{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OK6OAJFEQLJSXYMK2SGPAKUEVR","short_pith_number":"pith:OK6OAJFE","schema_version":"1.0","canonical_sha256":"72bce024a482d32be18ad48cf02a84ac64eeaeb313893293b80825a4e8a520ff","source":{"kind":"arxiv","id":"1710.10737","version":2},"attestation_state":"computed","paper":{"title":"Linearly convergent stochastic heavy ball method for minimizing generalization error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.OC","authors_text":"Nicolas Loizou, Peter Richt\\'arik","submitted_at":"2017-10-30T01:49:34Z","abstract_excerpt":"In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder problem. While in the analysis we constrain ourselves to quadratic loss, the overall objective is not necessarily 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":"1710.10737","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-30T01:49:34Z","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"title_canon_sha256":"3cf169a9bfe30e2bc46ffff8dd05021d91527f6272b6dcd124370756f128f382","abstract_canon_sha256":"b76cf4a2651cc6e20ae1ef90aca752e6266874a12c343857433f27e8d6fb2203"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:18.488868Z","signature_b64":"LEJJ6OztgM46DOwpVgcrlhW9avXbCN4arZAqBvw5/xpedyi6fsAbIT7sZgCayfcvz1ui7HGqZtiS5zWMoanlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72bce024a482d32be18ad48cf02a84ac64eeaeb313893293b80825a4e8a520ff","last_reissued_at":"2026-05-18T00:27:18.488194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:18.488194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linearly convergent stochastic heavy ball method for minimizing generalization error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.OC","authors_text":"Nicolas Loizou, Peter Richt\\'arik","submitted_at":"2017-10-30T01:49:34Z","abstract_excerpt":"In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder problem. While in the analysis we constrain ourselves to quadratic loss, the overall objective is not necessarily strongly convex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10737","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":"1710.10737","created_at":"2026-05-18T00:27:18.488367+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10737v2","created_at":"2026-05-18T00:27:18.488367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10737","created_at":"2026-05-18T00:27:18.488367+00:00"},{"alias_kind":"pith_short_12","alias_value":"OK6OAJFEQLJS","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OK6OAJFEQLJSXYMK","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OK6OAJFE","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.18609","citing_title":"Perfect Parallelization in Mini-Batch SGD with Classical Momentum Acceleration","ref_index":36,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR","json":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR.json","graph_json":"https://pith.science/api/pith-number/OK6OAJFEQLJSXYMK2SGPAKUEVR/graph.json","events_json":"https://pith.science/api/pith-number/OK6OAJFEQLJSXYMK2SGPAKUEVR/events.json","paper":"https://pith.science/paper/OK6OAJFE"},"agent_actions":{"view_html":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR","download_json":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR.json","view_paper":"https://pith.science/paper/OK6OAJFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10737&json=true","fetch_graph":"https://pith.science/api/pith-number/OK6OAJFEQLJSXYMK2SGPAKUEVR/graph.json","fetch_events":"https://pith.science/api/pith-number/OK6OAJFEQLJSXYMK2SGPAKUEVR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR/action/storage_attestation","attest_author":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR/action/author_attestation","sign_citation":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR/action/citation_signature","submit_replication":"https://pith.science/pith/OK6OAJFEQLJSXYMK2SGPAKUEVR/action/replication_record"}},"created_at":"2026-05-18T00:27:18.488367+00:00","updated_at":"2026-05-18T00:27:18.488367+00:00"}