{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XVIIYCYFBEJQ324V6CZRLMLOJH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5a30dff972f8e08d44ccc0b97ae3bee55d0acfe78287de76a47bad459ec25909","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-09-10T14:16:24Z","title_canon_sha256":"f1f71d65076b4c84205e42e58b7dd06a411491ca1804d5ee191938c19a41136e"},"schema_version":"1.0","source":{"id":"2509.08619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.08619","created_at":"2026-07-05T12:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"2509.08619v1","created_at":"2026-07-05T12:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.08619","created_at":"2026-07-05T12:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"XVIIYCYFBEJQ","created_at":"2026-07-05T12:08:33Z"},{"alias_kind":"pith_short_16","alias_value":"XVIIYCYFBEJQ324V","created_at":"2026-07-05T12:08:33Z"},{"alias_kind":"pith_short_8","alias_value":"XVIIYCYF","created_at":"2026-07-05T12:08:33Z"}],"graph_snapshots":[{"event_id":"sha256:66cf6423f1f71f3d1b0dd24d6f0c2b5a206dc7698164c12252aa769a8107f1a0","target":"graph","created_at":"2026-07-05T12:08:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.08619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The unadjusted Langevin algorithm is widely used for sampling from complex high-dimensional distributions. It is well known to be biased, with the bias typically scaling linearly with the dimension when measured in squared Wasserstein distance. However, the recent paper of Chen et al. (2024) identifies an intriguing new delocalization effect: For a class of distributions with sparse interactions, the bias between low-dimensional marginals scales only with the lower dimension, not the full dimension. In this work, we strengthen the results of Chen et al. (2024) in the sparse interaction regime ","authors_text":"Daniel Lacker, Fuzhong Zhou","cross_cats":["cs.LG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-09-10T14:16:24Z","title":"A hierarchical entropy method for the delocalization of bias in high-dimensional Langevin Monte Carlo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08619","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:53023a3876154f86547ef0b8d088cbdb1790ebda6f8523b273a94c9ae69914c6","target":"record","created_at":"2026-07-05T12:08:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5a30dff972f8e08d44ccc0b97ae3bee55d0acfe78287de76a47bad459ec25909","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-09-10T14:16:24Z","title_canon_sha256":"f1f71d65076b4c84205e42e58b7dd06a411491ca1804d5ee191938c19a41136e"},"schema_version":"1.0","source":{"id":"2509.08619","kind":"arxiv","version":1}},"canonical_sha256":"bd508c0b0509130deb95f0b315b16e49d702557cdb1e7bda03e933395a2d4f18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd508c0b0509130deb95f0b315b16e49d702557cdb1e7bda03e933395a2d4f18","first_computed_at":"2026-07-05T12:08:33.261892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:08:33.261892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MOM5LriVBWlRBHom4gqE+CMcD+gVWhLxZZX3U6wLRLV1UlwSlf3/lK1q7lfkbySjMBnqXx9Sg4niTBZ3FBtEDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:08:33.262372Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.08619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53023a3876154f86547ef0b8d088cbdb1790ebda6f8523b273a94c9ae69914c6","sha256:66cf6423f1f71f3d1b0dd24d6f0c2b5a206dc7698164c12252aa769a8107f1a0"],"state_sha256":"12937947cad9378e1d98f4215fc102cfb42cac229905c8265f0d46f645d9de4d"}