","math.PR","stat.CO"],"title_canon_sha256":"3d8bd2baa6d383106924def0b9418800a2f0be6542a0aa303920da25f186cd65","abstract_canon_sha256":"ff4a6e44688d23a55c1cd06885bcf91946f766f074da4e089237e86dcd792791"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:04:27.861799Z","signature_b64":"8MtyRvREIiXtGEiE2El3DU1Ec4m02d662inc8PPs8UIwns9/3qJaXNkOvyapdMlqySJ7X5AC4V+GTcuvb3/IDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc2da1fea2e2188416d049c6cbe76987005b302bfd99dee4a01d2792054c282","last_reissued_at":"2026-07-05T12:04:27.861182Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:04:27.861182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.CO"],"primary_cat":"stat.ML","authors_text":"Jonathan Niles-Weed, Jonathan Weare, Xiaoou Cheng, Yifan Chen","submitted_at":"2024-08-20T01:24:54Z","abstract_excerpt":"The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension $d$ of the problem increases, the number of iterations required to ensure convergence within a desired error in the $W_2$ metric scales in proportion to $d$ or $\\sqrt{d}$. In this paper, we argue that, despite this poor scaling of the $W_2$ error for the full set of variables, the behavior for a small number of variables can be significantly better: a numbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.13115","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.13115/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2408.13115","created_at":"2026-07-05T12:04:27.861255+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.13115v2","created_at":"2026-07-05T12:04:27.861255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.13115","created_at":"2026-07-05T12:04:27.861255+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTBNUH7KFYQY","created_at":"2026-07-05T12:04:27.861255+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTBNUH7KFYQYQQLN","created_at":"2026-07-05T12:04:27.861255+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTBNUH7K","created_at":"2026-07-05T12:04:27.861255+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB","json":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB.json","graph_json":"https://pith.science/api/pith-number/LTBNUH7KFYQYQQLNASOGZPTWTB/graph.json","events_json":"https://pith.science/api/pith-number/LTBNUH7KFYQYQQLNASOGZPTWTB/events.json","paper":"https://pith.science/paper/LTBNUH7K"},"agent_actions":{"view_html":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB","download_json":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB.json","view_paper":"https://pith.science/paper/LTBNUH7K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.13115&json=true","fetch_graph":"https://pith.science/api/pith-number/LTBNUH7KFYQYQQLNASOGZPTWTB/graph.json","fetch_events":"https://pith.science/api/pith-number/LTBNUH7KFYQYQQLNASOGZPTWTB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB/action/storage_attestation","attest_author":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB/action/author_attestation","sign_citation":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB/action/citation_signature","submit_replication":"https://pith.science/pith/LTBNUH7KFYQYQQLNASOGZPTWTB/action/replication_record"}},"created_at":"2026-07-05T12:04:27.861255+00:00","updated_at":"2026-07-05T12:04:27.861255+00:00"}