{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UBL4MN7OLW7GFUPPCRQUNNF7UP","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":"fe7f5e74f424f2edd73bfe39bea3dac9e859cd40a6e3eb38abb93a3a4b451a3d","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-11T01:13:18Z","title_canon_sha256":"d3e2ca4741d8e1360781390c8ffba17b5e683a7a15a9756d1b5f0cec441fea71"},"schema_version":"1.0","source":{"id":"1902.03694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03694","created_at":"2026-07-05T00:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03694v2","created_at":"2026-07-05T00:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03694","created_at":"2026-07-05T00:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"UBL4MN7OLW7G","created_at":"2026-07-05T00:16:32Z"},{"alias_kind":"pith_short_16","alias_value":"UBL4MN7OLW7GFUPP","created_at":"2026-07-05T00:16:32Z"},{"alias_kind":"pith_short_8","alias_value":"UBL4MN7O","created_at":"2026-07-05T00:16:32Z"}],"graph_snapshots":[{"event_id":"sha256:ceaa3789dab799d6262e4ddbcac959c0ac582981d346ca0c9cfd712344754baa","target":"graph","created_at":"2026-07-05T00:16:32Z","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/1902.03694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization schemes: an explicit Euler scheme, an implicit Euler scheme, and a symplectic scheme. We show that the optimization algorithm generated by applying the symplectic scheme to a high-resolution ODE proposed by Shi et al. [2018] achieves an accelerated rate for minimizing smooth strongly convex functions. On the other hand, the resulting algorithm either fails to ach","authors_text":"Bin Shi, Michael I. Jordan, Simon S. Du, Weijie J. Su","cross_cats":["cs.LG","cs.NA","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-11T01:13:18Z","title":"Acceleration via Symplectic Discretization of High-Resolution Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03694","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:b813c8b038e94e178f7e2a905b92aab33ab2861b16582ac809f1e5f25cf248a9","target":"record","created_at":"2026-07-05T00:16:32Z","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":"fe7f5e74f424f2edd73bfe39bea3dac9e859cd40a6e3eb38abb93a3a4b451a3d","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-11T01:13:18Z","title_canon_sha256":"d3e2ca4741d8e1360781390c8ffba17b5e683a7a15a9756d1b5f0cec441fea71"},"schema_version":"1.0","source":{"id":"1902.03694","kind":"arxiv","version":2}},"canonical_sha256":"a057c637ee5dbe62d1ef146146b4bfa3efa19a23c9d9bb51aceaf0f3d0a61860","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a057c637ee5dbe62d1ef146146b4bfa3efa19a23c9d9bb51aceaf0f3d0a61860","first_computed_at":"2026-07-05T00:16:32.731558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:32.731558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PF4cB2i/ojtr+Dyhr61522InUYO/uqbD1JS2XWMXjUbF6cjVnulgXq80cS9BCCEAVKWZke0P4epZVft7pKWBDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:32.732089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b813c8b038e94e178f7e2a905b92aab33ab2861b16582ac809f1e5f25cf248a9","sha256:ceaa3789dab799d6262e4ddbcac959c0ac582981d346ca0c9cfd712344754baa"],"state_sha256":"78cfcfe0861cf90a6f3ced7841997f4186d0ead4ebafebbf9b13713890c35eff"}