{"as_of":"2026-08-23T11:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ae71f95a17dfd8e7f8d496e0508909379ae15f58632c96b7f3d4e4e3498c0176","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:28:29.910469Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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/2412.20496/citation-record","integrity":"/paper/2412.20496/integrity","json":"/paper/2412.20496/citation-record.json","paper":"/paper/2412.20496"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1903.10563","last_updated":"2019-12-06T15:50:33Z","snapshot_observed_at":"2026-08-14T16:56:59.844743Z","submitted_at":"2019-03-25T19:34:24Z","title":"Machine learning and the physical sciences","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.10563","snapshot_observed_at":"2026-08-10T23:28:29.613387Z","title":"Carleo, I","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.613387Z"},"links":{"cited_paper":"/paper/1903.10563","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:b9d303ba30fd0d31a0f865864cc7bb18367fdceae29d15dea476ff64f058e187","observation_id":"6089b4a9-5fc6-4761-9b6b-b29d81c70382","resolution":{"observed_at":"2026-08-10T23:28:29.613387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.16427","last_updated":"2024-12-17T19:13:36Z","snapshot_observed_at":"2026-08-21T11:53:03.878174Z","submitted_at":"2024-07-23T12:25:50Z","title":"Stochastic weight matrix dynamics during learning and Dyson Brownian motion","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.16427","snapshot_observed_at":"2026-08-10T23:28:29.618836Z","title":"Aarts, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.618836Z"},"links":{"cited_paper":"/paper/2407.16427","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:4498c67e3993823e039096eb57388415424ef14947773204429eb3449c78e4f4","observation_id":"8328b243-39fb-4031-afab-862be59c7ddb","resolution":{"observed_at":"2026-08-10T23:28:29.618836Z","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":"2026-08-10T23:28:30.707992Z","title":"Wigner,Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics 62(1955) 548","venue":null,"work_id":"6f28deed-db49-4e36-b6af-a18f63832d24","year":1955},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.623971Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:ce6899b892c8c9f5dafeb43ac831b8dcddb008ada1264463a09e8ba25e884c18","observation_id":"fd68be48-a4a9-4b57-8d64-6264d884c59a","resolution":{"observed_at":"2026-08-10T23:28:30.713111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.694389Z","title":"Wigner,Conference on Neutron Physics by Time-of-Flight, p","venue":null,"work_id":"45cb8470-7f64-4dcc-b6df-f51b61819275","year":1956},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.628859Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:435c4d4498d931fedc1b9c1e6d5d93e00750fb0cc57d2c6c85c3295f6814f36e","observation_id":"af0c86ac-4062-4930-a617-ac54c77cb83f","resolution":{"observed_at":"2026-08-10T23:28:30.698820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.681245Z","title":"Dyson,Statistical theory of the energy levels of complex systems","venue":null,"work_id":"77e72f47-d79f-49a3-9004-2c77f555e745","year":1962},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.633517Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:c0bea477f3347a3b949c59901b6a549d02299bfe9a2cea78b2064f8d77a471c7","observation_id":"30a6c6e8-4443-4ace-b2dd-a2e34e762309","resolution":{"observed_at":"2026-08-10T23:28:30.685806Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.668331Z","title":"Dyson,Statistical theory of the energy levels of complex systems","venue":null,"work_id":"fffc16ee-18de-42bb-9c7a-5f1d5780d07e","year":1962},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.637909Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:5857ed107737b28e31493e0a9cf358610a5c24b1598e18740609fb065adf364d","observation_id":"d99e7409-7f9e-4764-9344-24a1dde9a0db","resolution":{"observed_at":"2026-08-10T23:28:30.672054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:29.642536Z","title":"Dyson,Statistical Theory of the Energy Levels of Complex Systems","venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.642536Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:d90b8c6557994e8431335921718329dfdab6224704154bdca2313a6f8fcf1c2a","observation_id":"7e5a285f-9cf8-49ae-ac63-2bcca123822c","resolution":{"observed_at":"2026-08-10T23:28:29.642536Z","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":"2026-08-10T23:28:30.649072Z","title":"Dyson,A Brownian-Motion Model for the Eigenvalues of a Random Matrix, J","venue":null,"work_id":"ba6b6570-ce97-4a52-afc6-63320088061f","year":1962},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.646669Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:9a97ee64c08545ac75930410330e8e914572495c47c9c360a0bb51e0d5873f82","observation_id":"75d1b192-6563-4b90-a5ac-a310d0845d1a","resolution":{"observed_at":"2026-08-10T23:28:30.653040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.635215Z","title":"Mehta,Random Matrices, Academic Press, New York, 3rd ed","venue":null,"work_id":"0f098ac8-6c3a-4d9d-97d3-4dffd7ad5987","year":2004},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.650670Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:2e6b0fba152c7a3c3a32191ef8e666eaa8c67e05cc0db614411b8a7b7ac8b4b0","observation_id":"5be17bfb-a670-40a9-a38c-6e600a531b79","resolution":{"observed_at":"2026-08-10T23:28:30.639847Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.08276","last_updated":"2019-01-24T08:20:42Z","snapshot_observed_at":"2026-08-14T17:26:38.187837Z","submitted_at":"2019-01-24T08:20:42Z","title":"Traditional and Heavy-Tailed Self Regularization in Neural Network Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.08276","snapshot_observed_at":"2026-08-10T23:28:29.668149Z","title":"Martin and M.W","venue":null,"work_id":null,"year":1901},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.668149Z"},"links":{"cited_paper":"/paper/1901.08276","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:71bf8ecb9f09b7ad8dae4402190c1171690f0dc2eb332c02fbef99f21483d369","observation_id":"db6e851d-868b-4491-9710-422ebac0848d","resolution":{"observed_at":"2026-08-10T23:28:29.668149Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2102.06740","last_updated":"2021-12-24T11:22:13Z","snapshot_observed_at":"2026-08-16T18:45:53.546884Z","submitted_at":"2021-02-12T19:49:19Z","title":"Appearance of Random Matrix Theory in Deep Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2102.06740","snapshot_observed_at":"2026-08-10T23:28:29.746912Z","title":"Baskerville, D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.746912Z"},"links":{"cited_paper":"/paper/2102.06740","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:22f9b39709d5a4bacbd4370d10e268a1662e07b12df697d9f1f3e8fe7aa755ed","observation_id":"09f95c5e-559e-4280-a923-29b80a7bca90","resolution":{"observed_at":"2026-08-10T23:28:29.746912Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1706.02677","last_updated":"2018-04-30T21:53:41Z","snapshot_observed_at":"2026-08-09T05:23:26.365677Z","submitted_at":"2017-06-08T16:51:53Z","title":"Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1706.02677","snapshot_observed_at":"2026-08-10T23:28:29.822946Z","title":"Goyal, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.822946Z"},"links":{"cited_paper":"/paper/1706.02677","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:76933c9a8f3f1132d77575739fad1cd53b345eb3e9b3d9280db6aa482849232d","observation_id":"7e14ae5e-2fe6-4c8a-9ee6-8f59ecdc3f0e","resolution":{"observed_at":"2026-08-10T23:28:29.822946Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.06451","last_updated":"2018-02-14T19:42:20Z","snapshot_observed_at":"2026-08-19T18:09:06.929945Z","submitted_at":"2017-10-17T18:08:04Z","title":"A Bayesian Perspective on Generalization and Stochastic Gradient Descent","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.06451","snapshot_observed_at":"2026-08-10T23:28:29.857819Z","title":"Smith and Q.V","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.857819Z"},"links":{"cited_paper":"/paper/1710.06451","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:731281609b8a5c3043cf85740ab4050728eca4df7ae5e394fa259663115fd068","observation_id":"44128a12-7b6b-40b7-b165-94d13b4e16d4","resolution":{"observed_at":"2026-08-10T23:28:29.857819Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.00489","last_updated":"2018-02-24T00:16:12Z","snapshot_observed_at":"2026-08-14T20:17:53.425800Z","submitted_at":"2017-11-01T18:04:31Z","title":"Don't Decay the Learning Rate, Increase the Batch Size","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.00489","snapshot_observed_at":"2026-08-10T23:28:29.861538Z","title":"Smith, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.861538Z"},"links":{"cited_paper":"/paper/1711.00489","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:19bad192b66c965f478fc51ee7f41f3ff1710c3affb2095df0cb0e217cb9d0e2","observation_id":"e4d4bd3b-ba18-493e-ae28-7ab8f2fd6627","resolution":{"observed_at":"2026-08-10T23:28:29.861538Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.09597","last_updated":"2018-11-28T18:07:24Z","snapshot_observed_at":"2026-08-14T18:59:28.724763Z","submitted_at":"2018-06-25T17:47:42Z","title":"Stochastic natural gradient descent draws posterior samples in function space","version":4},"cited_work":{"arxiv_id":"1806.09597","doi":null,"metadata_source":"pith","pith_arxiv_id":"1806.09597","snapshot_observed_at":"2026-08-10T23:28:30.171006Z","title":"Stochastic natural gradient descent draws posterior samples in function space","venue":"cs.LG","work_id":"19210bc9-fe4d-46fc-9017-fdec60e2b46b","year":2018},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.865871Z"},"links":{"cited_paper":"/paper/1806.09597","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:604fa2503ae71a32d1822d33f44ce2172950c59832cb21166ef65418a210cb03","observation_id":"4db84599-6cd3-4fdd-9ec1-60a6fd87ef4a","resolution":{"observed_at":"2026-08-10T23:28:30.175791Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.13512","last_updated":"2024-11-20T18:05:39Z","snapshot_observed_at":"2026-08-20T18:50:28.288371Z","submitted_at":"2024-11-20T18:05:39Z","title":"Dyson Brownian motion and random matrix dynamics of weight matrices during learning","version":1},"cited_work":{"arxiv_id":"2411.13512","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.13512","snapshot_observed_at":"2026-08-10T23:28:30.153324Z","title":"Dyson Brownian motion and random matrix dynamics of weight matrices during learning","venue":"cond-mat.dis-nn","work_id":"5cd3d081-ce23-4bee-8822-d80b459639c7","year":2024},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.870383Z"},"links":{"cited_paper":"/paper/2411.13512","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:41d6f8815637b8a032bd96c2d233403644567400b3b24ce3ab866cfbfd1e74d6","observation_id":"6db49146-4169-4690-81e3-a8e35bdde80d","resolution":{"observed_at":"2026-08-10T23:28:30.157260Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.455299Z","title":"Mandt, M.D","venue":null,"work_id":"bb28677a-3ce1-44f5-a0ea-acc8d743ddd2","year":2015},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.874606Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:1292bce813b91db65c01842ae964a209998ad33726106f2d4aba16f356fe2839","observation_id":"6623dc00-3d59-4ca7-b475-0f1c2d73c23d","resolution":{"observed_at":"2026-08-10T23:28:30.590276Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1511.06251","last_updated":"2017-06-20T13:56:33Z","snapshot_observed_at":"2026-08-14T22:22:12.117081Z","submitted_at":"2015-11-19T16:49:33Z","title":"Stochastic modified equations and adaptive stochastic gradient algorithms","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.06251","snapshot_observed_at":"2026-08-10T23:28:29.878141Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.878141Z"},"links":{"cited_paper":"/paper/1511.06251","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:f6598824fade1c9aadce2fd1fc065590738567ba7b222c7441611922d427f669","observation_id":"1d2af006-3339-4cdb-9268-c9ef3a052146","resolution":{"observed_at":"2026-08-10T23:28:29.878141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.00004","last_updated":"2018-12-21T16:09:27Z","snapshot_observed_at":"2026-08-14T18:21:56.930627Z","submitted_at":"2018-09-28T18:00:00Z","title":"Fluctuation-dissipation relations for stochastic gradient descent","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.00004","snapshot_observed_at":"2026-08-10T23:28:29.881681Z","title":"Yaida,Fluctuation-dissipation relations for stochastic gradient descent, inInternational Conference on Learning Representations, 2019 [1810.00004]","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.881681Z"},"links":{"cited_paper":"/paper/1810.00004","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:282294920d685548c33f857c520846ee70f215f036d9e010c6ec926eca4c3c3b","observation_id":"574837fe-b827-4eb4-8fe9-f145bc1434b5","resolution":{"observed_at":"2026-08-10T23:28:29.881681Z","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":"2026-08-10T23:28:30.331308Z","title":"Smolensky,Chapter 6: Information processing in dynamical systems: Foundations of harmony theory, inParallel Distributed Processing: Volume 1, D","venue":null,"work_id":"15bdeba5-09cf-4239-8a66-5ca5d6c261e9","year":1986},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.886363Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:97c0ccd97b14a3a00bcb3f39484c31b5ddc8c856f8a0321246e715c939ebadff","observation_id":"d3d1a7b6-0e19-4af4-9c4c-efc9cb3b72d5","resolution":{"observed_at":"2026-08-10T23:28:30.408975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.318507Z","title":"Hinton,Training Products of Experts by Minimizing Contrastive Divergence,Neural Computation 14(2002) 1771","venue":null,"work_id":"c6deec55-b2db-464a-933a-8e2539f9fcda","year":2002},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.889927Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:f735efcd1a0bc2f38d5b2ed82c801c4da2c3f9a185bcdccaaec7703adc6cace1","observation_id":"79601bbc-f0e9-44a2-abb9-bce5d58a1167","resolution":{"observed_at":"2026-08-10T23:28:30.322809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2011.11307","last_updated":"2021-05-28T08:32:54Z","snapshot_observed_at":"2026-08-16T19:04:00.148938Z","submitted_at":"2020-11-23T10:08:53Z","title":"Restricted Boltzmann Machine, recent advances and mean-field theory","version":2},"cited_work":{"arxiv_id":"2011.11307","doi":null,"metadata_source":"pith","pith_arxiv_id":"2011.11307","snapshot_observed_at":"2026-08-10T23:28:30.111383Z","title":"Restricted Boltzmann Machine, recent advances and mean-field theory","venue":"cond-mat.dis-nn","work_id":"a17ddf83-3295-45a9-abfd-13e13ae9d8e7","year":2020},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.893326Z"},"links":{"cited_paper":"/paper/2011.11307","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:0f6f70b72c829c8d6afdb38e1b1fe6b23174df825ed3380762081c51e6ce789f","observation_id":"dd562bc2-10f6-4d75-b2c3-e422525d335b","resolution":{"observed_at":"2026-08-10T23:28:30.116524Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.15002","last_updated":"2024-03-01T15:45:49Z","snapshot_observed_at":"2026-08-19T08:05:16.723896Z","submitted_at":"2023-09-26T15:17:43Z","title":"Scalar field Restricted Boltzmann Machine as an ultraviolet regulator","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.15002","snapshot_observed_at":"2026-08-10T23:28:29.898270Z","title":"Aarts, B","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.898270Z"},"links":{"cited_paper":"/paper/2309.15002","citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:63059c9b422bba9d423a002aae16db61363923cb6b2c8e42b63825ff029ec9de","observation_id":"abe8ed9d-685c-4f4e-8298-9b423ba980ca","resolution":{"observed_at":"2026-08-10T23:28:29.898270Z","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":"2026-08-10T23:28:30.304902Z","title":"Bahri, J","venue":null,"work_id":"2e8c476e-e4b5-40cc-80a1-667c2e9b6867","year":2020},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.902693Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:e143bb136e3046914f9f47f10f1312630df43e939904139eda8813e66a9023eb","observation_id":"f6fd0ae5-26d3-4ddc-b75f-1297d8efe006","resolution":{"observed_at":"2026-08-10T23:28:30.310214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-10T23:28:30.291457Z","title":"Goldt, M.S","venue":null,"work_id":"a372dc0a-25c7-440f-abd0-714e04f5efed","year":2020},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.906548Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:313037ad646381793b3079089e593ed4cfb2030854bac32dd76adbc48b085859","observation_id":"7265edc5-efa4-45d7-8175-336bb58d2ecf","resolution":{"observed_at":"2026-08-10T23:28:30.295808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5281/zenodo.13310439","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:28:29.958833Z","title":null,"venue":null,"work_id":"0a2859c5-ab28-458e-ba23-d84464d6b425","year":2024},"citing_paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:28:29.910469Z"},"links":{"citing_paper":"/paper/2412.20496"},"observation_digest":"sha256:71e7fdad61af928c9022a2d91c19ae14392e25a1d228c8e2c5f6250152955f2e","observation_id":"a6144477-72c0-47ab-997e-576fe07619fa","resolution":{"observed_at":"2026-08-10T23:28:30.035604Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.20496","last_updated":"2024-12-29T15:21:13Z","latest_version":1,"primary_category":"hep-lat","snapshot_observed_at":"2026-08-19T21:57:47.484659Z","submitted_at":"2024-12-29T15:21:13Z","title":"Random Matrix Theory for Stochastic Gradient Descent"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":4,"verified_fuzzy":11},"total_outbound_references":26},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2412.20496."}