{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3Q4H5O6T6MR53TZWU7PJTOCGYP","short_pith_number":"pith:3Q4H5O6T","schema_version":"1.0","canonical_sha256":"dc387ebbd3f323ddcf36a7de99b846c3e8c5b7280ac4da3402a9f375c877f5f7","source":{"kind":"arxiv","id":"2506.18075","version":4},"attestation_state":"computed","paper":{"title":"On the Linear Speedup of the Push-Pull Method for Decentralized Optimization over Digraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gan Luo, Kun Yuan, Liyuan Liang","submitted_at":"2025-06-22T15:41:29Z","abstract_excerpt":"The linear speedup property is essential for demonstrating the advantage of distributed algorithms over their single-node counterparts. In this paper, we study the stochastic Push-Pull method, a widely adopted decentralized optimization algorithm over directed graphs (digraphs). Unlike methods that rely solely on row-stochastic or column-stochastic mixing matrices, Push-Pull avoids nonlinear correction and has shown superior empirical performance across a variety of settings. However, its theoretical analysis remains challenging, and the linear speedup property has not been generally establish"},"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":"2506.18075","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-22T15:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"3da35ead73379dab959df89e56b66ad322d0b13f908732c41ac37922083de62f","abstract_canon_sha256":"049b87115da4ec884137eba896550e4be4801892511dfcc69cd81d9d11142492"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:25.378382Z","signature_b64":"g+fS08Bp81Fl6MPwgq3av0yz6tku7ny3hRuSCbKHeoceiZX1a7OoGkrX/2Gxd8lya09ronMvzdaB6pqjnwuCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc387ebbd3f323ddcf36a7de99b846c3e8c5b7280ac4da3402a9f375c877f5f7","last_reissued_at":"2026-07-07T02:18:25.377494Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:25.377494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Linear Speedup of the Push-Pull Method for Decentralized Optimization over Digraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gan Luo, Kun Yuan, Liyuan Liang","submitted_at":"2025-06-22T15:41:29Z","abstract_excerpt":"The linear speedup property is essential for demonstrating the advantage of distributed algorithms over their single-node counterparts. In this paper, we study the stochastic Push-Pull method, a widely adopted decentralized optimization algorithm over directed graphs (digraphs). Unlike methods that rely solely on row-stochastic or column-stochastic mixing matrices, Push-Pull avoids nonlinear correction and has shown superior empirical performance across a variety of settings. However, its theoretical analysis remains challenging, and the linear speedup property has not been generally establish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18075","kind":"arxiv","version":4},"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/2506.18075/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":"2506.18075","created_at":"2026-07-07T02:18:25.377649+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.18075v4","created_at":"2026-07-07T02:18:25.377649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18075","created_at":"2026-07-07T02:18:25.377649+00:00"},{"alias_kind":"pith_short_12","alias_value":"3Q4H5O6T6MR5","created_at":"2026-07-07T02:18:25.377649+00:00"},{"alias_kind":"pith_short_16","alias_value":"3Q4H5O6T6MR53TZW","created_at":"2026-07-07T02:18:25.377649+00:00"},{"alias_kind":"pith_short_8","alias_value":"3Q4H5O6T","created_at":"2026-07-07T02:18:25.377649+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.08219","citing_title":"Stochastic Momentum Tracking Push-Pull for Decentralized Optimization over Directed Graphs","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP","json":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP.json","graph_json":"https://pith.science/api/pith-number/3Q4H5O6T6MR53TZWU7PJTOCGYP/graph.json","events_json":"https://pith.science/api/pith-number/3Q4H5O6T6MR53TZWU7PJTOCGYP/events.json","paper":"https://pith.science/paper/3Q4H5O6T"},"agent_actions":{"view_html":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP","download_json":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP.json","view_paper":"https://pith.science/paper/3Q4H5O6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.18075&json=true","fetch_graph":"https://pith.science/api/pith-number/3Q4H5O6T6MR53TZWU7PJTOCGYP/graph.json","fetch_events":"https://pith.science/api/pith-number/3Q4H5O6T6MR53TZWU7PJTOCGYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP/action/storage_attestation","attest_author":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP/action/author_attestation","sign_citation":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP/action/citation_signature","submit_replication":"https://pith.science/pith/3Q4H5O6T6MR53TZWU7PJTOCGYP/action/replication_record"}},"created_at":"2026-07-07T02:18:25.377649+00:00","updated_at":"2026-07-07T02:18:25.377649+00:00"}