{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:IAXP55U22TQDKXXXZAMLZTYW6J","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":"4f518623b8651b2db2a0a436b259bd5dea7a5bfd930ad576c5996d35af34b199","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-25T06:06:31Z","title_canon_sha256":"67bb091ca08072dfbe9b2b3d9fbdb59e0bfb9f4bebb640b67b7c46232960a3f8"},"schema_version":"1.0","source":{"id":"2401.13971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.13971","created_at":"2026-07-05T09:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"2401.13971v2","created_at":"2026-07-05T09:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.13971","created_at":"2026-07-05T09:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"IAXP55U22TQD","created_at":"2026-07-05T09:31:29Z"},{"alias_kind":"pith_short_16","alias_value":"IAXP55U22TQDKXXX","created_at":"2026-07-05T09:31:29Z"},{"alias_kind":"pith_short_8","alias_value":"IAXP55U2","created_at":"2026-07-05T09:31:29Z"}],"graph_snapshots":[{"event_id":"sha256:7600c953b9285da9012a655b1c77cad4a5d35bbd335642bea145ba259e88cc5f","target":"graph","created_at":"2026-07-05T09:31:29Z","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/2401.13971/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the $\\mathcal{O} ( 1 / \\sqrt{K})$ convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of $\\|x\\|$ or locally estimated through independent random samples.","authors_text":"Qi Deng, Wenzhi Gao","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-25T06:06:31Z","title":"Stochastic Weakly Convex Optimization Beyond Lipschitz Continuity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.13971","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":"sha256:5faf7b6466bad4893ab52b5d0cef075eabaeda070333749352ff7bed788b7188","target":"record","created_at":"2026-07-05T09:31:29Z","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":"4f518623b8651b2db2a0a436b259bd5dea7a5bfd930ad576c5996d35af34b199","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-25T06:06:31Z","title_canon_sha256":"67bb091ca08072dfbe9b2b3d9fbdb59e0bfb9f4bebb640b67b7c46232960a3f8"},"schema_version":"1.0","source":{"id":"2401.13971","kind":"arxiv","version":2}},"canonical_sha256":"402efef69ad4e0355ef7c818bccf16f26e9e65fcddfa1ad1391287088c1af396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"402efef69ad4e0355ef7c818bccf16f26e9e65fcddfa1ad1391287088c1af396","first_computed_at":"2026-07-05T09:31:29.437652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:31:29.437652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8gtnSbQbv+GNQau5L0fOGNa6QEK4RkpotoD18rsEiqShV2/U8D3KocdZWv0cc0ZTEvqps0BeLLgw9UEfOlI7AA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:31:29.438174Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.13971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5faf7b6466bad4893ab52b5d0cef075eabaeda070333749352ff7bed788b7188","sha256:7600c953b9285da9012a655b1c77cad4a5d35bbd335642bea145ba259e88cc5f"],"state_sha256":"e6bbad03267e78f933711df506b1fb1cb2500f430dcaabe8db1441d10bb62ca4"}