{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:S664DPNJ6SOBDODCJ7W7AEMZCU","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":"b4cce9f47bc748bd124ab2dfa2a0ee44d43ac6733f8e621e0da042389de1a444","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-08-21T14:57:47Z","title_canon_sha256":"530bde5ffbb1623a2b89a9b48a1702e92e35cdbeb1ce7865d3bdd47c2c16c71e"},"schema_version":"1.0","source":{"id":"2208.09900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09900","created_at":"2026-07-05T08:35:33Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09900v2","created_at":"2026-07-05T08:35:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09900","created_at":"2026-07-05T08:35:33Z"},{"alias_kind":"pith_short_12","alias_value":"S664DPNJ6SOB","created_at":"2026-07-05T08:35:33Z"},{"alias_kind":"pith_short_16","alias_value":"S664DPNJ6SOBDODC","created_at":"2026-07-05T08:35:33Z"},{"alias_kind":"pith_short_8","alias_value":"S664DPNJ","created_at":"2026-07-05T08:35:33Z"}],"graph_snapshots":[{"event_id":"sha256:8cac3764a148af40475c3a93e95b502fc4c45eb5d4b534d350e975522829d982","target":"graph","created_at":"2026-07-05T08:35:33Z","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/2208.09900/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Adam rely on the bounded smoothness assumption, referred to as the \\emph{L-smooth condition}. Unfortunately, this assumption does not hold for many deep learning tasks. Moreover, we believe that this assumption obscures the true benefit of Adam, as the algorithm can adapt its update magnitude according to local smoothness. This important feature of Adam becomes irrelevant when assuming globally bounded smoothness. This","authors_text":"Bohan Wang, Huishuai Zhang, Qi Meng, Ruoyu Sun, Tie-Yan Liu, Wei Chen, Yushun Zhang, Zhi-Ming Ma, Zhi-Quan Luo","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-08-21T14:57:47Z","title":"Provable Adaptivity of Adam under Non-uniform Smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09900","kind":"arxiv","version":2},"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:dbbd081a137a79ef45c092baa9e4acbc34c916925063578895e58b50baa76d64","target":"record","created_at":"2026-07-05T08:35:33Z","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":"b4cce9f47bc748bd124ab2dfa2a0ee44d43ac6733f8e621e0da042389de1a444","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-08-21T14:57:47Z","title_canon_sha256":"530bde5ffbb1623a2b89a9b48a1702e92e35cdbeb1ce7865d3bdd47c2c16c71e"},"schema_version":"1.0","source":{"id":"2208.09900","kind":"arxiv","version":2}},"canonical_sha256":"97bdc1bda9f49c11b8624fedf01199151adfe4d873cdc957f667778d63ebbabd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97bdc1bda9f49c11b8624fedf01199151adfe4d873cdc957f667778d63ebbabd","first_computed_at":"2026-07-05T08:35:33.593278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:35:33.593278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"opmqfdqHoyc9YtDFuAeEj/AyraHdJUbpjjNM8nidhqmP85yrfYxo0nSSEU4ZZVH4AVDyUkJqYebRtWIOr/UcDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:35:33.593808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.09900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbbd081a137a79ef45c092baa9e4acbc34c916925063578895e58b50baa76d64","sha256:8cac3764a148af40475c3a93e95b502fc4c45eb5d4b534d350e975522829d982"],"state_sha256":"96a0a79c5376f0ecf760ef51562e0d167f04f135a32df4384d468b0b727b645f"}