{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZDPKG2NDIWOJB6WNNM4GJC4KX2","short_pith_number":"pith:ZDPKG2ND","schema_version":"1.0","canonical_sha256":"c8dea369a3459c90facd6b38648b8abe89e84f23cb0d29455930ee68f6b24243","source":{"kind":"arxiv","id":"2512.23178","version":3},"attestation_state":"computed","paper":{"title":"Clipped Gradient Methods for Nonsmooth Convex Optimization under Heavy-Tailed Noise: A Refined Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Zijian Liu","submitted_at":"2025-12-29T03:35:53Z","abstract_excerpt":"Optimization under heavy-tailed noise has become popular recently, since it better fits many modern machine learning tasks, as captured by empirical observations. Concretely, instead of a finite second moment on gradient noise, a bounded ${\\frak p}$-th moment where ${\\frak p}\\in(1,2]$ has been recognized to be more realistic (say being upper bounded by $\\sigma_{\\frak l}^{\\frak p}$ for some $\\sigma_{\\frak l}\\ge0$). A simple yet effective operation, gradient clipping, is known to handle this new challenge successfully. Specifically, Clipped Stochastic Gradient Descent (Clipped SGD) guarantees a "},"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":"2512.23178","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-12-29T03:35:53Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"d471e07369b9f4a15a5ddf6fb010df02a39770d4d25778e1db1698c668c091d9","abstract_canon_sha256":"d8a353c7e5383d4a21de6eeba03cfee5bfb8280c9681309d6ea96fb6e6dbebd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:19.639216Z","signature_b64":"ksJjNlASV89zd0VNCJ9oODCaeuLSYUD2gJ6yJG292g4uSAXS/5wmATX6og+6ztdKK94HGSs50z937FIg+5oODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8dea369a3459c90facd6b38648b8abe89e84f23cb0d29455930ee68f6b24243","last_reissued_at":"2026-05-20T00:04:19.638042Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:19.638042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clipped Gradient Methods for Nonsmooth Convex Optimization under Heavy-Tailed Noise: A Refined Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Zijian Liu","submitted_at":"2025-12-29T03:35:53Z","abstract_excerpt":"Optimization under heavy-tailed noise has become popular recently, since it better fits many modern machine learning tasks, as captured by empirical observations. Concretely, instead of a finite second moment on gradient noise, a bounded ${\\frak p}$-th moment where ${\\frak p}\\in(1,2]$ has been recognized to be more realistic (say being upper bounded by $\\sigma_{\\frak l}^{\\frak p}$ for some $\\sigma_{\\frak l}\\ge0$). A simple yet effective operation, gradient clipping, is known to handle this new challenge successfully. Specifically, Clipped Stochastic Gradient Descent (Clipped SGD) guarantees a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.23178","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/2512.23178/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":"2512.23178","created_at":"2026-05-20T00:04:19.638626+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.23178v3","created_at":"2026-05-20T00:04:19.638626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.23178","created_at":"2026-05-20T00:04:19.638626+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDPKG2NDIWOJ","created_at":"2026-05-20T00:04:19.638626+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDPKG2NDIWOJB6WN","created_at":"2026-05-20T00:04:19.638626+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDPKG2ND","created_at":"2026-05-20T00:04:19.638626+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2","json":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2.json","graph_json":"https://pith.science/api/pith-number/ZDPKG2NDIWOJB6WNNM4GJC4KX2/graph.json","events_json":"https://pith.science/api/pith-number/ZDPKG2NDIWOJB6WNNM4GJC4KX2/events.json","paper":"https://pith.science/paper/ZDPKG2ND"},"agent_actions":{"view_html":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2","download_json":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2.json","view_paper":"https://pith.science/paper/ZDPKG2ND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.23178&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDPKG2NDIWOJB6WNNM4GJC4KX2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDPKG2NDIWOJB6WNNM4GJC4KX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2/action/storage_attestation","attest_author":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2/action/author_attestation","sign_citation":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2/action/citation_signature","submit_replication":"https://pith.science/pith/ZDPKG2NDIWOJB6WNNM4GJC4KX2/action/replication_record"}},"created_at":"2026-05-20T00:04:19.638626+00:00","updated_at":"2026-05-20T00:04:19.638626+00:00"}