{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WMG6U4TNWJL6RUE3HWMNOWHSXD","short_pith_number":"pith:WMG6U4TN","canonical_record":{"source":{"id":"1904.01145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-01T23:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"c14a10cf3787fe05da659f498b01794747e4d9d99117d00fa3fa94e593075376","abstract_canon_sha256":"a2b4cae696a57cadd7afa136f6ab17760b20d90dde22c78627590373e4e08ea2"},"schema_version":"1.0"},"canonical_sha256":"b30dea726db257e8d09b3d98d758f2b8da81293cdefb14cf9cdd97c0235f4f4d","source":{"kind":"arxiv","id":"1904.01145","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01145","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01145v2","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01145","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"WMG6U4TNWJL6","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WMG6U4TNWJL6RUE3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WMG6U4TN","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WMG6U4TNWJL6RUE3HWMNOWHSXD","target":"record","payload":{"canonical_record":{"source":{"id":"1904.01145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-01T23:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"c14a10cf3787fe05da659f498b01794747e4d9d99117d00fa3fa94e593075376","abstract_canon_sha256":"a2b4cae696a57cadd7afa136f6ab17760b20d90dde22c78627590373e4e08ea2"},"schema_version":"1.0"},"canonical_sha256":"b30dea726db257e8d09b3d98d758f2b8da81293cdefb14cf9cdd97c0235f4f4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:35.612780Z","signature_b64":"46p/5QDM/OQ7UwvrSgeHP55FT50hQf56QZq1mxdy06xfQg1r7hCex0qJQ5uQUfjk/BZnoORc8B8MEy/RDT3VCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b30dea726db257e8d09b3d98d758f2b8da81293cdefb14cf9cdd97c0235f4f4d","last_reissued_at":"2026-05-17T23:47:35.612339Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:35.612339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.01145","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBhLsYYk4d/zQwhbxVkAmEbr57+bmU1u0gk3ayAJ1fXbPm7hlSa3vIoRCv8iPOsYjWTxniIKUlftoAux2KzUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T22:22:38.979393Z"},"content_sha256":"21428145f148c90b4c01532df815065bbab9ac4195e4527f3db10cb3bac70bf8","schema_version":"1.0","event_id":"sha256:21428145f148c90b4c01532df815065bbab9ac4195e4527f3db10cb3bac70bf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WMG6U4TNWJL6RUE3HWMNOWHSXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Subspace Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alireza Doostan, David Kozak, Luis Tenorio, Stephen Becker","submitted_at":"2019-04-01T23:47:28Z","abstract_excerpt":"We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and machine learning problems. The basic algorithm projects the gradient onto a random subspace at each iteration, similar to coordinate descent but without restricting directional derivatives to be along the axes. This algorithm is previously known but we provide new analysis. We also extend the popular SVRG method to this framework but without requirin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01145","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/fb/S2KBSbexKAX5wnfzAnvgCxCtZQKDVptpckqt97MmqHGtuTfmF86ncU2n5hZMmYDvgD3uRBEZZckw5AzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T22:22:38.980033Z"},"content_sha256":"c94a12e47b5059c56980e3460882b8ccb2f21eb793a17080ba0d4a5f3026a550","schema_version":"1.0","event_id":"sha256:c94a12e47b5059c56980e3460882b8ccb2f21eb793a17080ba0d4a5f3026a550"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD/bundle.json","state_url":"https://pith.science/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD/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":"2026-05-21T22:22:38Z","links":{"resolver":"https://pith.science/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD","bundle":"https://pith.science/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD/bundle.json","state":"https://pith.science/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMG6U4TNWJL6RUE3HWMNOWHSXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WMG6U4TNWJL6RUE3HWMNOWHSXD","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":"a2b4cae696a57cadd7afa136f6ab17760b20d90dde22c78627590373e4e08ea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-01T23:47:28Z","title_canon_sha256":"c14a10cf3787fe05da659f498b01794747e4d9d99117d00fa3fa94e593075376"},"schema_version":"1.0","source":{"id":"1904.01145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01145","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01145v2","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01145","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"WMG6U4TNWJL6","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WMG6U4TNWJL6RUE3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WMG6U4TN","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c94a12e47b5059c56980e3460882b8ccb2f21eb793a17080ba0d4a5f3026a550","target":"graph","created_at":"2026-05-17T23:47:35Z","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":"We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and machine learning problems. The basic algorithm projects the gradient onto a random subspace at each iteration, similar to coordinate descent but without restricting directional derivatives to be along the axes. This algorithm is previously known but we provide new analysis. We also extend the popular SVRG method to this framework but without requirin","authors_text":"Alireza Doostan, David Kozak, Luis Tenorio, Stephen Becker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-01T23:47:28Z","title":"Stochastic Subspace Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01145","kind":"arxiv","version":2},"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":"sha256:21428145f148c90b4c01532df815065bbab9ac4195e4527f3db10cb3bac70bf8","target":"record","created_at":"2026-05-17T23:47:35Z","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":"a2b4cae696a57cadd7afa136f6ab17760b20d90dde22c78627590373e4e08ea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-01T23:47:28Z","title_canon_sha256":"c14a10cf3787fe05da659f498b01794747e4d9d99117d00fa3fa94e593075376"},"schema_version":"1.0","source":{"id":"1904.01145","kind":"arxiv","version":2}},"canonical_sha256":"b30dea726db257e8d09b3d98d758f2b8da81293cdefb14cf9cdd97c0235f4f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b30dea726db257e8d09b3d98d758f2b8da81293cdefb14cf9cdd97c0235f4f4d","first_computed_at":"2026-05-17T23:47:35.612339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:35.612339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"46p/5QDM/OQ7UwvrSgeHP55FT50hQf56QZq1mxdy06xfQg1r7hCex0qJQ5uQUfjk/BZnoORc8B8MEy/RDT3VCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:35.612780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21428145f148c90b4c01532df815065bbab9ac4195e4527f3db10cb3bac70bf8","sha256:c94a12e47b5059c56980e3460882b8ccb2f21eb793a17080ba0d4a5f3026a550"],"state_sha256":"6e2250a3840de074b4b3cc6bddf7d31257f2fcf57045ddb8e7c8bfda07f2b959"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q4KuwS13BW0hglmsxvHQuzW3FJ1F8MGgSHrpiLZ6Cao/dzXJI/+71mcByxJn4i0ZyMXo4/TowHzAn/B37/duAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T22:22:38.983271Z","bundle_sha256":"4af793d5a30ec1a3e56474d5efc72eff761ecca7b837038b55fbdad2ba6dd89e"}}