{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KZ4EWVOCEQGE5J6O63OOPA7G2D","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":"04bfbd0ebb9ddd5a73a1e5f02f39b7fc1cd61b901ee59a3b50e611410355f5d9","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-02-11T19:16:03Z","title_canon_sha256":"9b64ae78abc4d5f044875631ee401aaec6ca85621a40a5b8b23fa896714031f2"},"schema_version":"1.0","source":{"id":"2102.06229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06229","created_at":"2026-07-05T02:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06229v1","created_at":"2026-07-05T02:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06229","created_at":"2026-07-05T02:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"KZ4EWVOCEQGE","created_at":"2026-07-05T02:14:45Z"},{"alias_kind":"pith_short_16","alias_value":"KZ4EWVOCEQGE5J6O","created_at":"2026-07-05T02:14:45Z"},{"alias_kind":"pith_short_8","alias_value":"KZ4EWVOC","created_at":"2026-07-05T02:14:45Z"}],"graph_snapshots":[{"event_id":"sha256:c33e2732b9a53eaf49d7b604e2f8d7c9b5e7d0529d0765f296c466b57abcae57","target":"graph","created_at":"2026-07-05T02:14:45Z","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/2102.06229/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a novel approach to analyze generalization error for discretizations of Langevin diffusion, such as the stochastic gradient Langevin dynamics (SGLD). For an $\\epsilon$ tolerance of expected generalization error, it is known that a first order discretization can reach this target if we run $\\Omega(\\epsilon^{-1} \\log (\\epsilon^{-1}) )$ iterations with $\\Omega(\\epsilon^{-1})$ samples. In this article, we show that with additional smoothness assumptions, even first order methods can achieve arbitrarily runtime complexity. More precisely, for each $N>0$, we provide a sufficient smoothnes","authors_text":"Maxime Gazeau, Mufan Bill Li","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-02-11T19:16:03Z","title":"Higher Order Generalization Error for First Order Discretization of Langevin Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06229","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":"sha256:4e524f899439ba68dac9c036ae430fe15bb6fdba9617b4016070efd6ff67f0f0","target":"record","created_at":"2026-07-05T02:14:45Z","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":"04bfbd0ebb9ddd5a73a1e5f02f39b7fc1cd61b901ee59a3b50e611410355f5d9","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-02-11T19:16:03Z","title_canon_sha256":"9b64ae78abc4d5f044875631ee401aaec6ca85621a40a5b8b23fa896714031f2"},"schema_version":"1.0","source":{"id":"2102.06229","kind":"arxiv","version":1}},"canonical_sha256":"56784b55c2240c4ea7cef6dce783e6d0dcbb309a127f1716542600be1888a04c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56784b55c2240c4ea7cef6dce783e6d0dcbb309a127f1716542600be1888a04c","first_computed_at":"2026-07-05T02:14:45.932735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:45.932735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PePUyE58CRDWq0eJ1MA8Wty9fXP2fh9DIeo1KUAjRd9FOveeU3154KR2RlDmoeDMSgY4atLeIPBVAEJ/Fpp4Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:45.933109Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.06229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e524f899439ba68dac9c036ae430fe15bb6fdba9617b4016070efd6ff67f0f0","sha256:c33e2732b9a53eaf49d7b604e2f8d7c9b5e7d0529d0765f296c466b57abcae57"],"state_sha256":"de27c4b3c70a3ea726f757c8a6f7bf1c06eff3d6339c88967596a5313e050aff"}