{"as_of":"2026-08-05T11:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:45c2e98dfc65cf63f3b7ae267f53e901173ed56b9d9f9cabdda5fea21931be48","coverage":[{"denominator":47,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":47,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-12T04:38:25.480020Z","state":"measured"},{"denominator":47,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":47,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-05T06:32:48.257954+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/2605.09331/citation-record","integrity":"/paper/2605.09331/integrity","json":"/paper/2605.09331/citation-record.json","paper":"/paper/2605.09331"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2002.09018","last_updated":"2021-03-05T06:29:48Z","snapshot_observed_at":"2026-08-03T21:55:15.856477Z","submitted_at":"2020-02-20T20:51:33Z","title":"Scalable Second Order Optimization for Deep Learning","version":2},"cited_work":{"arxiv_id":"2002.09018","doi":"10.48550/arxiv.2002.09018","metadata_source":"pith","pith_arxiv_id":"2002.09018","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"arXiv preprint arXiv:2002.09018 , year =","venue":"cs.LG","work_id":"9c7f025f-ec0e-4000-b1d0-db6e212787c5","year":2020},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2002.09018","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:81bfd6ed43c9f69aa68b771763f5fd630b8f4f07b052ee589cdffd69c9b1d8c2","observation_id":"f59a6df3-1a9a-430d-8349-2f6ee65504ca","resolution":{"observed_at":"2026-05-12T06:01:26.497710Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"On the convergence of muon and beyond","venue":null,"work_id":"a09edb5b-98c6-46b1-abb4-c5c695d098af","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:29af863d3e2dfb0adba19efd74c2d6debc22a3fc8650a0448bda8bc820142f5c","observation_id":"860b0d2d-f36e-46ff-acb5-32e01043af0c","resolution":{"observed_at":"2026-05-12T14:11:37.247245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2509.15816","last_updated":"2026-05-10T06:58:46Z","snapshot_observed_at":"2026-07-06T22:30:17.163909Z","submitted_at":"2025-09-19T09:43:37Z","title":"On the Convergence of Muon and Beyond","version":5},"cited_work":{"arxiv_id":"2509.15816","doi":null,"metadata_source":"pith","pith_arxiv_id":"2509.15816","snapshot_observed_at":"2026-07-04T07:29:38.596450Z","title":"On the Convergence of Muon and Beyond","venue":"cs.LG","work_id":"4a43859c-1056-4934-bc0b-1d3e33bbc5b0","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2509.15816","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:085993953decbd333cb7f481630c407c35a61c70f857968d006a3c7848d8247c","observation_id":"5f970727-f34b-4895-a93e-edd55e3de221","resolution":{"observed_at":"2026-05-12T06:01:26.501307Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.0233","last_updated":"2015-01-21T22:25:26Z","snapshot_observed_at":"2026-08-04T23:10:05.993602Z","submitted_at":"2014-11-30T15:48:16Z","title":"The Loss Surfaces of Multilayer Networks","version":3},"cited_work":{"arxiv_id":"1412.0233","doi":"10.48550/arxiv.1412.0233","metadata_source":"pith","pith_arxiv_id":"1412.0233","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The loss surfaces of multilayer networks","venue":"cs.LG","work_id":"78665672-99ec-4d71-8e98-2add9ad50907","year":2014},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1412.0233","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:8e9920ae19cfc73453b01ca9d91674e951370a9c194bf0edd4e5aca5289ff1f9","observation_id":"2227f415-4769-44a8-82c3-7fdefa3a0edf","resolution":{"observed_at":"2026-05-12T06:01:26.493478Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1803.05999","last_updated":"2018-09-16T16:18:17Z","snapshot_observed_at":"2026-07-06T06:28:33.221907Z","submitted_at":"2018-03-15T20:48:06Z","title":"Escaping Saddles with Stochastic Gradients","version":2},"cited_work":{"arxiv_id":"1803.05999","doi":null,"metadata_source":"pith","pith_arxiv_id":"1803.05999","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Escaping Saddles with Stochastic Gradients","venue":"cs.LG","work_id":"c7c4f3f3-c67a-48c7-8c60-e950b3e0ff9e","year":2018},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1803.05999","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:1e4f35988ea818f4cc0a7f5426438fb0ca9e79d461c1cc0d9b1b63625e4ee1d8","observation_id":"2c78eefc-018e-4761-befa-679d4fec984c","resolution":{"observed_at":"2026-05-12T06:01:26.489593Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1406.2572","last_updated":"2014-06-10T14:52:14Z","snapshot_observed_at":"2026-07-06T03:45:59.079055Z","submitted_at":"2014-06-10T14:52:14Z","title":"Identifying and attacking the saddle point problem in high-dimensional non-convex optimization","version":1},"cited_work":{"arxiv_id":"1406.2572","doi":null,"metadata_source":"pith","pith_arxiv_id":"1406.2572","snapshot_observed_at":"2026-07-04T05:39:40.933683Z","title":"Identifying and attacking the saddle point problem in high-dimensional non-convex optimization","venue":"cs.LG","work_id":"2e7e0566-13d2-4bf5-817a-b08735476dbd","year":2014},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1406.2572","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:343f99c7f41a6351f48a8f10522020ff95d2ef65aeb8742ce1bf40550e7d8d89","observation_id":"28e869b9-887e-4231-ba0a-d6ad2d30c6e2","resolution":{"observed_at":"2026-05-12T06:01:26.507724Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.03404","last_updated":"2023-08-01T14:27:08Z","snapshot_observed_at":"2026-07-06T10:47:03.826810Z","submitted_at":"2021-03-05T00:39:05Z","title":"Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth","version":2},"cited_work":{"arxiv_id":"2103.03404","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2103.03404","snapshot_observed_at":"2026-07-04T06:19:38.253882Z","title":"arXiv preprint arXiv:2103.03404 , year=","venue":null,"work_id":"7886c794-14ad-4e4f-bb5b-d9d6c465cf12","year":2021},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2103.03404","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:365036053c55a727bc845b1e17f6fd5de3d0f78629739c7a04f692b6b33d0b91","observation_id":"455cf994-a3e2-4173-9470-ac528c70ac49","resolution":{"observed_at":"2026-05-12T06:01:26.403986Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2210.04488","last_updated":"2023-07-30T21:56:18Z","snapshot_observed_at":"2026-07-06T14:02:57.535982Z","submitted_at":"2022-10-10T08:33:05Z","title":"Optimal Eigenvalue Shrinkage in the Semicircle Limit","version":2},"cited_work":{"arxiv_id":"2210.04488","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2210.04488","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Donoho and Michael J","venue":null,"work_id":"2d567fcf-0d2b-4bb7-a93e-c2cb3c1fe8ed","year":2023},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2210.04488","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:bb2ede47a1a5529b1172c5d5f0115d309fe56e681462cf1e43db379108d47a42","observation_id":"3228e01b-1420-4276-be24-0f89292dad8e","resolution":{"observed_at":"2026-05-12T06:01:26.407392Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2604.01472","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T14:39:55.258294Z","title":"Du and W","venue":null,"work_id":"ef25ad07-851b-4ed1-b640-baa0802a2892","year":2026},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:b9d60d4366453f78e21edcc57017080e52d882ad624b38b9587692342c9e7f57","observation_id":"2d015a04-8a3a-41e8-96ac-af5a723f731f","resolution":{"observed_at":"2026-05-12T06:01:26.379256Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Escaping from saddle points—online stochastic gradient for tensor decomposition.COLT","venue":null,"work_id":"e9f6794b-d1b9-408c-988e-79575bb4be3b","year":2015},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:cda6e854b47787b7d64a701c5ff46477534681d559c316d6d9005cb402676602","observation_id":"850892ed-ef5a-46ee-9292-91325d1636f2","resolution":{"observed_at":"2026-05-12T14:11:37.265424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2506.10935","doi":"10.48550/arxiv.2506.10935","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Grishina, M","venue":"arXiv (Cornell University)","work_id":"e0965fe0-a555-4f58-8bc2-33b219db9443","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:06f8d7a6803e30e172844addf22001e8574813f38ba04dc092cc3b78e513ea82","observation_id":"2d55c43e-2454-490b-9db9-0bd7d7a06e08","resolution":{"observed_at":"2026-05-12T06:01:26.428453Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.09568","last_updated":"2018-03-02T00:12:58Z","snapshot_observed_at":"2026-07-06T06:25:29.112809Z","submitted_at":"2018-02-26T19:36:41Z","title":"Shampoo: Preconditioned Stochastic Tensor Optimization","version":2},"cited_work":{"arxiv_id":"1802.09568","doi":"10.48550/arxiv.1802.09568","metadata_source":"pith","pith_arxiv_id":"1802.09568","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Shampoo: Preconditioned Stochastic Tensor Optimization","venue":"cs.LG","work_id":"85339699-854e-4bf1-aa39-0d8b72be6def","year":2018},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1802.09568","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:e1d9c4b3cbe43ed72fa9acd0f1e9bf05434a63a8ad6233ed3920f6ce2b6c26d2","observation_id":"ca8b3c90-6e90-44b3-b0ee-e77d537ca140","resolution":{"observed_at":"2026-05-12T06:01:26.324437Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2511.20626","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T16:38:41.039569Z","title":"arXiv preprint arXiv:2511.20626 , year=","venue":null,"work_id":"ba262780-00f3-4016-9a23-e030aba1d13d","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:ff280a9848a0c437bdb2babf84332409b99df3c1ff6413c4ac6892056e517fc7","observation_id":"aab4b2e2-d315-4b82-935b-1ec91e011771","resolution":{"observed_at":"2026-05-12T06:01:26.396409Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1703.00887","last_updated":"2017-03-02T18:35:24Z","snapshot_observed_at":"2026-07-06T05:32:08.391642Z","submitted_at":"2017-03-02T18:35:24Z","title":"How to Escape Saddle Points Efficiently","version":1},"cited_work":{"arxiv_id":"1703.00887","doi":null,"metadata_source":"pith","pith_arxiv_id":"1703.00887","snapshot_observed_at":"2026-07-04T14:49:54.831935Z","title":"How to Escape Saddle Points Efficiently","venue":"cs.LG","work_id":"ae5d890b-373d-496d-83d3-15c57e63af9c","year":2017},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1703.00887","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:ae146d8d10bfc5a986f48acaae869f17607a1af357c1c4f2a17487b99e526035","observation_id":"16620d68-01b8-46f6-8c52-e69ab571c383","resolution":{"observed_at":"2026-05-12T06:01:26.483521Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-07-10T02:06:42.431452Z","title":"Muon: An optimizer for hidden layers in neural networks","venue":null,"work_id":"92f732c8-b19c-4c2c-8d8d-be2096093467","year":2024},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:adcfb558601dd55e4935448d4248b391d661720e006b3a6db3e83e98ba834549","observation_id":"a6d9215a-7f7c-495a-b5ac-c199a1fa8e20","resolution":{"observed_at":"2026-05-12T14:11:37.254340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2001.08361","last_updated":"2020-01-23T03:59:20Z","snapshot_observed_at":"2026-07-06T08:52:12.656082Z","submitted_at":"2020-01-23T03:59:20Z","title":"Scaling Laws for Neural Language Models","version":1},"cited_work":{"arxiv_id":"2001.08361","doi":"10.1145/3616855.3635845","metadata_source":"pith","pith_arxiv_id":"2001.08361","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Scaling Laws for Neural Language Models","venue":"cs.LG","work_id":"b7dd8749-9c45-4977-ab9b-64478dce1ae8","year":2020},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2001.08361","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:8e1c8b2c2bb47d6666692d074825b70336e180796b32fcd2636f8140ae86af40","observation_id":"3f3b7c94-a42a-4c64-85cb-9505c0e3b736","resolution":{"observed_at":"2026-05-12T06:01:26.443101Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"The isotropic semicircle law and deformation of wigner matrices","venue":null,"work_id":"7c03d774-2918-4c92-917b-00b63f8bd256","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:b822b34ef2f3eb4bcfa1daa4a4186dcd32b85fbad00fc1f24b42b45509ad6295","observation_id":"739cf1f6-369e-41e5-ae5c-36893d148efd","resolution":{"observed_at":"2026-05-12T14:11:37.257018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1110.6449","last_updated":"2012-05-22T18:31:00Z","snapshot_observed_at":"2026-07-06T02:36:36.820418Z","submitted_at":"2011-10-28T20:02:15Z","title":"The Isotropic Semicircle Law and Deformation of Wigner Matrices","version":2},"cited_work":{"arxiv_id":"1110.6449","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1110.6449","snapshot_observed_at":"2026-07-04T18:06:30.586525Z","title":null,"venue":null,"work_id":"f7d4036d-496f-43af-8bc8-37b0c75f67e6","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1110.6449","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:1751dfa162601406270836f6d5b5455f3253ed7edbe3973873fc7bbdc634fdea","observation_id":"479b4d0b-e687-4e18-b49e-6b1dc2190a98","resolution":{"observed_at":"2026-07-04T18:06:30.586525Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.12645","last_updated":"2025-04-08T16:47:42Z","snapshot_observed_at":"2026-07-06T20:53:31.919637Z","submitted_at":"2025-03-16T20:49:34Z","title":"Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization","version":2},"cited_work":{"arxiv_id":"2503.12645","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2503.12645","snapshot_observed_at":"2026-07-04T07:29:38.574824Z","title":"arXiv preprint arXiv:2503.12645 , year=","venue":null,"work_id":"fe62cb1b-f9dc-4379-8586-5c2f591ba7e5","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2503.12645","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:1e095e5b1a0aff99d41e8fb01a4195e9689c8df9ead4fa266f3a613e1460231e","observation_id":"c5e23c37-b1b4-4987-a14c-ec5eacfec255","resolution":{"observed_at":"2026-05-12T06:01:26.384083Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2602.05725","last_updated":"2026-06-03T16:40:26Z","snapshot_observed_at":"2026-08-03T04:14:09.367178Z","submitted_at":"2026-02-05T14:49:40Z","title":"Muon in Associative Memory Learning: Training Dynamics and Scaling Laws","version":3},"cited_work":{"arxiv_id":"2602.05725","doi":null,"metadata_source":"pith","pith_arxiv_id":"2602.05725","snapshot_observed_at":"2026-07-02T07:16:44.437267Z","title":"Muon in associative memory learning: Training dynamics and scaling laws","venue":"cs.LG","work_id":"9c07bb03-2084-4fb4-9d9a-1aa47375851d","year":2026},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2602.05725","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:defe6759b63f17364dd02d6ee41b3086a881e0a82afc9c34150c1e59bbfb902a","observation_id":"7feb29eb-f14a-45c4-ab4a-acfd356b6c2e","resolution":{"observed_at":"2026-05-26T03:04:11.161880Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.16982","last_updated":"2025-02-24T09:12:29Z","snapshot_observed_at":"2026-08-02T00:32:51.000665Z","submitted_at":"2025-02-24T09:12:29Z","title":"Muon is Scalable for LLM Training","version":1},"cited_work":{"arxiv_id":"2502.16982","doi":"10.48550/arxiv.2502.16982","metadata_source":"pith","pith_arxiv_id":"2502.16982","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Muon is Scalable for LLM Training","venue":"cs.LG","work_id":"a818f37a-b985-49e6-879d-603a00525f65","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2502.16982","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:cd0dd62816b63071135305fb772b479cbcd48125717871b240fa3c7734b902f7","observation_id":"cd84be3b-6c64-4028-b4bf-6b52a458b634","resolution":{"observed_at":"2026-05-12T06:01:26.345270Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Specinfer: Ac- celerating generative llm serving with speculative inference and token tree verification","venue":null,"work_id":"03b26643-f34f-428b-9d96-0e3e4027f8b7","year":2023},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:fd85872c1fd26440ec1e8faf7743bf38aa7cafe3a6f4295557565f7ed93b35fc","observation_id":"7de2fc96-f8da-428e-b62c-8c049a6c9e6d","resolution":{"observed_at":"2026-05-12T14:11:37.262835Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1706.07993","last_updated":"2018-10-08T17:09:35Z","snapshot_observed_at":"2026-07-06T05:48:16.374831Z","submitted_at":"2017-06-24T19:06:54Z","title":"Behavior of Accelerated Gradient Methods Near Critical Points of Nonconvex Functions","version":3},"cited_work":{"arxiv_id":"1706.07993","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1706.07993","snapshot_observed_at":"2026-07-04T23:06:18.256341Z","title":null,"venue":null,"work_id":"655b8da2-09fd-46b7-a833-a7335badff0b","year":2018},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1706.07993","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:1ffb85611410f4b1e2a75cbcdb33c91f71737a7f847002361df0eeb2706beb09","observation_id":"a2a717b1-2f1d-4543-ac23-d247d64e2d64","resolution":{"observed_at":"2026-07-04T23:06:18.256341Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Large-scale distributed second-order optimization using kronecker-factored approximate cur- vature for deep convolutional neural networks","venue":null,"work_id":"3c783618-c1d6-48fd-9c00-84af0b1d3bba","year":2019},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:53512d3335d617a60f56c97963da8ed65c8d5b742eebca854b99492964b6d0e5","observation_id":"31d05a58-e970-4715-baff-0ad003873fe2","resolution":{"observed_at":"2026-05-12T14:11:37.271341Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"stable/2430769","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Asymptotics of sample eigenstructure for a large dimensional spiked covariance model.Statistica Sinica, 17(4):1617–1642","venue":null,"work_id":"303f3517-afd6-45a2-ae86-c55fa0b86f7d","year":2007},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:0adc76bcd8098b3604ca1f49cf8f950babe2a78864d4fd925fc2346b3ea39779","observation_id":"aa298b80-d942-45f0-b8a6-06136e6156e7","resolution":{"observed_at":"2026-05-12T06:01:26.317345Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.17557","last_updated":"2024-10-31T11:37:49Z","snapshot_observed_at":"2026-08-02T15:25:02.551919Z","submitted_at":"2024-06-25T13:50:56Z","title":"The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale","version":2},"cited_work":{"arxiv_id":"2406.17557","doi":"10.48550/arxiv.2406.17557","metadata_source":"pith","pith_arxiv_id":"2406.17557","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale","venue":"cs.CL","work_id":"1ac90585-1330-4f90-8836-6382fa63c4eb","year":2024},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2406.17557","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:92b7b42f18caa08d61a3f51d221a3839f235036465b7d6589309c967f7b998fc","observation_id":"61b32963-0f94-40a8-898c-80f337a1b65e","resolution":{"observed_at":"2026-05-13T04:36:45.776658Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Geometry of neural network loss surfaces via random matrix theory","venue":null,"work_id":"7cea7e21-2f8d-4835-be0e-793668054407","year":2017},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:13765ad9da907e461f2c81348761465fa850aee3e4bed1f6ff958b478923cb2a","observation_id":"9d6fecd1-0225-47fd-94ff-0578a4537e20","resolution":{"observed_at":"2026-05-12T14:11:37.279576Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1709.01434","last_updated":"2017-09-05T14:58:15Z","snapshot_observed_at":"2026-07-06T05:58:12.969533Z","submitted_at":"2017-09-05T14:58:15Z","title":"A Generic Approach for Escaping Saddle points","version":1},"cited_work":{"arxiv_id":"1709.01434","doi":null,"metadata_source":"pith","pith_arxiv_id":"1709.01434","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A Generic Approach for Escaping Saddle points","venue":"cs.LG","work_id":"42a079bc-31ac-452f-8027-eceda8b5fe9a","year":2017},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1709.01434","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:ae7ded0275c9ee2d30885678369c1b2668f9443ce9538d0637e2c06413c81eec","observation_id":"56ac1282-7192-403b-873c-dbd8f6d51870","resolution":{"observed_at":"2026-05-12T06:01:26.374440Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1306.2872","last_updated":"2013-10-01T17:09:19Z","snapshot_observed_at":"2026-07-06T03:15:42.389331Z","submitted_at":"2013-06-12T15:54:52Z","title":"Hanson-Wright inequality and sub-gaussian concentration","version":3},"cited_work":{"arxiv_id":"1306.2872","doi":null,"metadata_source":"pith","pith_arxiv_id":"1306.2872","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hanson-Wright inequality and sub-gaussian concentration","venue":"math.PR","work_id":"ecbcf384-6597-462b-9527-e263946b4cf7","year":2013},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1306.2872","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:d71f7ad814d23f5545d1ca9a634cf6fe4af56db2add153c5bc4f16371ecf896d","observation_id":"19947cad-324d-49cc-9d1d-06ad9cbeece0","resolution":{"observed_at":"2026-05-12T06:01:26.400049Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.09149","last_updated":"2020-02-03T18:39:59Z","snapshot_observed_at":"2026-07-30T21:43:30.917305Z","submitted_at":"2019-01-26T03:12:14Z","title":"Escaping Saddle Points with Adaptive Gradient Methods","version":2},"cited_work":{"arxiv_id":"1901.09149","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1901.09149","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:1901.09149 , year=","venue":null,"work_id":"2d5767b1-8c2f-4ca8-be4a-956af828c0bd","year":1901},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1901.09149","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:268439c8523d4530985c0904f9873c42083427fe982f1655ebf533ee092d4fe1","observation_id":"0c29467b-652e-436e-9146-ef5df46b6b30","resolution":{"observed_at":"2026-05-12T06:01:26.466683Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.07491","last_updated":"2025-06-23T13:45:50Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-04-10T06:48:26Z","title":"Kimi-VL Technical Report","version":3},"cited_work":{"arxiv_id":"2504.07491","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.07491","snapshot_observed_at":"2026-07-08T06:34:41.884360Z","title":"Kimi-VL Technical Report","venue":"cs.CV","work_id":"c876520f-8a20-44f3-b92a-bf7d35bd430f","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2504.07491","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:2977d75547161ce6c3a0a286295e24bc7ccd17db8cc79309a314e496b1e555ea","observation_id":"44c20eae-566d-41b6-a340-09f19488e962","resolution":{"observed_at":"2026-05-12T06:01:26.439415Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.13971","last_updated":"2023-02-27T17:11:15Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2023-02-27T17:11:15Z","title":"LLaMA: Open and Efficient Foundation Language Models","version":1},"cited_work":{"arxiv_id":"2302.13971","doi":"10.48550/arxiv.2302.13971","metadata_source":"pith","pith_arxiv_id":"2302.13971","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"LLaMA: Open and Efficient Foundation Language Models","venue":"cs.CL","work_id":"c018fc23-6f3f-4035-9d02-28a2173b2b9d","year":2023},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2302.13971","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:0627d4474c5d41a4b47448b9425c80852d1137b0ecbf654332996104b3884f72","observation_id":"c6e98094-9d31-4e2d-9bd8-b66ef739dd97","resolution":{"observed_at":"2026-05-12T06:01:26.361365Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-01T11:08:05.851253+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-01T11:08:05.851253+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/25-aos2582","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Analysis of singular subspaces under random perturbations.The Annals of Statistics, 54(2):667 – 691","venue":"The Annals of Statistics","work_id":"3c849394-9c4f-4dd5-9048-92fcb6304bdf","year":2026},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:c28dc02799929253507fa2586d7a852da7914a1d23dabf9a9b7eff36aa66e811","observation_id":"5ef40fd0-929c-459c-beb5-8f91b85b802c","resolution":{"observed_at":"2026-05-12T04:41:20.585383Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2509.26030","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T06:29:38.185587Z","title":"Muon outperforms adam in tail-end associative memory learning","venue":null,"work_id":"557e3d1a-f8b7-4fbe-9dc8-9432aa0bb507","year":2025},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:373d095c7c9dafe6e04ce32cfa1223979bc999532028940d3896790e185aff69","observation_id":"1f869155-3ee0-4605-b58b-c7316c105ac5","resolution":{"observed_at":"2026-05-12T06:01:26.474432Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.03495","last_updated":"2021-01-15T14:57:46Z","snapshot_observed_at":"2026-07-06T08:55:58.482745Z","submitted_at":"2020-02-10T02:04:49Z","title":"A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima","version":14},"cited_work":{"arxiv_id":"2002.03495","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.03495","snapshot_observed_at":"2026-07-02T16:47:10.361461Z","title":"A diffusion theory for deep learning dynamics: Stochastic gradient descent exponentially favors flat minima","venue":null,"work_id":"1c1ac655-d127-43e9-ab9c-a16d9c68df53","year":2002},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2002.03495","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:a954fc74c8cc8c26f91e0be50a55450f2d26582206c28fc2bec046c0ea678b1c","observation_id":"a73c2707-3f8c-4199-a448-fc8893299004","resolution":{"observed_at":"2026-05-12T06:01:26.388383Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.15815","last_updated":"2022-06-14T15:25:21Z","snapshot_observed_at":"2026-07-06T09:33:32.306176Z","submitted_at":"2020-06-29T05:21:02Z","title":"Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum","version":11},"cited_work":{"arxiv_id":"2006.15815","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2006.15815","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Adaptive inertia: Disentangling the effects of adaptive learning rate and momentum","venue":null,"work_id":"6f3920e8-40dc-4a68-8055-1fd6e6ca0950","year":2022},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2006.15815","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:e88d178c3e98ad99ea8f7dbe8d35cec68f78c5b76bbc8e270c85924fc6fbb9f1","observation_id":"d9f5da7a-132f-4dd7-a240-c2b0d449895f","resolution":{"observed_at":"2026-05-12T06:01:26.462784Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.17182","last_updated":"2022-08-30T13:14:57Z","snapshot_observed_at":"2026-07-06T10:55:22.506340Z","submitted_at":"2021-03-31T16:08:06Z","title":"Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization","version":5},"cited_work":{"arxiv_id":"2103.17182","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2103.17182","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Positive-negative momen- tum: Manipulating stochastic gradient noise to improve generalization","venue":null,"work_id":"6ecb704f-b011-404e-908b-4d806bba2569","year":2022},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2103.17182","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:ea9df70b408d80b2b49737eef52c9ae35692b765e9b948a90013fd89208ef33c","observation_id":"f1281a6f-6027-4366-b9d4-6ead6757ef18","resolution":{"observed_at":"2026-05-12T06:01:26.470681Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.02083","last_updated":"2023-10-20T11:29:13Z","snapshot_observed_at":"2026-07-06T14:26:48.098982Z","submitted_at":"2022-12-05T07:55:22Z","title":"On the Overlooked Structure of Stochastic Gradients","version":3},"cited_work":{"arxiv_id":"2212.02083","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2212.02083","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the overlooked structure of stochastic gradients","venue":null,"work_id":"d34b3357-ffd0-4b56-a67c-16b6cf542034","year":2023},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/2212.02083","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:97e8626d37b42b0caff116b9c214bfe5c6e5efd61eb57acbc3ab48c798d8fbe5","observation_id":"00b8f7d7-5b24-4c4a-b031-4c5b8d6ef34e","resolution":{"observed_at":"2026-05-12T06:01:26.392329Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.03096","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T14:29:54.488148Z","title":"Prism: Structured optimization via anisotropic spectral shaping","venue":null,"work_id":"9c0a8e9e-d387-4786-9ed4-1c5fc9c69a9b","year":2026},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:349084d23167cd2d8da19839699cb21e15dfc1a3ebc45c367af2f4a0fbeab87c","observation_id":"11669c50-0a47-4b36-8474-1d3be3fd0604","resolution":{"observed_at":"2026-05-12T06:01:26.432115Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2603.09697","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T16:38:41.010083Z","title":"arXiv preprint arXiv:2603.09697 , year=","venue":null,"work_id":"8801f6cb-07ef-4ae8-b042-1634e9db582d","year":2026},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:a3de2bdf9d711f037bcf4723bc1ec629db7946a4ebc63ad711973379d91be9b6","observation_id":"3d435b8b-b38b-4b2d-a19f-3d5128be4c08","resolution":{"observed_at":"2026-05-12T06:01:26.454031Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.07811","last_updated":"2020-10-19T06:09:39Z","snapshot_observed_at":"2026-08-04T23:49:19.065149Z","submitted_at":"2018-06-20T16:01:09Z","title":"Stochastic Nested Variance Reduction for Nonconvex Optimization","version":2},"cited_work":{"arxiv_id":"1806.07811","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1806.07811","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Stochastic nested variance reduction for nonconvex optimization","venue":null,"work_id":"ff1a8d53-bd48-48d7-b236-252c5a1b2bbd","year":2020},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1806.07811","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:8f88ec2b3fe32da90e3d536361a7041b42815a11162777e04cec6e436fd74638","observation_id":"c2cc530e-7c23-4149-ae60-1706e36e6dfc","resolution":{"observed_at":"2026-05-12T06:01:26.478380Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1803.00195","last_updated":"2019-06-10T05:19:32Z","snapshot_observed_at":"2026-07-06T06:26:01.372123Z","submitted_at":"2018-03-01T03:46:36Z","title":"The Anisotropic Noise in Stochastic Gradient Descent: Its Behavior of Escaping from Sharp Minima and Regularization Effects","version":5},"cited_work":{"arxiv_id":"1803.00195","doi":null,"metadata_source":"pith","pith_arxiv_id":"1803.00195","snapshot_observed_at":"2026-07-02T16:47:10.364915Z","title":"The Anisotropic Noise in Stochastic Gradient Descent: Its Behavior of Escaping from Sharp Minima and Regularization Effects","venue":"stat.ML","work_id":"e1f822fa-3518-4f82-b201-a70139abf79d","year":2018},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"cited_paper":"/paper/1803.00195","citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:d6554c092eb073c8cb70a5004b161613477226b9caf5bf0a25eb8754af25ad04","observation_id":"f3863c38-a9a1-4abd-ac77-65079a2daf25","resolution":{"observed_at":"2026-05-12T06:01:26.335370Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"50b6a9b9-a903-47b2-a8bf-8d014c2fa4a9","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:efe083e9f68712ca1347cbe48fc70ea91c9d6c6670e4691a2f18f8068b1e38ba","observation_id":"f03697e6-b4f6-4bb5-bbac-7de47b00768e","resolution":{"observed_at":"2026-05-12T14:11:37.268417Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"59c812e8-120c-442b-b4ee-abb2d0c40065","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:9ec17d4bc5843c9911d11437d273ed1166b1191319a04f37ab86fbe965c55748","observation_id":"56434c55-76c6-4e75-a239-e46055769c5c","resolution":{"observed_at":"2026-05-12T14:11:37.274459Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"born locked","venue":null,"work_id":"99550e48-a2ff-4e2e-8e5a-854d9d1582b4","year":2052},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:f58742d08b551dbcc5332953bea1009e0c7e774e5e62519d50151ff3ed5b8a79","observation_id":"3d9fbb5c-2f79-4eff-a196-b15a5e5faeff","resolution":{"observed_at":"2026-05-12T14:11:37.259965Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a7ff6e52-fb38-4f22-a876-5a2629d09c9b","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:cea34f3504e036ddcec74dbce3b85e6229f5440ea765b9080f561a02317f647c","observation_id":"13d255e9-8c74-478d-98fa-b9bc50284aa4","resolution":{"observed_at":"2026-05-12T14:11:37.251525Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Spike Range","venue":null,"work_id":"45a50d4a-dfab-49db-85b4-f41195dd6d57","year":null},"citing_paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-12T04:38:25.480020Z"},"links":{"citing_paper":"/paper/2605.09331"},"observation_digest":"sha256:605dd066a298e8dd2e23cae9678c7807187b4cb861a8d275b66476afe6516647","observation_id":"f68ea294-c385-4453-a800-bc78fb1a9fe8","resolution":{"observed_at":"2026-05-12T14:11:37.277025Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.09331","last_updated":"2026-05-10T05:06:07Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T23:21:26.017420Z","submitted_at":"2026-05-10T05:06:07Z","title":"Dimension-Free Saddle-Point Escape in Muon"},"reference_resolution":{"displayed":47,"state_counts":{"malformed_identifier":1,"metadata_mismatch":9,"parse_uncertain":0,"unresolved":3,"verified_exact":26,"verified_fuzzy":8},"total_outbound_references":47},"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":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"thesis":"As of 5 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2605.09331."}