{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4MH74DMXXSC24GJPBL7B5QMHLD","short_pith_number":"pith:4MH74DMX","schema_version":"1.0","canonical_sha256":"e30ffe0d97bc85ae192f0afe1ec18758d993e81a58aba99bd45e3853e3b86e03","source":{"kind":"arxiv","id":"1811.11989","version":1},"attestation_state":"computed","paper":{"title":"Sample Efficient Stochastic Variance-Reduced Cubic Regularization Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Dongruo Zhou, Pan Xu, Quanquan Gu","submitted_at":"2018-11-29T07:10:44Z","abstract_excerpt":"We propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum efficiently in nonconvex optimization. The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods. At the heart of our analysis is the choice of a constant batch size of Hessian matrix computation at each iteration and the stochastic variance reduction techniques. In detail, for a nonconvex function with $n$ component functions, Lite-SVRC converges to the local minimum within $\\tilde{O}(n"},"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":"1811.11989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-29T07:10:44Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"0fdd596869a1c27e4959dcac1c7c6571c7a66b32deb0e20a0c8444b9d4590207","abstract_canon_sha256":"aa215cc731c61c6e93d9306d7f61a519becd2ce501bef1af03c71487c34408fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:34.808102Z","signature_b64":"1XlTeTE9R2j2is2BwUn8jCFR9zWAF5AiWtyR8/XA5lVyaHh2LpsrzQtd7eHxJVLOVe9hHlvI8Eiid6g+8O1gCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e30ffe0d97bc85ae192f0afe1ec18758d993e81a58aba99bd45e3853e3b86e03","last_reissued_at":"2026-05-17T23:59:34.807457Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:34.807457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sample Efficient Stochastic Variance-Reduced Cubic Regularization Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Dongruo Zhou, Pan Xu, Quanquan Gu","submitted_at":"2018-11-29T07:10:44Z","abstract_excerpt":"We propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum efficiently in nonconvex optimization. The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods. At the heart of our analysis is the choice of a constant batch size of Hessian matrix computation at each iteration and the stochastic variance reduction techniques. In detail, for a nonconvex function with $n$ component functions, Lite-SVRC converges to the local minimum within $\\tilde{O}(n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11989","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":"1811.11989","created_at":"2026-05-17T23:59:34.807551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.11989v1","created_at":"2026-05-17T23:59:34.807551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11989","created_at":"2026-05-17T23:59:34.807551+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MH74DMXXSC2","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MH74DMXXSC24GJP","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MH74DMX","created_at":"2026-05-18T12:32:05.422762+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/4MH74DMXXSC24GJPBL7B5QMHLD","json":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD.json","graph_json":"https://pith.science/api/pith-number/4MH74DMXXSC24GJPBL7B5QMHLD/graph.json","events_json":"https://pith.science/api/pith-number/4MH74DMXXSC24GJPBL7B5QMHLD/events.json","paper":"https://pith.science/paper/4MH74DMX"},"agent_actions":{"view_html":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD","download_json":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD.json","view_paper":"https://pith.science/paper/4MH74DMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.11989&json=true","fetch_graph":"https://pith.science/api/pith-number/4MH74DMXXSC24GJPBL7B5QMHLD/graph.json","fetch_events":"https://pith.science/api/pith-number/4MH74DMXXSC24GJPBL7B5QMHLD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD/action/storage_attestation","attest_author":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD/action/author_attestation","sign_citation":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD/action/citation_signature","submit_replication":"https://pith.science/pith/4MH74DMXXSC24GJPBL7B5QMHLD/action/replication_record"}},"created_at":"2026-05-17T23:59:34.807551+00:00","updated_at":"2026-05-17T23:59:34.807551+00:00"}