{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IGBZDH5WGAFLKQYXTGPQ42CVBU","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":"05a0c93b69e387cb48e6f90756df1f56c9967d8294c44104dab6ce7bb04c3e5f","cross_cats_sorted":["math.CA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-04T07:03:50Z","title_canon_sha256":"0fd8eca05aa77b85482cc93e96f6c1ad83657c8006818ae639f29c1c554a461c"},"schema_version":"1.0","source":{"id":"1503.01243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01243","created_at":"2026-05-18T01:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01243v2","created_at":"2026-05-18T01:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01243","created_at":"2026-05-18T01:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"IGBZDH5WGAFL","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IGBZDH5WGAFLKQYX","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IGBZDH5W","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:a9b853fc9aa1b5a5fb779eb9d0fd5c7411711dfefd9c04896e345b3b5f68f0a2","target":"graph","created_at":"2026-05-18T01:28:38Z","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"},"paper":{"abstract_excerpt":"We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov's scheme. As a byproduct, we obtain a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov's scheme leading to an algorithm, which can be rigorously proven to converge at a linear rate whenever the objective is strongly convex.","authors_text":"Emmanuel J. Candes, Stephen Boyd, Weijie Su","cross_cats":["math.CA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-04T07:03:50Z","title":"A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01243","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":"sha256:2d80f2b0d542c2fdc7ceffce87a46ef66ee9562f223c896d34d1c54e6ab19ed6","target":"record","created_at":"2026-05-18T01:28:38Z","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":"05a0c93b69e387cb48e6f90756df1f56c9967d8294c44104dab6ce7bb04c3e5f","cross_cats_sorted":["math.CA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-04T07:03:50Z","title_canon_sha256":"0fd8eca05aa77b85482cc93e96f6c1ad83657c8006818ae639f29c1c554a461c"},"schema_version":"1.0","source":{"id":"1503.01243","kind":"arxiv","version":2}},"canonical_sha256":"4183919fb6300ab54317999f0e68550d1b7cce4d324bb5fb6785d8735477f35c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4183919fb6300ab54317999f0e68550d1b7cce4d324bb5fb6785d8735477f35c","first_computed_at":"2026-05-18T01:28:38.680308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:38.680308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MhfM5/45Iw5SuIwzrGo9hhlg9Q1HPGbNr0+WVcEt85UBdsAMDkE09yG9RM4JJ2otYJ1Bp/B6hMuHJezIt3kpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:38.680999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d80f2b0d542c2fdc7ceffce87a46ef66ee9562f223c896d34d1c54e6ab19ed6","sha256:a9b853fc9aa1b5a5fb779eb9d0fd5c7411711dfefd9c04896e345b3b5f68f0a2"],"state_sha256":"94e77905a9f9919f47879c8e42520bc08f9678f04b49c7c1319834ae47d2cc93"}