{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IGBZDH5WGAFLKQYXTGPQ42CVBU","short_pith_number":"pith:IGBZDH5W","schema_version":"1.0","canonical_sha256":"4183919fb6300ab54317999f0e68550d1b7cce4d324bb5fb6785d8735477f35c","source":{"kind":"arxiv","id":"1503.01243","version":2},"attestation_state":"computed","paper":{"title":"A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OC"],"primary_cat":"stat.ML","authors_text":"Emmanuel J. Candes, Stephen Boyd, Weijie Su","submitted_at":"2015-03-04T07:03:50Z","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."},"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":"1503.01243","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-03-04T07:03:50Z","cross_cats_sorted":["math.CA","math.OC"],"title_canon_sha256":"0fd8eca05aa77b85482cc93e96f6c1ad83657c8006818ae639f29c1c554a461c","abstract_canon_sha256":"05a0c93b69e387cb48e6f90756df1f56c9967d8294c44104dab6ce7bb04c3e5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:38.680999Z","signature_b64":"MhfM5/45Iw5SuIwzrGo9hhlg9Q1HPGbNr0+WVcEt85UBdsAMDkE09yG9RM4JJ2otYJ1Bp/B6hMuHJezIt3kpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4183919fb6300ab54317999f0e68550d1b7cce4d324bb5fb6785d8735477f35c","last_reissued_at":"2026-05-18T01:28:38.680308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:38.680308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OC"],"primary_cat":"stat.ML","authors_text":"Emmanuel J. Candes, Stephen Boyd, Weijie Su","submitted_at":"2015-03-04T07:03:50Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01243","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1503.01243","created_at":"2026-05-18T01:28:38.680425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01243v2","created_at":"2026-05-18T01:28:38.680425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01243","created_at":"2026-05-18T01:28:38.680425+00:00"},{"alias_kind":"pith_short_12","alias_value":"IGBZDH5WGAFL","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IGBZDH5WGAFLKQYX","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IGBZDH5W","created_at":"2026-05-18T12:29:25.134429+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.14108","citing_title":"Momentum Further Constrains Sharpness at the Edge of Stochastic Stability","ref_index":40,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU","json":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU.json","graph_json":"https://pith.science/api/pith-number/IGBZDH5WGAFLKQYXTGPQ42CVBU/graph.json","events_json":"https://pith.science/api/pith-number/IGBZDH5WGAFLKQYXTGPQ42CVBU/events.json","paper":"https://pith.science/paper/IGBZDH5W"},"agent_actions":{"view_html":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU","download_json":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU.json","view_paper":"https://pith.science/paper/IGBZDH5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01243&json=true","fetch_graph":"https://pith.science/api/pith-number/IGBZDH5WGAFLKQYXTGPQ42CVBU/graph.json","fetch_events":"https://pith.science/api/pith-number/IGBZDH5WGAFLKQYXTGPQ42CVBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU/action/storage_attestation","attest_author":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU/action/author_attestation","sign_citation":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU/action/citation_signature","submit_replication":"https://pith.science/pith/IGBZDH5WGAFLKQYXTGPQ42CVBU/action/replication_record"}},"created_at":"2026-05-18T01:28:38.680425+00:00","updated_at":"2026-05-18T01:28:38.680425+00:00"}