{"as_of":"2026-08-22T13:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:196002e62041b47a722b92b37a993378a4571e9feacb8506400a59b4fd216310","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T15:13:02.118812Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.02419/citation-record","integrity":"/paper/1908.02419/integrity","json":"/paper/1908.02419/citation-record.json","paper":"/paper/1908.02419"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.006096Z","title":"On the capabilities of multilayer perceptro ns,","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.006096Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:7015241dd96a056a20727bf9833d6a766a63e97eac493b1a44733efd21028bd5","observation_id":"6e7acdae-8136-48ee-be41-b4abb108316c","resolution":{"observed_at":"2026-08-14T15:13:02.006096Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1109/pgec.196","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.155960Z","title":"Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognit ion,","venue":null,"work_id":"69c14a95-8506-4b17-bf1d-cc8a79703747","year":1965},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.012025Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:57343945966caecdcdf60747bac6e8da9c2051aa84430159b7cb4a27303f9831","observation_id":"7a8fa5cb-bba6-4f4d-b0b6-bcc7bc81ea87","resolution":{"observed_at":"2026-08-14T15:13:02.164268Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.018617Z","title":"Learning capability and storage capacity of t wo- hidden-layer feedforward networks,","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.018617Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:c667abefd0a2c61d9f136f5b7383a32eb9a3468f4da18c638df275fa75eec243","observation_id":"60e96cc1-2e27-4f84-9188-cb8af3b544f3","resolution":{"observed_at":"2026-08-14T15:13:02.018617Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.532754Z","title":"Bounds on the number of hidden neur ons in multilayer perceptrons,","venue":null,"work_id":"da579136-20d6-42cd-bffc-96bcbef52c01","year":1991},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.023492Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:bf6f241b7a8b24448ffd2b62df0310494b94617e21d972f547fe0ed27b9911b5","observation_id":"ffece35b-ebf7-4dac-b1c0-19747dbfb751","resolution":{"observed_at":"2026-08-14T15:13:02.537769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.518350Z","title":"Upper bounds on the number of hid den neurons in feedforward networks with arbitrary bounded non linear activation functions,","venue":null,"work_id":"19faa23d-6a4b-485d-8589-2018c435071e","year":1998},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.028910Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:6d77f53bb59339d68f8484e2fb4905146b12f6f8743b3bc16492ee03123a1e50","observation_id":"54f169f9-db32-4e41-b2d9-b68399c6ee8b","resolution":{"observed_at":"2026-08-14T15:13:02.522975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.503692Z","title":"The lower bound of the capacity for a neural network with multiple hidden layers,","venue":null,"work_id":"17bc292a-9d9e-467b-b418-1b4e113ff2c8","year":1993},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.033395Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:ef73223fce855b8c99f0bedeffc65dc1996a0d2dbe43a8f6f04b19a9b0e82c1a","observation_id":"c89272af-d367-434e-a1a4-8a0b2d30b1aa","resolution":{"observed_at":"2026-08-14T15:13:02.508836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.07770","last_updated":"2019-10-29T05:22:58Z","snapshot_observed_at":"2026-08-19T18:27:22.230186Z","submitted_at":"2018-10-17T20:21:43Z","title":"Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.07770","snapshot_observed_at":"2026-08-14T15:13:02.038044Z","title":"Small relu networks are powerful memorizers: a tight analysis of memorization capacity,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.038044Z"},"links":{"cited_paper":"/paper/1810.07770","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:b739dfb3d7f2392a5b72f4c91689069c7deb9cb9924a6faaecf6c3391ec25fc2","observation_id":"a6d3ebc9-4ddb-427e-83b2-c1f5c1c1ebe1","resolution":{"observed_at":"2026-08-14T15:13:02.038044Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.489994Z","title":"Identity matters in deep learning,","venue":null,"work_id":"cadc8a44-069a-4f90-ba48-fb1d966486ca","year":2017},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.043052Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:1b0b90405417dff4537c1b424258eedb074a8d7c37436233f775f4dc240d1561","observation_id":"fab85cc0-1dd1-43bc-bdc9-fbb86d2dabca","resolution":{"observed_at":"2026-08-14T15:13:02.494215Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.476904Z","title":"Optimization landscape and expre ssivity of deep cnns,","venue":null,"work_id":"190fc081-370c-4eb1-a606-393084b9a7c9","year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.048207Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:6eb2fe1791cec4ef8a8a63eac585ed4e8206a54a4bfe89bdaf7a96cb8149f083","observation_id":"b8b6b97a-022d-4361-bc23-e3df696bdfe5","resolution":{"observed_at":"2026-08-14T15:13:02.481216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.461394Z","title":"Hardness results for neu ral network approximation problems,","venue":null,"work_id":"55ad37d0-93ff-4ed3-bbac-5518fc72392a","year":1999},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.052824Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:b6ecac42e566fac66100b4a2d382a674b53592ca2f64fedfa4899516d06629db","observation_id":"d9d0f5e9-4836-40af-9432-24efc8d1784e","resolution":{"observed_at":"2026-08-14T15:13:02.465949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.447266Z","title":"Training a 3-node neural netwo rk is np-complete,","venue":null,"work_id":"906625cb-171b-4838-a851-7352b71ba972","year":1989},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.057073Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:7b183b800ef5b2f4ad3096e0c81929d9edfe91cbad63de73e3c62dac669a55d7","observation_id":"e5e950a6-84f3-46a1-afe6-79e20f099d70","resolution":{"observed_at":"2026-08-14T15:13:02.452598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.433801Z","title":"On the comp utational efﬁciency of training neural networks,","venue":null,"work_id":"a9b8ee09-2c2a-4a2b-a80b-f61a7eb95c1e","year":2014},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.063119Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:863ca8a5e37145e99502c4b3537aba3f1b74379277970594f0800c3cdfe2e877","observation_id":"0b66dabb-91db-4937-9b22-cb34f739d3ea","resolution":{"observed_at":"2026-08-14T15:13:02.438195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.067007Z","title":"Learning overparameterized neural networks via stochastic gradient descent on structured data,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.067007Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:de576be5a57805fdacf70ad947aecdee0f48b72f99ea66cf340073a8eeed8e82","observation_id":"95bb0f26-e34a-4e62-a4f9-c3fdf2e32521","resolution":{"observed_at":"2026-08-14T15:13:02.067007Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.02054","last_updated":"2019-02-05T01:59:59Z","snapshot_observed_at":"2026-08-20T07:39:09.579125Z","submitted_at":"2018-10-04T04:47:47Z","title":"Gradient Descent Provably Optimizes Over-parameterized Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.02054","snapshot_observed_at":"2026-08-14T15:13:02.072458Z","title":"Gradient desc ent provably optimizes over-parameterized neural networks,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.072458Z"},"links":{"cited_paper":"/paper/1810.02054","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:393e1c0d271ecd301814c4939b332470547b0a04b6a77b493fa5af5b3cd08eb6","observation_id":"c71fdfb4-b2e5-49e9-92da-d910d6944777","resolution":{"observed_at":"2026-08-14T15:13:02.072458Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.03593","last_updated":"2020-02-18T11:17:58Z","snapshot_observed_at":"2026-08-20T21:00:08.314207Z","submitted_at":"2019-06-09T08:36:35Z","title":"Quadratic Suffices for Over-parametrization via Matrix Chernoff Bound","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.03593","snapshot_observed_at":"2026-08-14T15:13:02.077002Z","title":"Quadratic sufﬁces for over-parame trization via matrix chernoff bound,","venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.077002Z"},"links":{"cited_paper":"/paper/1906.03593","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:2510aef7b9db86dec306fc05add6d7bdb1846c774c1a2262b21d3f373158af5e","observation_id":"befe36de-8c92-47f3-8e29-797b1f0a8743","resolution":{"observed_at":"2026-08-14T15:13:02.077002Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.03962","last_updated":"2019-06-17T06:39:04Z","snapshot_observed_at":"2026-08-15T12:33:17.579745Z","submitted_at":"2018-11-09T15:16:13Z","title":"A Convergence Theory for Deep Learning via Over-Parameterization","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.03962","snapshot_observed_at":"2026-08-14T15:13:02.081931Z","title":"A convergence theory f or deep learning via over-parameterization,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.081931Z"},"links":{"cited_paper":"/paper/1811.03962","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:f77a676908a0baa3b2e325f709e520ab65be9a04afabb03a9bd6e45fff683780","observation_id":"3ecdd18b-cb6c-4cef-89aa-d5f93d52993b","resolution":{"observed_at":"2026-08-14T15:13:02.081931Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.03804","last_updated":"2019-05-28T19:01:22Z","snapshot_observed_at":"2026-08-20T00:06:43.502080Z","submitted_at":"2018-11-09T07:39:59Z","title":"Gradient Descent Finds Global Minima of Deep Neural Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.03804","snapshot_observed_at":"2026-08-14T15:13:02.086434Z","title":"Gradi- ent descent ﬁnds global minima of deep neural networks,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.086434Z"},"links":{"cited_paper":"/paper/1811.03804","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:88aa5958a1880a214451addb48b08762e1dc59330f864e50b28595ee70e75740","observation_id":"beb30428-637a-400a-b2d6-119d16b8b79b","resolution":{"observed_at":"2026-08-14T15:13:02.086434Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.08888","last_updated":"2018-12-27T18:57:43Z","snapshot_observed_at":"2026-08-14T17:55:27.705967Z","submitted_at":"2018-11-21T18:58:46Z","title":"Stochastic Gradient Descent Optimizes Over-parameterized Deep ReLU Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.08888","snapshot_observed_at":"2026-08-14T15:13:02.090787Z","title":"Stochastic gradient d escent optimizes over-parameterized deep relu networks,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.090787Z"},"links":{"cited_paper":"/paper/1811.08888","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:6783361fe6582a4b52d0150852fe30e02056d005f5daae62f471f1f39702402a","observation_id":"b7290fee-7f34-42a5-bd1d-c83a1f4073b6","resolution":{"observed_at":"2026-08-14T15:13:02.090787Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.04688","last_updated":"2019-06-11T16:40:46Z","snapshot_observed_at":"2026-08-19T18:25:47.735885Z","submitted_at":"2019-06-11T16:40:46Z","title":"An Improved Analysis of Training Over-parameterized Deep Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.04688","snapshot_observed_at":"2026-08-14T15:13:02.095110Z","title":"An improved analysis of training over-parameterized deep neural networks,","venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.095110Z"},"links":{"cited_paper":"/paper/1906.04688","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:99a0f8190e284699618bd4aa27192c957658f99ecd6b250feed12c4b3cf3dc77","observation_id":"8913bb73-3894-4f11-a7cf-03c81627f2de","resolution":{"observed_at":"2026-08-14T15:13:02.095110Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1512.07276","last_updated":"2015-12-22T22:01:22Z","snapshot_observed_at":"2026-08-14T22:17:19.284360Z","submitted_at":"2015-12-22T22:01:22Z","title":"The Zero Set of a Real Analytic Function","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1512.07276","snapshot_observed_at":"2026-08-14T15:13:02.100067Z","title":"The zero set of a real analytic function,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.100067Z"},"links":{"cited_paper":"/paper/1512.07276","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:d9f802b460783c100890252fe8173cd4ba40759eb84eb75df34f646a3c61ca7f","observation_id":"94233533-c566-4533-bf6f-ff1440613c23","resolution":{"observed_at":"2026-08-14T15:13:02.100067Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.413598Z","title":"Gradien t-based learning applied to document recognition,","venue":null,"work_id":"c4ce3029-c827-4f46-be72-761029d06f99","year":1998},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.104766Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:5cbd7b6eda9be40c63014b1af175e18b26724329ffb2e2c07c4579559ffbb42d","observation_id":"d949762c-1f3b-4ec1-bf96-e02f22f6de60","resolution":{"observed_at":"2026-08-14T15:13:02.418071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.09038","last_updated":"2019-07-09T14:59:54Z","snapshot_observed_at":"2026-08-20T21:00:00.875457Z","submitted_at":"2018-10-21T22:38:32Z","title":"Depth with Nonlinearity Creates No Bad Local Minima in ResNets","version":3},"cited_work":{"arxiv_id":"1810.09038","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.09038","snapshot_observed_at":"2026-08-14T15:13:02.214851Z","title":"Depth with Nonlinearity Creates No Bad Local Minima in ResNets","venue":"stat.ML","work_id":"e6dbaefa-b1e0-4b42-bbab-94913ee9e9a4","year":2018},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.108923Z"},"links":{"cited_paper":"/paper/1810.09038","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:4de67e0d57f3194d0f22dd99f7a389557bc257ef3172305d198b33dad1d13654","observation_id":"392d1edb-14e8-435f-9372-d0a481192d15","resolution":{"observed_at":"2026-08-14T15:13:02.219877Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1904.03673","last_updated":"2019-11-15T23:04:15Z","snapshot_observed_at":"2026-08-20T21:00:00.307333Z","submitted_at":"2019-04-07T15:43:59Z","title":"Every Local Minimum Value is the Global Minimum Value of Induced Model in Non-convex Machine Learning","version":3},"cited_work":{"arxiv_id":"1904.03673","doi":null,"metadata_source":"pith","pith_arxiv_id":"1904.03673","snapshot_observed_at":"2026-08-14T15:13:02.191610Z","title":"Every Local Minimum Value is the Global Minimum Value of Induced Model in Non-convex Machine Learning","venue":"stat.ML","work_id":"71be5293-2f51-4f37-ab3b-b269fae52487","year":2019},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.114280Z"},"links":{"cited_paper":"/paper/1904.03673","citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:8144436ab0e2df1093fd1b5dc46b68e63754391dbc84128b8a34904866c0fe8a","observation_id":"4b9c0bbf-0014-42f7-a525-d1aa559d14a0","resolution":{"observed_at":"2026-08-14T15:13:02.196780Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:13:02.399685Z","title":"Empirical margin di stributions and bounding the generalization error of combined classiﬁers,","venue":null,"work_id":"ba801cee-f897-4653-853b-666bc9eb53da","year":2002},"citing_paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T15:13:02.118812Z"},"links":{"citing_paper":"/paper/1908.02419"},"observation_digest":"sha256:388f2af88b9454106238fbb0015fd22937470b8a310faa11c6c65afd4a643eb8","observation_id":"2e4ec549-8830-42db-a09c-4a580a7c51e2","resolution":{"observed_at":"2026-08-14T15:13:02.404253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.02419","last_updated":"2020-06-16T19:40:44Z","latest_version":3,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-19T18:26:07.767237Z","submitted_at":"2019-08-05T20:19:39Z","title":"Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":3,"verified_fuzzy":10},"total_outbound_references":24},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:1908.02419."}