{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YUKXPARGHXMGCZKGAKFDJJY3PT","short_pith_number":"pith:YUKXPARG","schema_version":"1.0","canonical_sha256":"c5157782263dd8616546028a34a71b7cfae85a7dcd82262c363e8946c968f33c","source":{"kind":"arxiv","id":"1202.6258","version":4},"attestation_state":"computed","paper":{"title":"A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Francis Bach (INRIA Paris - Rocquencourt, LIENS), Mark Schmidt (INRIA Paris - Rocquencourt, Nicolas Le Roux (INRIA Paris - Rocquencourt","submitted_at":"2012-02-28T15:42:51Z","abstract_excerpt":"We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard algorithms, both in terms of optimizing the training error and reducing the test error quickly."},"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":"1202.6258","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-02-28T15:42:51Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"223164d273a4bfec1f663766af3e6d32be1a6b15312393bbf7ed5301ccb89550","abstract_canon_sha256":"25fec5f5c60a57028e392cda26a1aa19e0a3c14f555db7e8f0c7b3746f8e82cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:30.815202Z","signature_b64":"inALBYBk5vsyykklP+NYQpf7+/YqsMjHiSOQ5SeTUINSvAg1LABaZvnobyghuxDBA1fU9H1OTQQ6DhilUv8zBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5157782263dd8616546028a34a71b7cfae85a7dcd82262c363e8946c968f33c","last_reissued_at":"2026-05-18T03:31:30.814616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:30.814616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Francis Bach (INRIA Paris - Rocquencourt, LIENS), Mark Schmidt (INRIA Paris - Rocquencourt, Nicolas Le Roux (INRIA Paris - Rocquencourt","submitted_at":"2012-02-28T15:42:51Z","abstract_excerpt":"We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard algorithms, both in terms of optimizing the training error and reducing the test error quickly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6258","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":""},"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":"1202.6258","created_at":"2026-05-18T03:31:30.814705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.6258v4","created_at":"2026-05-18T03:31:30.814705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6258","created_at":"2026-05-18T03:31:30.814705+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUKXPARGHXMG","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUKXPARGHXMGCZKG","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUKXPARG","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT","json":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT.json","graph_json":"https://pith.science/api/pith-number/YUKXPARGHXMGCZKGAKFDJJY3PT/graph.json","events_json":"https://pith.science/api/pith-number/YUKXPARGHXMGCZKGAKFDJJY3PT/events.json","paper":"https://pith.science/paper/YUKXPARG"},"agent_actions":{"view_html":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT","download_json":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT.json","view_paper":"https://pith.science/paper/YUKXPARG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.6258&json=true","fetch_graph":"https://pith.science/api/pith-number/YUKXPARGHXMGCZKGAKFDJJY3PT/graph.json","fetch_events":"https://pith.science/api/pith-number/YUKXPARGHXMGCZKGAKFDJJY3PT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT/action/storage_attestation","attest_author":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT/action/author_attestation","sign_citation":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT/action/citation_signature","submit_replication":"https://pith.science/pith/YUKXPARGHXMGCZKGAKFDJJY3PT/action/replication_record"}},"created_at":"2026-05-18T03:31:30.814705+00:00","updated_at":"2026-05-18T03:31:30.814705+00:00"}