{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HM7HHTFXSDRM25QROHVJT3JXC4","short_pith_number":"pith:HM7HHTFX","schema_version":"1.0","canonical_sha256":"3b3e73ccb790e2cd761171ea99ed37170f00b8cf7031d506d1560a51b227f5bd","source":{"kind":"arxiv","id":"1411.3803","version":1},"attestation_state":"computed","paper":{"title":"Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Ethan X. Fang, Han Liu, Mengdi Wang","submitted_at":"2014-11-14T05:49:01Z","abstract_excerpt":"Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form $\\min_x \\mathbf{E}_v [f_v\\big(\\mathbf{E}_w [g_w(x)]\\big)]$. In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasi-gradient method. SCGD update the solutions based on noisy sample gradient"},"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":"1411.3803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-11-14T05:49:01Z","cross_cats_sorted":[],"title_canon_sha256":"1688fe76a88502debdf3857cb4ec3c14af02c0c99eeec18f12c92a60ac751aad","abstract_canon_sha256":"cd9c5a4e027e8e4861c32bb53df7f3e98995de0aac6ea8d46b095ae77aa9c23f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:37.654057Z","signature_b64":"GcnyX0XiG0el8mWdCNuvRq3ojrrE90iUbJlcQrgxsb5cGoVPShL/AGz++y3tBx0Q8kVtX5OYIk9YpwAklrnvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b3e73ccb790e2cd761171ea99ed37170f00b8cf7031d506d1560a51b227f5bd","last_reissued_at":"2026-05-18T02:37:37.653493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:37.653493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Ethan X. Fang, Han Liu, Mengdi Wang","submitted_at":"2014-11-14T05:49:01Z","abstract_excerpt":"Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form $\\min_x \\mathbf{E}_v [f_v\\big(\\mathbf{E}_w [g_w(x)]\\big)]$. In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasi-gradient method. SCGD update the solutions based on noisy sample gradient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3803","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":"1411.3803","created_at":"2026-05-18T02:37:37.653580+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.3803v1","created_at":"2026-05-18T02:37:37.653580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3803","created_at":"2026-05-18T02:37:37.653580+00:00"},{"alias_kind":"pith_short_12","alias_value":"HM7HHTFXSDRM","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HM7HHTFXSDRM25QR","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HM7HHTFX","created_at":"2026-05-18T12:28:30.664211+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/HM7HHTFXSDRM25QROHVJT3JXC4","json":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4.json","graph_json":"https://pith.science/api/pith-number/HM7HHTFXSDRM25QROHVJT3JXC4/graph.json","events_json":"https://pith.science/api/pith-number/HM7HHTFXSDRM25QROHVJT3JXC4/events.json","paper":"https://pith.science/paper/HM7HHTFX"},"agent_actions":{"view_html":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4","download_json":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4.json","view_paper":"https://pith.science/paper/HM7HHTFX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.3803&json=true","fetch_graph":"https://pith.science/api/pith-number/HM7HHTFXSDRM25QROHVJT3JXC4/graph.json","fetch_events":"https://pith.science/api/pith-number/HM7HHTFXSDRM25QROHVJT3JXC4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/action/storage_attestation","attest_author":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/action/author_attestation","sign_citation":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/action/citation_signature","submit_replication":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/action/replication_record"}},"created_at":"2026-05-18T02:37:37.653580+00:00","updated_at":"2026-05-18T02:37:37.653580+00:00"}