{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HM7HHTFXSDRM25QROHVJT3JXC4","short_pith_number":"pith:HM7HHTFX","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"},"canonical_sha256":"3b3e73ccb790e2cd761171ea99ed37170f00b8cf7031d506d1560a51b227f5bd","source":{"kind":"arxiv","id":"1411.3803","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3803","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3803v1","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3803","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"HM7HHTFXSDRM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HM7HHTFXSDRM25QR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HM7HHTFX","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HM7HHTFXSDRM25QROHVJT3JXC4","target":"record","payload":{"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"},"canonical_sha256":"3b3e73ccb790e2cd761171ea99ed37170f00b8cf7031d506d1560a51b227f5bd","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"},"source_kind":"arxiv","source_id":"1411.3803","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKlLYBhbAVRLabtk5FMiHJe1EhaCtXf55X/YOd/nBP9bALulymFOagr9Encs/uY1qa4ukNlcXk0RD/RFmScWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:02:06.500816Z"},"content_sha256":"b9273b042e825487e1a032510f819d7fe5faf57a7975932f57dc25053090ab36","schema_version":"1.0","event_id":"sha256:b9273b042e825487e1a032510f819d7fe5faf57a7975932f57dc25053090ab36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HM7HHTFXSDRM25QROHVJT3JXC4","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EelIthgbUASUz/5NDeisLvdXN3TdIHQsjK1s6/kFO4Oq0+v+yCxwPoUF+VfvudK3Y2WGG7WFqbQaPp7fQvr1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:02:06.501414Z"},"content_sha256":"4a9dd7a4a1b957b3554ac667e7c1203e84ed542c4b377a78e9d5ded317a2d9f0","schema_version":"1.0","event_id":"sha256:4a9dd7a4a1b957b3554ac667e7c1203e84ed542c4b377a78e9d5ded317a2d9f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/bundle.json","state_url":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HM7HHTFXSDRM25QROHVJT3JXC4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T03:02:06Z","links":{"resolver":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4","bundle":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/bundle.json","state":"https://pith.science/pith/HM7HHTFXSDRM25QROHVJT3JXC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HM7HHTFXSDRM25QROHVJT3JXC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HM7HHTFXSDRM25QROHVJT3JXC4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cd9c5a4e027e8e4861c32bb53df7f3e98995de0aac6ea8d46b095ae77aa9c23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-11-14T05:49:01Z","title_canon_sha256":"1688fe76a88502debdf3857cb4ec3c14af02c0c99eeec18f12c92a60ac751aad"},"schema_version":"1.0","source":{"id":"1411.3803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3803","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3803v1","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3803","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"HM7HHTFXSDRM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HM7HHTFXSDRM25QR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HM7HHTFX","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:4a9dd7a4a1b957b3554ac667e7c1203e84ed542c4b377a78e9d5ded317a2d9f0","target":"graph","created_at":"2026-05-18T02:37:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Ethan X. Fang, Han Liu, Mengdi Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-11-14T05:49:01Z","title":"Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3803","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b9273b042e825487e1a032510f819d7fe5faf57a7975932f57dc25053090ab36","target":"record","created_at":"2026-05-18T02:37:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cd9c5a4e027e8e4861c32bb53df7f3e98995de0aac6ea8d46b095ae77aa9c23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-11-14T05:49:01Z","title_canon_sha256":"1688fe76a88502debdf3857cb4ec3c14af02c0c99eeec18f12c92a60ac751aad"},"schema_version":"1.0","source":{"id":"1411.3803","kind":"arxiv","version":1}},"canonical_sha256":"3b3e73ccb790e2cd761171ea99ed37170f00b8cf7031d506d1560a51b227f5bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b3e73ccb790e2cd761171ea99ed37170f00b8cf7031d506d1560a51b227f5bd","first_computed_at":"2026-05-18T02:37:37.653493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:37.653493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GcnyX0XiG0el8mWdCNuvRq3ojrrE90iUbJlcQrgxsb5cGoVPShL/AGz++y3tBx0Q8kVtX5OYIk9YpwAklrnvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:37.654057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9273b042e825487e1a032510f819d7fe5faf57a7975932f57dc25053090ab36","sha256:4a9dd7a4a1b957b3554ac667e7c1203e84ed542c4b377a78e9d5ded317a2d9f0"],"state_sha256":"aec76834b3cfa05a93d559564d028a5b4ef641a0d079523c5e12df51fe54bde6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FHreH+UMBlnlf2kuv4G1gnG2o45hdAV8oaCVmBU0n8xw+c6Oi7eqwcy0sSXHgetfjSRXP/ps8kigMJ+Wo59zBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T03:02:06.505027Z","bundle_sha256":"f33b4457d6192682148076366c00e1562cf014335a61156440b2d88cdd1da59e"}}