{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OM7CJYVMVKEVACZFA6SYTHEOEK","short_pith_number":"pith:OM7CJYVM","schema_version":"1.0","canonical_sha256":"733e24e2acaa89500b2507a5899c8e2288e055cdaf2c0d8baec12c950b6b4f67","source":{"kind":"arxiv","id":"2503.11104","version":2},"attestation_state":"computed","paper":{"title":"Convergence Analysis of EXTRA in Non-convex Distributed Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lei Qin, Ye Pu","submitted_at":"2025-03-14T05:50:31Z","abstract_excerpt":"Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as \\textbf{EXTRA} (decentralized exact first-order algorithm), have been proposed to address these challenges. In this paper, we analyze the convergence properties of \\textbf{EXTRA} in the context of smooth, non-convex optimization. By interpreting its updates as a nonlinear dynamical system, we show novel insights into its convergence properties. Specifically, i) \\text"},"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":"2503.11104","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-03-14T05:50:31Z","cross_cats_sorted":[],"title_canon_sha256":"4324e1f324cdb687d2f58efc2b001ec494dfd029010a42e5a74d0083e8e96e85","abstract_canon_sha256":"049affd5ba762790971f9648400f5eb33a1d0e23a99f74e388c289ea886cbfea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:21.413975Z","signature_b64":"Y2ywM2pNzFCGiLZK9HDAJy0808NTgDTVwT+SgA5q311nmiKFtZ6dBwiLDbfmnXhClkSdjkNsdjWlR/dqMkasBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"733e24e2acaa89500b2507a5899c8e2288e055cdaf2c0d8baec12c950b6b4f67","last_reissued_at":"2026-07-05T11:33:21.413489Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:21.413489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Analysis of EXTRA in Non-convex Distributed Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lei Qin, Ye Pu","submitted_at":"2025-03-14T05:50:31Z","abstract_excerpt":"Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as \\textbf{EXTRA} (decentralized exact first-order algorithm), have been proposed to address these challenges. In this paper, we analyze the convergence properties of \\textbf{EXTRA} in the context of smooth, non-convex optimization. By interpreting its updates as a nonlinear dynamical system, we show novel insights into its convergence properties. Specifically, i) \\text"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.11104","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.11104/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":"2503.11104","created_at":"2026-07-05T11:33:21.413552+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.11104v2","created_at":"2026-07-05T11:33:21.413552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.11104","created_at":"2026-07-05T11:33:21.413552+00:00"},{"alias_kind":"pith_short_12","alias_value":"OM7CJYVMVKEV","created_at":"2026-07-05T11:33:21.413552+00:00"},{"alias_kind":"pith_short_16","alias_value":"OM7CJYVMVKEVACZF","created_at":"2026-07-05T11:33:21.413552+00:00"},{"alias_kind":"pith_short_8","alias_value":"OM7CJYVM","created_at":"2026-07-05T11:33:21.413552+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.15537","citing_title":"Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity","ref_index":42,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK","json":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK.json","graph_json":"https://pith.science/api/pith-number/OM7CJYVMVKEVACZFA6SYTHEOEK/graph.json","events_json":"https://pith.science/api/pith-number/OM7CJYVMVKEVACZFA6SYTHEOEK/events.json","paper":"https://pith.science/paper/OM7CJYVM"},"agent_actions":{"view_html":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK","download_json":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK.json","view_paper":"https://pith.science/paper/OM7CJYVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.11104&json=true","fetch_graph":"https://pith.science/api/pith-number/OM7CJYVMVKEVACZFA6SYTHEOEK/graph.json","fetch_events":"https://pith.science/api/pith-number/OM7CJYVMVKEVACZFA6SYTHEOEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK/action/storage_attestation","attest_author":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK/action/author_attestation","sign_citation":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK/action/citation_signature","submit_replication":"https://pith.science/pith/OM7CJYVMVKEVACZFA6SYTHEOEK/action/replication_record"}},"created_at":"2026-07-05T11:33:21.413552+00:00","updated_at":"2026-07-05T11:33:21.413552+00:00"}