{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4ALTJVN7VRJY455CF5UUCGSZ73","short_pith_number":"pith:4ALTJVN7","schema_version":"1.0","canonical_sha256":"e01734d5bfac538e77a22f69411a59fee74d70aff2b6c72e3f2021cd4ff0314f","source":{"kind":"arxiv","id":"1603.06159","version":1},"attestation_state":"computed","paper":{"title":"Fast Incremental Method for Nonconvex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Alex Smola, Barnabas Poczos, Sashank J. Reddi, Suvrit Sra","submitted_at":"2016-03-19T23:28:44Z","abstract_excerpt":"We analyze a fast incremental aggregated gradient method for optimizing nonconvex problems of the form $\\min_x \\sum_i f_i(x)$. Specifically, we analyze the SAGA algorithm within an Incremental First-order Oracle framework, and show that it converges to a stationary point provably faster than both gradient descent and stochastic gradient descent. We also discuss a Polyak's special class of nonconvex problems for which SAGA converges at a linear rate to the global optimum. Finally, we analyze the practically valuable regularized and minibatch variants of SAGA. To our knowledge, this paper presen"},"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":"1603.06159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-19T23:28:44Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"82b252e89724a67ea4ac3ba87febfc2f4dd602767bb409b44a1e0bf066d281f5","abstract_canon_sha256":"fb99d45eaf3cfa2e840e1b269214203265601d469423bb4f65da374c39bdcfe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:50.162597Z","signature_b64":"rMehbBCjTHSgeJ3tbsDKPRJA9109cyOqsucYwTKMZ7hUkwWYbkexvd4g9BL4/HnKKR/fkrVPswYtk0DofRr3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e01734d5bfac538e77a22f69411a59fee74d70aff2b6c72e3f2021cd4ff0314f","last_reissued_at":"2026-05-18T01:18:50.161932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:50.161932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Incremental Method for Nonconvex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Alex Smola, Barnabas Poczos, Sashank J. Reddi, Suvrit Sra","submitted_at":"2016-03-19T23:28:44Z","abstract_excerpt":"We analyze a fast incremental aggregated gradient method for optimizing nonconvex problems of the form $\\min_x \\sum_i f_i(x)$. Specifically, we analyze the SAGA algorithm within an Incremental First-order Oracle framework, and show that it converges to a stationary point provably faster than both gradient descent and stochastic gradient descent. We also discuss a Polyak's special class of nonconvex problems for which SAGA converges at a linear rate to the global optimum. Finally, we analyze the practically valuable regularized and minibatch variants of SAGA. To our knowledge, this paper presen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06159","kind":"arxiv","version":1},"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":"1603.06159","created_at":"2026-05-18T01:18:50.162028+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06159v1","created_at":"2026-05-18T01:18:50.162028+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06159","created_at":"2026-05-18T01:18:50.162028+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ALTJVN7VRJY","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ALTJVN7VRJY455C","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ALTJVN7","created_at":"2026-05-18T12:29:58.707656+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/4ALTJVN7VRJY455CF5UUCGSZ73","json":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73.json","graph_json":"https://pith.science/api/pith-number/4ALTJVN7VRJY455CF5UUCGSZ73/graph.json","events_json":"https://pith.science/api/pith-number/4ALTJVN7VRJY455CF5UUCGSZ73/events.json","paper":"https://pith.science/paper/4ALTJVN7"},"agent_actions":{"view_html":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73","download_json":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73.json","view_paper":"https://pith.science/paper/4ALTJVN7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06159&json=true","fetch_graph":"https://pith.science/api/pith-number/4ALTJVN7VRJY455CF5UUCGSZ73/graph.json","fetch_events":"https://pith.science/api/pith-number/4ALTJVN7VRJY455CF5UUCGSZ73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73/action/storage_attestation","attest_author":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73/action/author_attestation","sign_citation":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73/action/citation_signature","submit_replication":"https://pith.science/pith/4ALTJVN7VRJY455CF5UUCGSZ73/action/replication_record"}},"created_at":"2026-05-18T01:18:50.162028+00:00","updated_at":"2026-05-18T01:18:50.162028+00:00"}