{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SLNLNQRHZHPIM34EPGM2CM53RI","short_pith_number":"pith:SLNLNQRH","schema_version":"1.0","canonical_sha256":"92dab6c227c9de866f847999a133bb8a11777b87fdaeb04345110308ff9a8015","source":{"kind":"arxiv","id":"1712.01906","version":2},"attestation_state":"computed","paper":{"title":"On the linear convergence of the stochastic gradient method with constant step-size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bang Cong Vu, Volkan Cevher","submitted_at":"2017-12-05T20:23:48Z","abstract_excerpt":"The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size $\\gamma$ (SGM-CS). In this paper, we provide a necessary condition, for the linear convergence of SGM-CS, that is weaker than SGC. Moreover, when this necessary is violated up to a additive perturbation $\\sigma$, we show that both the projected stochastic gradient method using a constant step-size (PSGM-CS) and the proximal stochastic gradient method exhibit linear convergence to a noise dominated region, whose distance to the optimal solut"},"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":"1712.01906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-05T20:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"4c60f7013653b2d79528d665fe7482ef03b4e9b75b903569b00c8a3ea3b40ab4","abstract_canon_sha256":"27a5bfeff7a48c2271a22f91e91f03128a348b91dcadfd1e23c4fd4e398c398d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:05.004073Z","signature_b64":"GbuRiZV28z3XRKpoTiL5+3IZqXp7prxmjkHFs2YbxgL6z4CrOcd3X241WECtl+IIP9ND5//bJ8r95bZi4mhpBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92dab6c227c9de866f847999a133bb8a11777b87fdaeb04345110308ff9a8015","last_reissued_at":"2026-05-18T00:13:05.003493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:05.003493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the linear convergence of the stochastic gradient method with constant step-size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bang Cong Vu, Volkan Cevher","submitted_at":"2017-12-05T20:23:48Z","abstract_excerpt":"The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size $\\gamma$ (SGM-CS). In this paper, we provide a necessary condition, for the linear convergence of SGM-CS, that is weaker than SGC. Moreover, when this necessary is violated up to a additive perturbation $\\sigma$, we show that both the projected stochastic gradient method using a constant step-size (PSGM-CS) and the proximal stochastic gradient method exhibit linear convergence to a noise dominated region, whose distance to the optimal solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01906","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":"1712.01906","created_at":"2026-05-18T00:13:05.003590+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.01906v2","created_at":"2026-05-18T00:13:05.003590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01906","created_at":"2026-05-18T00:13:05.003590+00:00"},{"alias_kind":"pith_short_12","alias_value":"SLNLNQRHZHPI","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SLNLNQRHZHPIM34E","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SLNLNQRH","created_at":"2026-05-18T12:31:43.269735+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/SLNLNQRHZHPIM34EPGM2CM53RI","json":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI.json","graph_json":"https://pith.science/api/pith-number/SLNLNQRHZHPIM34EPGM2CM53RI/graph.json","events_json":"https://pith.science/api/pith-number/SLNLNQRHZHPIM34EPGM2CM53RI/events.json","paper":"https://pith.science/paper/SLNLNQRH"},"agent_actions":{"view_html":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI","download_json":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI.json","view_paper":"https://pith.science/paper/SLNLNQRH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.01906&json=true","fetch_graph":"https://pith.science/api/pith-number/SLNLNQRHZHPIM34EPGM2CM53RI/graph.json","fetch_events":"https://pith.science/api/pith-number/SLNLNQRHZHPIM34EPGM2CM53RI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI/action/storage_attestation","attest_author":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI/action/author_attestation","sign_citation":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI/action/citation_signature","submit_replication":"https://pith.science/pith/SLNLNQRHZHPIM34EPGM2CM53RI/action/replication_record"}},"created_at":"2026-05-18T00:13:05.003590+00:00","updated_at":"2026-05-18T00:13:05.003590+00:00"}