{"as_of":"2026-08-21T11:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cfe020f3b3e8fd4a36b4bd1128a8643eac1ce7f341295dd4ac93d86700032340","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":9,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:47:24.843115Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-02T07:36:45.174590Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":"1902.04811","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-07-02T07:36:45.174590Z","title":"Stochas- tic gradient descent escapes saddle points efficiently","venue":null,"work_id":"7d604b92-f948-4aa5-b5c4-d99955d9da7f","year":2019},"citing_paper":{"arxiv_id":"1907.01848","last_updated":"2019-07-03T11:06:11Z","snapshot_observed_at":"2026-08-15T23:56:31.655626Z","submitted_at":"2019-07-03T11:06:11Z","title":"Distributed Learning in Non-Convex Environments -- Part I: Agreement at a Linear Rate","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-25T10:24:33.527480Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/1907.01848"},"observation_digest":"sha256:00081fd9da434770234198fc6e5f375bdfaf88b500d9d54bcc43578d815ab8dd","observation_id":"1dd7419e-d602-486b-91bf-1021caae4a54","resolution":{"observed_at":"2026-05-25T10:25:38.607286Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":"1902.04811","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-07-02T07:36:45.174590Z","title":"Stochas- tic gradient descent escapes saddle points efficiently","venue":null,"work_id":"7d604b92-f948-4aa5-b5c4-d99955d9da7f","year":2019},"citing_paper":{"arxiv_id":"1907.01849","last_updated":"2019-07-03T11:06:43Z","snapshot_observed_at":"2026-08-18T17:26:14.848780Z","submitted_at":"2019-07-03T11:06:43Z","title":"Distributed Learning in Non-Convex Environments -- Part II: Polynomial Escape from Saddle-Points","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-25T09:52:34.427619Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/1907.01849"},"observation_digest":"sha256:0b0f6f0a1471230178f74288d6998e1ac720f7fcd68b0ac19d99545e4bbfd097","observation_id":"2f123d49-9a9a-4cf4-9cc6-d8625eafd6d8","resolution":{"observed_at":"2026-05-25T09:55:36.558456Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-08-14T12:47:24.843115Z","title":"Stochastic gradient descent escapes saddle points efficiently,","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"1908.06693","last_updated":"2019-08-19T11:08:37Z","snapshot_observed_at":"2026-08-19T18:09:35.829616Z","submitted_at":"2019-08-19T11:08:37Z","title":"Distributed Stochastic Gradient Method for Non-Convex Problems with Applications in Supervised Learning","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T12:47:24.843115Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/1908.06693"},"observation_digest":"sha256:1e661ba28e3d9e2b7e4084c066fa84417eeefa91dc6909b5be1d0daa9c0021a4","observation_id":"0ba4b784-de7f-4123-84e1-5d03894fab8a","resolution":{"observed_at":"2026-08-14T12:47:24.843115Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-08-14T12:38:57.556595Z","title":"Stochas- tic gradient descent escapes saddle points efficiently,","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"1908.07023","last_updated":"2019-08-19T18:56:40Z","snapshot_observed_at":"2026-08-19T18:13:56.211078Z","submitted_at":"2019-08-19T18:56:40Z","title":"Second-Order Guarantees of Stochastic Gradient Descent in Non-Convex Optimization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:38:57.556595Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/1908.07023"},"observation_digest":"sha256:3ba84f8939bc6324d431b52423cd449f556bb18da7c495a86064ae2c0510d47b","observation_id":"225efb58-aadc-4cae-98ad-130710dfabd3","resolution":{"observed_at":"2026-08-14T12:38:57.556595Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-08-06T13:09:59.968238Z","title":"Kakade, and Michael I","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2507.21205","last_updated":"2025-07-28T17:54:15Z","snapshot_observed_at":"2026-08-16T23:05:30.522047Z","submitted_at":"2025-07-28T17:54:15Z","title":"Learning from Limited and Imperfect Data","version":1},"reference_index":123,"source":"pdf_text","source_observed_at":"2026-08-06T13:09:59.968238Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/2507.21205"},"observation_digest":"sha256:6a882e7d264438ff8600493e7701974d41755fb1dd02f0b5637c1e07a75b292d","observation_id":"28ebbe59-f608-4d49-b083-eabef028782a","resolution":{"observed_at":"2026-08-06T13:09:59.968238Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-08-05T12:46:30.602557Z","title":"Keller Jordan, Yuchen Jin, Vlado Boza, Jiacheng You, Franz Cesista, Laker Newhouse, and Jeremy Bernstein","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2509.01329","last_updated":"2025-09-01T10:12:13Z","snapshot_observed_at":"2026-08-21T02:25:44.703852Z","submitted_at":"2025-09-01T10:12:13Z","title":"Globally aware optimization with resurgence","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T12:46:30.602557Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/2509.01329"},"observation_digest":"sha256:0396f85478e63ee81b3b6ecc618d4cd6a535a1a554af34c724403f7963dc6dcb","observation_id":"251df33f-3283-40a0-903c-faf888aaccea","resolution":{"observed_at":"2026-08-05T12:46:30.602557Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":"1902.04811","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-07-02T07:36:45.174590Z","title":"Stochas- tic gradient descent escapes saddle points efficiently","venue":null,"work_id":"7d604b92-f948-4aa5-b5c4-d99955d9da7f","year":2019},"citing_paper":{"arxiv_id":"2605.14345","last_updated":"2026-08-19T14:37:57Z","snapshot_observed_at":"2026-08-21T10:17:20.476540Z","submitted_at":"2026-05-14T04:09:51Z","title":"Convergence of difference inclusions: a diameter criterion and step-size conditions","version":1},"reference_index":291,"source":"arxiv_source","source_observed_at":"2026-05-15T02:21:30.228735Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/2605.14345"},"observation_digest":"sha256:0b06fa3c0d52c037d2ad9de8e66652837d12356d7949044489e4b7f0bc3b4983","observation_id":"824e1e3a-0fd3-407f-acec-4679c98c48a6","resolution":{"observed_at":"2026-05-15T02:23:31.781196Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":"1902.04811","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-07-02T07:36:45.174590Z","title":"Stochas- tic gradient descent escapes saddle points efficiently","venue":null,"work_id":"7d604b92-f948-4aa5-b5c4-d99955d9da7f","year":2019},"citing_paper":{"arxiv_id":"2606.05438","last_updated":"2026-06-03T21:01:21Z","snapshot_observed_at":"2026-08-16T20:18:23.959901Z","submitted_at":"2026-06-03T21:01:21Z","title":"Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T06:50:05.151386Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/2606.05438"},"observation_digest":"sha256:55a2d15c1a4caf6d181d62b7a0c3068194b28c1a86e60470621408f0ad23e8a9","observation_id":"c25847ea-ec12-4c43-ab3d-d04b28236c62","resolution":{"observed_at":"2026-07-02T07:36:45.176067Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.04811","snapshot_observed_at":"2026-08-08T04:30:36.947932Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.03001","last_updated":"2026-08-06T04:18:49Z","snapshot_observed_at":"2026-08-16T09:26:35.816981Z","submitted_at":"2026-08-04T01:34:36Z","title":"Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T04:30:36.947932Z"},"links":{"cited_paper":"/paper/1902.04811","citing_paper":"/paper/2608.03001"},"observation_digest":"sha256:e0127cb3a5e60d34553105fd0b54f0ed5a51cdaed64ac5e680af03f269b61c55","observation_id":"c5d90958-7f30-458b-9759-e8ee34f882d9","resolution":{"observed_at":"2026-08-08T04:30:36.947932Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1902.04811/citation-record","integrity":"/paper/1902.04811/integrity","json":"/paper/1902.04811/citation-record.json","paper":"/paper/1902.04811"},"outbound":[],"paper":{"arxiv_id":"1902.04811","last_updated":"2019-09-04T03:26:59Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-19T18:13:51.605150Z","submitted_at":"2019-02-13T09:44:02Z","title":"On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 9 inbound Pith citation observations for arXiv:1902.04811."}