{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:WGQYD7DWBA5K6ADV6OA3XXVQHT","short_pith_number":"pith:WGQYD7DW","schema_version":"1.0","canonical_sha256":"b1a181fc76083aaf0075f381bbdeb03cca06d5b5a928cf3c844bb397aeeb5ecc","source":{"kind":"arxiv","id":"2207.09304","version":3},"attestation_state":"computed","paper":{"title":"A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.PR","authors_text":"Lei Li, Yuliang Wang","submitted_at":"2022-07-19T14:38:52Z","abstract_excerpt":"We establish a sharp uniform-in-time error estimate for the Stochastic Gradient Langevin Dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obtain a uniform-in-time $O(\\eta^2)$ bound for the KL-divergence between the SGLD iteration and the Langevin diffusion, where $\\eta$ is the step size (or learning rate). Our analysis is also valid for varying step sizes. Consequently, we are able to derive an $O(\\eta)$ bound for the distance between the invariant measures of the SGLD iteration and the Langevin diffusion, in terms of Wasserstein or total variation distanc"},"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":"2207.09304","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-07-19T14:38:52Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"4586be74588ed1d5a80893e852eb272a03bcc087fdc357a8b042eb598a1ae6d5","abstract_canon_sha256":"cdaed0bb3d737ce8197442d187a9dcb0d38cffa402d62b964334d02ba5852d9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:34:35.659188Z","signature_b64":"25W3GCZbT5znRUsES7EsHcabtXKFNJilTWCd6bvqJYIDv/kx6nwzjF9BEDL5KXoi+weEliQ2hUPm3ykvfas6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1a181fc76083aaf0075f381bbdeb03cca06d5b5a928cf3c844bb397aeeb5ecc","last_reissued_at":"2026-07-05T10:34:35.658245Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:34:35.658245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.PR","authors_text":"Lei Li, Yuliang Wang","submitted_at":"2022-07-19T14:38:52Z","abstract_excerpt":"We establish a sharp uniform-in-time error estimate for the Stochastic Gradient Langevin Dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obtain a uniform-in-time $O(\\eta^2)$ bound for the KL-divergence between the SGLD iteration and the Langevin diffusion, where $\\eta$ is the step size (or learning rate). Our analysis is also valid for varying step sizes. Consequently, we are able to derive an $O(\\eta)$ bound for the distance between the invariant measures of the SGLD iteration and the Langevin diffusion, in terms of Wasserstein or total variation distanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.09304","kind":"arxiv","version":3},"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/2207.09304/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":"2207.09304","created_at":"2026-07-05T10:34:35.658354+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.09304v3","created_at":"2026-07-05T10:34:35.658354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.09304","created_at":"2026-07-05T10:34:35.658354+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGQYD7DWBA5K","created_at":"2026-07-05T10:34:35.658354+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGQYD7DWBA5K6ADV","created_at":"2026-07-05T10:34:35.658354+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGQYD7DW","created_at":"2026-07-05T10:34:35.658354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2406.09241","citing_title":"What is the long-run distribution of stochastic gradient descent? A large deviations analysis","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2409.02399","citing_title":"Guidance for twisted particle filter: a continuous-time perspective","ref_index":43,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT","json":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT.json","graph_json":"https://pith.science/api/pith-number/WGQYD7DWBA5K6ADV6OA3XXVQHT/graph.json","events_json":"https://pith.science/api/pith-number/WGQYD7DWBA5K6ADV6OA3XXVQHT/events.json","paper":"https://pith.science/paper/WGQYD7DW"},"agent_actions":{"view_html":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT","download_json":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT.json","view_paper":"https://pith.science/paper/WGQYD7DW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.09304&json=true","fetch_graph":"https://pith.science/api/pith-number/WGQYD7DWBA5K6ADV6OA3XXVQHT/graph.json","fetch_events":"https://pith.science/api/pith-number/WGQYD7DWBA5K6ADV6OA3XXVQHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT/action/storage_attestation","attest_author":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT/action/author_attestation","sign_citation":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT/action/citation_signature","submit_replication":"https://pith.science/pith/WGQYD7DWBA5K6ADV6OA3XXVQHT/action/replication_record"}},"created_at":"2026-07-05T10:34:35.658354+00:00","updated_at":"2026-07-05T10:34:35.658354+00:00"}