{"as_of":"2026-08-23T09:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9a1e017141254469356d3ae3ed8e2046b575cf1f88aa092ba49c2fc8122ecfd6","coverage":[{"denominator":194,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:05:46.090449Z","state":"measured"},{"denominator":100,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":100,"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/2608.04607/citation-record","integrity":"/paper/2608.04607/integrity","json":"/paper/2608.04607/citation-record.json","paper":"/paper/2608.04607"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2022.10164","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:47.178590Z","title":null,"venue":null,"work_id":"7e51d1ac-6b32-44a8-a532-af95e10c797a","year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.487584Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:ec0fce9e7b8f1cc478c85ae09d40380cba5a93dbb71f299310fd340ef336e43e","observation_id":"ef6edf53-fda0-45ea-9978-63c767d65255","resolution":{"observed_at":"2026-08-06T21:05:47.182646Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2026-08-06T21:05:39.532312Z","title":"2004 , PAGES =","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.532312Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:a9c65e67764fe12fd2056b09f611c70064afadc1be37fdcb02a3f54410a332ec","observation_id":"b624f69a-1bb4-409b-97cf-b3f04937c1a4","resolution":{"observed_at":"2026-08-06T21:05:39.532312Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:39.577389Z","title":"Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.577389Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:bedabbd9c6b64514b2a74e28b456e95d7d0423de52bb5f9fec5083fc38d62baf","observation_id":"134d5db5-0b63-4047-8621-722da46f0be7","resolution":{"observed_at":"2026-08-06T21:05:39.577389Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:39.642280Z","title":"Proceedings of The 33rd International Conference on Machine Learning , pages =","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.642280Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:268461a1675e28eb8d914f9b4fda06ca7502d00c7f06e594db39d392c2b6888e","observation_id":"f8d873f7-d16f-4a4c-a2aa-f9cc50d36565","resolution":{"observed_at":"2026-08-06T21:05:39.642280Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:39.697384Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.697384Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:e54bd1e8045771bb239d247ad748d17755d049148071a385caf24a455e1fc252","observation_id":"4ef98015-5e69-488b-8d77-f8e631eff3b8","resolution":{"observed_at":"2026-08-06T21:05:39.697384Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:39.823264Z","title":", TITLE =","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.823264Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:962dc8af5f7a442fc0fff4a06e4316ba51859716b286e941dae64988f4b219ea","observation_id":"1312d9bd-551b-4585-a375-9ede570d4a15","resolution":{"observed_at":"2026-08-06T21:05:39.823264Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:39.937152Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:39.937152Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:01274060928be7a9def94340dc0814b2a8f641d785d3555cdc81dca00cf8669d","observation_id":"224299ec-4c6a-44d9-93b9-b35e09640b81","resolution":{"observed_at":"2026-08-06T21:05:39.937152Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:40.050699Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.050699Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:08f29d5589c859ed4eb94f8877a31ebd9ab9a92a87fc9bc6fba194d445e2411b","observation_id":"4f23f5a6-4181-4e61-b114-43e7d881a5a5","resolution":{"observed_at":"2026-08-06T21:05:40.050699Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:40.134339Z","title":"Gentile and G","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.134339Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:bd052527ff2b7ec78514ab6b364aa3edd3445ccf5a21e5c5616829ece61311ff","observation_id":"30d6ef36-4bd3-416e-8fef-9b5864376c66","resolution":{"observed_at":"2026-08-06T21:05:40.134339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:40.267507Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.267507Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:efaa8d1b1ecb976455f4dfe1d36a836eb5de365dba952e0dd2ce11089f17d098","observation_id":"8da74a58-16f5-4c09-acc9-e495482ce73f","resolution":{"observed_at":"2026-08-06T21:05:40.267507Z","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":"2022.12660","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:47.101548Z","title":null,"venue":null,"work_id":"ed739a8a-e6b4-4893-8f86-818f6f671685","year":2023},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.396074Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:83b14430e91699795ddeef8b7061d5a2c4ea876afce87f18ad6a6f112c398505","observation_id":"16214046-2fe2-4cbc-b650-3f503ab17333","resolution":{"observed_at":"2026-08-06T21:05:47.106966Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"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":"2026-08-06T21:05:40.494251Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.494251Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:37405de4d7b5da91de616e85bc21743468be1e7b77b239bd54d41ead6d82b3ef","observation_id":"bb6a8790-928b-4025-a6c3-bbe5c28bf8b6","resolution":{"observed_at":"2026-08-06T21:05:40.494251Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:40.594667Z","title":"2017 , journal=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.594667Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:0d1c4ed073e18e3bb3d8ce072589533ce28b8def95753e4000845537d31215ef","observation_id":"ed335e24-56d7-4d00-9861-f5ee21770522","resolution":{"observed_at":"2026-08-06T21:05:40.594667Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:40.713091Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.713091Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:03d76f0dba50af7930c51fca6edecda4287c74894c2003d2f6881f93d71b6f9e","observation_id":"327c2b1a-dbf3-4884-b3cb-c3f6bba4997d","resolution":{"observed_at":"2026-08-06T21:05:40.713091Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:40.786196Z","title":"CSIAM Trans","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.786196Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:de0bd3f5e66ecde709604ced84d62aa7f749c79ced62f7978eae65967a7ef9f3","observation_id":"ee12193e-b86a-4d72-ab2e-bc274d84be74","resolution":{"observed_at":"2026-08-06T21:05:40.786196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00332-022-09823-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":null,"venue":"Journal of Nonlinear Science","work_id":"259e5097-5aec-40a8-9654-5f448fc99210","year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.900443Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:c31fb9d88756afef164673ef484cf60769a2b6a40c49792d1ba2eddc7b468e09","observation_id":"a7b50bf9-6316-4f9c-84e2-93ff68667936","resolution":{"observed_at":"2026-08-06T21:05:46.595743Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s40072-018-0116-y","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Exponential moments for numerical approximations of stochastic partial differential equations , JOURNAL =","venue":"Stochastic Partial Differential Equations Analysis and Computations","work_id":"fcc62db3-05d9-4520-8b26-4f71f8c19479","year":2018},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:40.962750Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:05d1d490ac403e79bbb469382c4a0b98d12854ab9e3536070ae2f443740b18cc","observation_id":"593ea46f-cbb8-4e5f-af11-d7e9b6f8bee6","resolution":{"observed_at":"2026-08-06T21:05:46.587933Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:41.097918Z","title":"2018 , eprint =","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:41.097918Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:061b518edb6d701957da9f4ba8d713c530533bdd5ce157e0068b8e6c1530c9f8","observation_id":"2da89d06-2b19-449c-a597-283623b74d1a","resolution":{"observed_at":"2026-08-06T21:05:41.097918Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1911.05620","last_updated":"2020-05-09T12:45:34Z","snapshot_observed_at":"2026-08-19T15:25:43.953147Z","submitted_at":"2019-11-13T17:01:36Z","title":"Neural networks for option pricing and hedging: a literature review","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1911.05620","snapshot_observed_at":"2026-08-06T21:05:41.250713Z","title":"arXiv:1911.05620 , archivePrefix =","venue":null,"work_id":null,"year":1911},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:41.250713Z"},"links":{"cited_paper":"/paper/1911.05620","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:dea509399f3f6f09670eb620e81f0166be0b0c4acd1df3859b29e824086925b8","observation_id":"ffb6ad7e-2edc-4f7b-9163-7a00721045e7","resolution":{"observed_at":"2026-08-06T21:05:41.250713Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-08-17T19:26:44.032537Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-06T21:05:42.628437Z","title":"Kingma and Jimmy Ba , year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:42.628437Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:2d7dcc2ae1cf61a794a6363525eba97f3254d1881f29a92f9d96f7746451327b","observation_id":"78ce05b8-9535-402a-804d-8c431dc2c420","resolution":{"observed_at":"2026-08-06T21:05:42.628437Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:43.139730Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.139730Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:9ad81c8e0ccce0159f54d30f5493aebfd3bf14cbf0c30ca9ee8bf38a8b3cb9c3","observation_id":"cd80d5b8-57dd-44ca-adc9-7fc222db7b4f","resolution":{"observed_at":"2026-08-06T21:05:43.139730Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.05155","last_updated":"2024-02-07T16:14:04Z","snapshot_observed_at":"2026-08-16T14:20:32.593954Z","submitted_at":"2024-02-07T16:14:04Z","title":"Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.05155","snapshot_observed_at":"2026-08-06T21:05:43.250760Z","title":"2402.05155 , archivePrefix=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.250760Z"},"links":{"cited_paper":"/paper/2402.05155","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:09e05974f3d7217b6464f5e73d35344c5483ff7a88444aed283b1a53ed6e2e1f","observation_id":"8a3224f1-d351-424e-8e55-7363201d016e","resolution":{"observed_at":"2026-08-06T21:05:43.250760Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:43.346829Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.346829Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:203e4f6df4f6dca45af3764cbb764c2148ddfe6126d517b4a291fd8550347efd","observation_id":"132d91df-9950-404e-997d-bbc318e8394a","resolution":{"observed_at":"2026-08-06T21:05:43.346829Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:43.432600Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.432600Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:8a6e96c226d0f1672d9bc72e5e609f4d0bee8b28d63d9ac9171ceffca61d87fe","observation_id":"f525b4c9-1aaa-435c-a322-f04803bfed8f","resolution":{"observed_at":"2026-08-06T21:05:43.432600Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:43.563926Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.563926Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:c6d2fdcff49c495bc3e8c6cb9200520724c9aa77e37f14a9736c537213a1561e","observation_id":"618d0095-64f3-47ba-a213-f06f08a17459","resolution":{"observed_at":"2026-08-06T21:05:43.563926Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.09358","last_updated":"2019-06-25T03:39:53Z","snapshot_observed_at":"2026-08-21T02:46:21.146100Z","submitted_at":"2018-11-23T04:26:47Z","title":"A Sufficient Condition for Convergences of Adam and RMSProp","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.09358","snapshot_observed_at":"2026-08-06T21:05:43.639872Z","title":"arXiv:1811.09358 , archivePrefix =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.639872Z"},"links":{"cited_paper":"/paper/1811.09358","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:ec231b4441d57a739fd1c0f0be185eac69a8a0d5530545739d717da2da686913","observation_id":"cd88d311-e2a6-44b7-84db-52eb666fc825","resolution":{"observed_at":"2026-08-06T21:05:43.639872Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.09632","last_updated":"2023-01-13T15:06:19Z","snapshot_observed_at":"2026-08-21T02:47:26.917659Z","submitted_at":"2022-08-20T08:12:37Z","title":"Adam Can Converge Without Any Modification On Update Rules","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.09632","snapshot_observed_at":"2026-08-06T21:05:43.655554Z","title":"arXiv:2208.09632 , archivePrefix =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.655554Z"},"links":{"cited_paper":"/paper/2208.09632","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:44d62e86523f22a453d24f7255dfb3253bb32e0b59fbf639e62d62f9055042d9","observation_id":"916294df-843c-4430-9434-fcfc2c38a0e0","resolution":{"observed_at":"2026-08-06T21:05:43.655554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07468","last_updated":"2020-12-20T22:30:36Z","snapshot_observed_at":"2026-08-20T23:40:08.913755Z","submitted_at":"2020-10-15T01:46:13Z","title":"AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07468","snapshot_observed_at":"2026-08-06T21:05:43.773193Z","title":"Duncan , year =","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.773193Z"},"links":{"cited_paper":"/paper/2010.07468","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:b9c51c01c850d16bd09c4e10c83af77dced40fc54a6876a8d9c97f013d6e83fc","observation_id":"9cf9df23-533e-4f94-b992-f2e69b06af43","resolution":{"observed_at":"2026-08-06T21:05:43.773193Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1111/mafi.12405","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Learning the random variables in","venue":"Mathematical Finance","work_id":"2cc93d97-6c3f-4245-8baa-d018b79ef621","year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.876268Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:e3a83bc5044d9abb093e9b94331d0b29ce18f4c976f389f5dc878067f0547714","observation_id":"c65fb4bf-89cf-4e7c-8d96-7de56644c7cc","resolution":{"observed_at":"2026-08-06T21:05:46.574752Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:43.978764Z","title":"IEEE Trans","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:43.978764Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:4919aa3a67fe1fc53f2ea215245e2a7163ed7aad2e1a7d989f6044d20a8eca1a","observation_id":"cda10e05-bbf7-461a-b47d-f937ebf221fa","resolution":{"observed_at":"2026-08-06T21:05:43.978764Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.02957","last_updated":"2019-05-08T08:38:30Z","snapshot_observed_at":"2026-08-14T16:35:39.161361Z","submitted_at":"2019-05-08T08:38:30Z","title":"SAdam: A Variant of Adam for Strongly Convex Functions","version":1},"cited_work":{"arxiv_id":"1905.02957","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.02957","snapshot_observed_at":"2026-08-06T21:05:46.851664Z","title":"SAdam: A Variant of Adam for Strongly Convex Functions","venue":"cs.LG","work_id":"123e975a-65ed-408e-b356-7f3cef70354e","year":2019},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.114584Z"},"links":{"cited_paper":"/paper/1905.02957","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:a8aea644b1ec73d1ed18090053c11403b9ec1cee4ac99c3ecd4734039324ce45","observation_id":"b3b74800-1914-4b02-8092-91d40ec6aa3f","resolution":{"observed_at":"2026-08-06T21:05:46.854531Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"1902.09843","last_updated":"2019-02-26T10:22:48Z","snapshot_observed_at":"2026-08-19T14:19:09.693041Z","submitted_at":"2019-02-26T10:22:48Z","title":"Adaptive Gradient Methods with Dynamic Bound of Learning Rate","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.09843","snapshot_observed_at":"2026-08-06T21:05:44.206473Z","title":"arXiv:1902.09843 , archivePrefix =","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.206473Z"},"links":{"cited_paper":"/paper/1902.09843","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:f913e5fb493a7d521fee6432baf6d6616f80a1d22aad3bfcd1e4ed61339d3f55","observation_id":"dd2838a0-3954-48f6-92aa-b270b4153fda","resolution":{"observed_at":"2026-08-06T21:05:44.206473Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2109.08282","last_updated":"2021-09-17T01:45:25Z","snapshot_observed_at":"2026-08-18T02:12:50.447344Z","submitted_at":"2021-09-17T01:45:25Z","title":"AdaLoss: A computationally-efficient and provably convergent adaptive gradient method","version":1},"cited_work":{"arxiv_id":"2109.08282","doi":null,"metadata_source":"pith","pith_arxiv_id":"2109.08282","snapshot_observed_at":"2026-08-06T21:05:46.832019Z","title":"AdaLoss: A computationally-efficient and provably convergent adaptive gradient method","venue":"stat.ML","work_id":"874f0942-f2d0-406a-98e2-a8fbb8763098","year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.297261Z"},"links":{"cited_paper":"/paper/2109.08282","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:fe8a0cffa3d8982635c861ab35f1cb4c286588486df8f0b7acc9410fd61cf4a3","observation_id":"4a427748-22ed-4098-910b-d3ec38d1d512","resolution":{"observed_at":"2026-08-06T21:05:46.835080Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"2312.15295","last_updated":"2023-12-23T16:32:29Z","snapshot_observed_at":"2026-08-20T16:29:28.337821Z","submitted_at":"2023-12-23T16:32:29Z","title":"AdamL: A fast adaptive gradient method incorporating loss function","version":1},"cited_work":{"arxiv_id":"2312.15295","doi":null,"metadata_source":"pith","pith_arxiv_id":"2312.15295","snapshot_observed_at":"2026-08-06T21:05:46.820965Z","title":"AdamL: A fast adaptive gradient method incorporating loss function","venue":"stat.ML","work_id":"d817e68b-3048-4d2d-94b1-88696001c73c","year":2023},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.401533Z"},"links":{"cited_paper":"/paper/2312.15295","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:01c7ff8c474baa4bb58ff9a8e48373dc600cfe690faf8bd5269ab0a2d450d637","observation_id":"c5a7f235-05fb-4d93-9277-1f554ca8c7d2","resolution":{"observed_at":"2026-08-06T21:05:46.824089Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"2011.02150","last_updated":"2020-11-04T06:39:44Z","snapshot_observed_at":"2026-08-23T08:37:03.694624Z","submitted_at":"2020-11-04T06:39:44Z","title":"EAdam Optimizer: How $\\epsilon$ Impact Adam","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2011.02150","snapshot_observed_at":"2026-08-06T21:05:44.491874Z","title":"arXiv:2011.02150 , archivePrefix =","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.491874Z"},"links":{"cited_paper":"/paper/2011.02150","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:54bced0bb779149e8c7663dc4270ae040f651a86ee882f80b4a1cd5668db8974","observation_id":"9074afea-ee3e-4338-b345-864366eec263","resolution":{"observed_at":"2026-08-06T21:05:44.491874Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:44.666983Z","title":"2017 , eprint=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.666983Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:4828cd152a32612b2f266878689bae2d67a4e6d92cce5df6b072e69e73012113","observation_id":"dbf6e088-0407-431f-aedd-bc40d64fc183","resolution":{"observed_at":"2026-08-06T21:05:44.666983Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/drz055","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"IMA J. Numer. Anal. , fjournal =. 2020 , abstract =","venue":"IMA Journal of Numerical Analysis","work_id":"5cea9df4-0e18-4022-b3e2-aa41ebdcdf86","year":2020},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.793316Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:0f5189729f4bc01cc4286a45257d7e23ca97db76de55a3246db465aae62402fd","observation_id":"52b803b2-b10c-4d3f-b041-941f7cae6726","resolution":{"observed_at":"2026-08-06T21:05:46.566861Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2303.08774","last_updated":"2024-03-04T06:01:33Z","snapshot_observed_at":"2026-08-17T09:58:46.058102Z","submitted_at":"2023-03-15T17:15:04Z","title":"GPT-4 Technical Report","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.08774","snapshot_observed_at":"2026-08-06T21:05:44.908911Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:44.908911Z"},"links":{"cited_paper":"/paper/2303.08774","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:1301016ee57697f6723a748442176146037e495514dd48564d3be20de21f07fe","observation_id":"4ac3128d-025b-41dc-96e4-2ef07b6eed7d","resolution":{"observed_at":"2026-08-06T21:05:44.908911Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.027669Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.027669Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:507dab2c6785578e0a66964f3d3dbd718bd3d9b9fd5ee5f12647ea454a674b2f","observation_id":"655bfaf9-48d4-4e3c-b307-b68f09496e54","resolution":{"observed_at":"2026-08-06T21:05:45.027669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.14165","last_updated":"2020-07-22T19:47:17Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2020-05-28T17:29:03Z","title":"Language Models are Few-Shot Learners","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.14165","snapshot_observed_at":"2026-08-06T21:05:45.159086Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.159086Z"},"links":{"cited_paper":"/paper/2005.14165","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:8fbd041fe4e16d1fc1a00484ab2db47dace656eff09e899ca79399294e501656","observation_id":"113350d9-4411-4d25-94cd-99b1f360fde8","resolution":{"observed_at":"2026-08-06T21:05:45.159086Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.257824Z","title":"2024 , eprint=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.257824Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:a6bb681d2002fc2e99e891ced3a84e4fa3ad3759ef068e0ed093ed27513a7c9b","observation_id":"3fef7b56-7cdb-44ce-be2e-17d1251ead28","resolution":{"observed_at":"2026-08-06T21:05:45.257824Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.417295Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.417295Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:79b5e8b55bacee9af7fdd85f2d96e9f9e5e1f5879d2aa96fcfe6b4ce5cdf1b1f","observation_id":"3e9058e8-f214-4ccc-bf0c-ff11b2e398c1","resolution":{"observed_at":"2026-08-06T21:05:45.417295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.09506","last_updated":"2021-05-20T04:14:55Z","snapshot_observed_at":"2026-08-16T18:23:30.323346Z","submitted_at":"2021-05-20T04:14:55Z","title":"Physics-informed neural networks (PINNs) for fluid mechanics: A review","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.09506","snapshot_observed_at":"2026-08-06T21:05:45.602889Z","title":"2105.09506 , archivePrefix=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.602889Z"},"links":{"cited_paper":"/paper/2105.09506","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:0e75b3fed36697533a3f8ba0ed9b06c379a92683b3e22add305443ad900a1b18","observation_id":"c21ec59b-74b9-4224-a17b-d2ef119b0399","resolution":{"observed_at":"2026-08-06T21:05:45.602889Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.755037Z","title":"2021 , eprint=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.755037Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:35e937416b09ef79a89bbda3d04292936683c399a6c62be5dc4bff737ad2ee36","observation_id":"271e7004-38ac-45c0-9d85-6f390262e10a","resolution":{"observed_at":"2026-08-06T21:05:45.755037Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.890701Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.890701Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:002ec6368ee8a6e6e0e1c1c727a25e298fc8ec3143997a95b885b0904b83a24f","observation_id":"28a00e1d-c232-43f6-ab35-fdf2c7069dac","resolution":{"observed_at":"2026-08-06T21:05:45.890701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/dcdsb.2022238","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Discrete Contin","venue":"Discrete and Continuous Dynamical Systems - B","work_id":"750fee2b-dca7-45d0-ba3a-31b0001378d9","year":2023},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.940791Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:0c3d4a657d73da078545be6155579d232d7cd16d25d4cbbe1f7357baf8ab972f","observation_id":"936873fd-e673-4463-b6ea-c41dc8bc6f04","resolution":{"observed_at":"2026-08-06T21:05:46.548865Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.945376Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.945376Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:b5742e6e11d0d13f80e14adf65a187bc66547dd2a1bdd63e63e356030f9b7d85","observation_id":"71ea76ee-ce58-4751-b697-a7c1c371dc23","resolution":{"observed_at":"2026-08-06T21:05:45.945376Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.952121Z","title":"2016 , eprint=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.952121Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:22991f662afb28a9a06f1ea16c733bfc9c1de937b064814aa227100626bbdefa","observation_id":"da743a29-7a52-40f8-8239-a373cb478296","resolution":{"observed_at":"2026-08-06T21:05:45.952121Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.954944Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.954944Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:cb1283093d0ee88575b6dcf61dc657fca3da183ffc3c1f8fe6cd1b81f5765ea0","observation_id":"b6ca29d9-bc46-4b86-82ec-7c7382548e95","resolution":{"observed_at":"2026-08-06T21:05:45.954944Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.957683Z","title":"and Perdikaris, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.957683Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:fd39c301fad3451911c5618abf1abcba4dd24d094dc84a7ae977b4e83b1f4126","observation_id":"db754b54-44f2-4b8a-9067-40dc487d7e42","resolution":{"observed_at":"2026-08-06T21:05:45.957683Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.960403Z","title":"2024 , eprint=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.960403Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:dcad282310ad8e36b29d8bbfefd1a2e52c311c0c3debbdf06fceb9df99ff17c3","observation_id":"dba54739-f6b2-4912-bd2c-1ad97020a6c8","resolution":{"observed_at":"2026-08-06T21:05:45.960403Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2102.12092","last_updated":"2021-02-26T23:26:05Z","snapshot_observed_at":"2026-07-06T10:44:09.403787Z","submitted_at":"2021-02-24T06:42:31Z","title":"Zero-Shot Text-to-Image Generation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2102.12092","snapshot_observed_at":"2026-08-06T21:05:45.963044Z","title":"2102.12092 , archivePrefix=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.963044Z"},"links":{"cited_paper":"/paper/2102.12092","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:5bc1fcc64f63160686b2e77dbaf0d358cb6b72bd568a93096f0ae6da608a1e3e","observation_id":"63e6af98-2245-4982-b6a8-789ff45f2788","resolution":{"observed_at":"2026-08-06T21:05:45.963044Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.966006Z","title":"Nonlinearity , FJOURNAL =","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.966006Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:fce181506e0c09b51d949d1b8ff45b9b9997492ce367834faa4722093d8922c3","observation_id":"a1a299e3-ad0f-45b5-b8ca-e7042b925e8c","resolution":{"observed_at":"2026-08-06T21:05:45.966006Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.968834Z","title":"(2004) , publisher=","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.968834Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:7ae184740ceaad0ecafedd7237793aaeeb57c13dcdea4e1499a620b69555bc82","observation_id":"3c4a2616-d829-4701-96e7-7f79aaba2d17","resolution":{"observed_at":"2026-08-06T21:05:45.968834Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.971779Z","title":"(2014), xii+638 , publisher=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.971779Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:0e57412bd648623ff7bd6349140bbeb18e4c649812a088d037bec8cf0cb15404","observation_id":"666d008b-54a2-4eea-8dbb-a83ba4ac4423","resolution":{"observed_at":"2026-08-06T21:05:45.971779Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.974277Z","title":"(2021), xii+946 , PAGES =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.974277Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:1eba94741459b800f17ad65143f9325a6d9ca4b9e4bb952dc57d7094f58c7d5c","observation_id":"3495882c-9527-4380-a56a-ec75828ea298","resolution":{"observed_at":"2026-08-06T21:05:45.974277Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.977230Z","title":"2012 , numpages =","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.977230Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:ed50f4594d102e593bfc7ede1c54422b1a365b8c739529825cd55b879e6a70bf","observation_id":"0c5e4bbb-4ab9-4a9c-863f-14ddacf91521","resolution":{"observed_at":"2026-08-06T21:05:45.977230Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.980040Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.980040Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:3676373e16eaf0583a7d58323357d5c3ae1f4e9b4f304e619f1cad96ac691989","observation_id":"05b3c1b1-c39b-4e39-999a-4887e28b5442","resolution":{"observed_at":"2026-08-06T21:05:45.980040Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.982716Z","title":"(2014), xviii+493 , PAGES =","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.982716Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:1c48d0473817ddc1e3b5324fae0078e4b99c69924ae760278a6299a8eb49b7f1","observation_id":"fde2b7ae-d8aa-4dca-af0c-4e7a4fd6aaa7","resolution":{"observed_at":"2026-08-06T21:05:45.982716Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.986570Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.986570Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:06784aecf275cdbfc28ba44c7cde6639937da272e72ec8b9a51665b315f69382","observation_id":"b05289f5-6412-4866-9761-f801d686ca29","resolution":{"observed_at":"2026-08-06T21:05:45.986570Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.989267Z","title":"and Lahiri, Soumendra N","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.989267Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:00fe60bd6b0c35691c7c10aa7fd7bc8d7e2690e12cc9293a1d733bf33763527a","observation_id":"4ce9fdcb-a434-450d-8e3f-46a0d6a9dfa0","resolution":{"observed_at":"2026-08-06T21:05:45.989267Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.991788Z","title":"Nature Reviews Physics , volume=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.991788Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:d6ea6212c9f6bbd479e2ad5037708c6e67ae81db72b7dfffe83b53ef7ca4d718","observation_id":"17b57d93-96c3-4f1f-89fd-609523e1efc1","resolution":{"observed_at":"2026-08-06T21:05:45.991788Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.994848Z","title":"European J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.994848Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:6154a752ada600a3bdbd95734e4036410f00b18684229476a329dc3d7ba8baad","observation_id":"5bbf577b-e4d6-4ea8-9ade-eb26d146b2a3","resolution":{"observed_at":"2026-08-06T21:05:45.994848Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:45.997845Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:45.997845Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:c62dbb093999ea5deb0e875fb58907147341c247d1981b79f4bdde6edfd271ec","observation_id":"5de6506a-a9bf-451c-8710-0f8a3eba76c3","resolution":{"observed_at":"2026-08-06T21:05:45.997845Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.000473Z","title":null,"venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.000473Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:cba47d0e769f2174e26a335bcaf27cb065fc5135fd43cd189034f2f4b4e371ef","observation_id":"3c19cc74-fb5f-496f-b65b-51ecc69aa5f1","resolution":{"observed_at":"2026-08-06T21:05:46.000473Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.003119Z","title":", TITLE =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.003119Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:53b552290ffe3b1f7709d29e2cfa07d451630d4dd57c0c9808628bed953e2967","observation_id":"a1d75aa5-d140-4b16-b7ff-85ae34942ced","resolution":{"observed_at":"2026-08-06T21:05:46.003119Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.005552Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.005552Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:d11a72806b43f2be6cc545ca9bcc66507ca3aba7758be27aa3f7d9303a62608a","observation_id":"680e00b8-0dea-4470-8857-a1d801fb1a4e","resolution":{"observed_at":"2026-08-06T21:05:46.005552Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/9781009028943.023","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"(2023), 426–452 , X=","venue":"Cambridge University Press eBooks","work_id":"c4b53919-491c-4f78-b874-df995c7b1bf7","year":2023},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.008274Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:441b7e2aee5e4a9e4a1474c5c920e0276884941437be970a45914478970cffee","observation_id":"ace1c0c9-e6ee-46fe-8608-0918f902d4ad","resolution":{"observed_at":"2026-08-06T21:05:46.490628Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.010931Z","title":"Optimization for deep learning: theory and algorithms , year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.010931Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:2ef3ba22e4d5374b81e74ba3655ac9b9c37288744fda08bf788fea807a2cda84","observation_id":"9b2be8f5-7ff3-4821-89f5-fa5b8b4b3d55","resolution":{"observed_at":"2026-08-06T21:05:46.010931Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.01370","last_updated":"2023-03-01T07:36:03Z","snapshot_observed_at":"2026-08-16T15:51:49.931877Z","submitted_at":"2023-03-01T07:36:03Z","title":"Non asymptotic analysis of Adaptive stochastic gradient algorithms and applications","version":1},"cited_work":{"arxiv_id":"2303.01370","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.01370","snapshot_observed_at":"2026-08-06T21:05:46.771223Z","title":"Non asymptotic analysis of Adaptive stochastic gradient algorithms and applications","venue":"math.OC","work_id":"b52ececc-d79a-44e1-a4c7-8c254ae5bbae","year":2023},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.013974Z"},"links":{"cited_paper":"/paper/2303.01370","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:54c82c32c8469a30db60e148885b6a9a001c325f162cbab9c22340de1b8c2ea0","observation_id":"44f502ab-686b-476a-8bef-d113b5caa7b1","resolution":{"observed_at":"2026-08-06T21:05:46.774098Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"10.1137/19m125649x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"SIAM Journal on Mathematics of Data Science , volume =","venue":"SIAM Journal on Mathematics of Data Science","work_id":"e891811f-e944-4b35-aa75-eb552f99b344","year":2020},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.017023Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:1fa3cdec532e9176a2c0ab311686499678273420ae251addf4a3f8b335a4a473","observation_id":"cd0fb3d7-0d90-43ba-afdb-8a3510797c7e","resolution":{"observed_at":"2026-08-06T21:05:46.481460Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.019594Z","title":"2021 , number =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.019594Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:9162e61d6fcf615536f0d4c971a9973ea371d0b75c276dbf614dfd9189153877","observation_id":"f6a43a63-ace8-4132-a38f-57d82434ac39","resolution":{"observed_at":"2026-08-06T21:05:46.019594Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.021984Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.021984Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:f57d969d7d59a1f32ed8bc8809009e54a5e0f36bae390945a3e590e0329a04ba","observation_id":"bcf0c3dd-7bbf-4d9c-a3b4-b140347e1af3","resolution":{"observed_at":"2026-08-06T21:05:46.021984Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.13794","last_updated":"2024-09-13T13:28:04Z","snapshot_observed_at":"2026-08-21T02:47:56.035651Z","submitted_at":"2024-02-21T13:24:14Z","title":"Revisiting Convergence of AdaGrad with Relaxed Assumptions","version":2},"cited_work":{"arxiv_id":"2402.13794","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.13794","snapshot_observed_at":"2026-08-06T21:05:46.760315Z","title":"Revisiting Convergence of AdaGrad with Relaxed Assumptions","venue":"math.OC","work_id":"e21c61be-aa21-4737-8c03-0847cb8c438e","year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.024462Z"},"links":{"cited_paper":"/paper/2402.13794","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:bc2d68bf35dcee9e07ce24a7cc2ba7017d535738be77ba25b251e1eb03e3530c","observation_id":"9be26feb-79ba-4624-a794-d45fe06393f6","resolution":{"observed_at":"2026-08-06T21:05:46.763234Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"2026-08-06T21:05:46.026932Z","title":"2024 , eprint=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.026932Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:02a99a29a48952cc49beea5c9af6a1f7b8ca10f5a2c1ffca6a235d3de3c9697f","observation_id":"b0895d6e-ca3c-494a-9ef8-c40093079df1","resolution":{"observed_at":"2026-08-06T21:05:46.026932Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.029335Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.029335Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:fbce8c3acd6c4e944a28f9a2febdc6397aa1274f5125a4a6d8acca5755b5ea40","observation_id":"f38bf10b-fc28-4631-b1c3-f59f796adda8","resolution":{"observed_at":"2026-08-06T21:05:46.029335Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.031913Z","title":"2016 , journal=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.031913Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:ed8e2151963cb5719ed308eb28e34ffd3dbe121d977a1eaddf7e86ac48b72fc6","observation_id":"fe6e7149-ed87-40e7-9380-9b4398ea84eb","resolution":{"observed_at":"2026-08-06T21:05:46.031913Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.20360","last_updated":"2025-07-15T18:49:51Z","snapshot_observed_at":"2026-08-21T02:47:29.046095Z","submitted_at":"2023-10-31T11:01:23Z","title":"Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.20360","snapshot_observed_at":"2026-08-06T21:05:46.034470Z","title":"2310.20360 , archivePrefix=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.034470Z"},"links":{"cited_paper":"/paper/2310.20360","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:017b57bf8cb8ccd227aa4ac42b8bb04ad7dc7ed3a3dc453e2320bc3618f30d9c","observation_id":"5cb91c23-7554-41a4-861b-7deacdb74107","resolution":{"observed_at":"2026-08-06T21:05:46.034470Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.037447Z","title":"2024 , ISBN =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.037447Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:6f4dcacf1626246c554377ad2f38a896b3b25f0847adc4681f402f5d534a78b1","observation_id":"fbc48e27-0ed3-4a34-9c3a-49b64e3093de","resolution":{"observed_at":"2026-08-06T21:05:46.037447Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.039807Z","title":", TITLE =","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.039807Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:cc3a4e76c9437b50c72b6913eea29d24cb8ce77ffa712fa48aea7e1d7ce9feac","observation_id":"31724c79-80b6-499e-a949-e531f8fcac33","resolution":{"observed_at":"2026-08-06T21:05:46.039807Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.042710Z","title":"2019 , eprint=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.042710Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:74f35c2a867e7f18d4071e9c5b2ad07adf10f2f1af4147fadaf4554fe7167733","observation_id":"fa6dc24e-0a64-4d15-a9f1-7d332399b3b6","resolution":{"observed_at":"2026-08-06T21:05:46.042710Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.045501Z","title":"Kingma and Jimmy Ba , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.045501Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:33f61c091f7390f54181d46756478dfa9ab81249717aa380650a63ee67aefe29","observation_id":"271322d3-a056-4038-8ca7-841bfc3f6dc2","resolution":{"observed_at":"2026-08-06T21:05:46.045501Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.047935Z","title":"Incorporating","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.047935Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:f8cb01f49ef489dca9a87cccb2bfaef20120eeea0454ec06b9b2ff1a82dcb3ee","observation_id":"01166245-1965-43f6-9f76-6726337de619","resolution":{"observed_at":"2026-08-06T21:05:46.047935Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.050368Z","title":"Zeiler , title=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.050368Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:56ef0427b81660fa838fd5d77d73986dbafefd0edb553f49ef0e091dd93631cd","observation_id":"7c5c1c11-65bc-4b8a-adc7-521f9c8c8cef","resolution":{"observed_at":"2026-08-06T21:05:46.050368Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.052669Z","title":"Journal of Machine Learning Research , year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.052669Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:743c51251e77f83513ab374291867193cb7d84bbabbf7dfbaeb0b3ff0de82e57","observation_id":"563c6af3-713c-486d-96df-e4d886cffaff","resolution":{"observed_at":"2026-08-06T21:05:46.052669Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.055088Z","title":"Proceedings of the USSR Academy of Sciences , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.055088Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:5322f1a422242cc8c357dbf0fc1b8832b48498c49c19ce71cc7fac912e583d2f","observation_id":"d0b6e99e-e1a4-4186-8bc3-283cb4983ddb","resolution":{"observed_at":"2026-08-06T21:05:46.055088Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/24m1639464","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"SIAM/ASA J","venue":"SIAM/ASA Journal on Uncertainty Quantification","work_id":"5feca0bf-d43a-47c7-9bd4-e987ac08e963","year":2025},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.057675Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:a3b157a0ac1801b5f3c6e246440ed790ea11c70bd76422956684243e3b72a0c8","observation_id":"800bd81c-f5d3-4628-bf4c-09e34a768288","resolution":{"observed_at":"2026-08-06T21:05:46.452822Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.060366Z","title":"Muller and Philippe von Wurstemberger , title=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.060366Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:ac2724ad94eafabe161bcd6b45577b166f1be2940f3208dc7a885451b4d301b5","observation_id":"c748cfbb-63c8-4edb-80f8-efd619b156cf","resolution":{"observed_at":"2026-08-06T21:05:46.060366Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.062751Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.062751Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:75712d075f076dbbe8037da8b2bd4efe335c049a71839080c0b47850f05c6a85","observation_id":"398ea0be-cd3f-4e77-ad7b-d9f61f127a72","resolution":{"observed_at":"2026-08-06T21:05:46.062751Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.065197Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.065197Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:61fd24c6b3c91a4430777e87b5e407190f1fdd7be1a83416a9857a1dbcfbd8ad","observation_id":"a56e1711-d39a-476f-9bb0-004303208d02","resolution":{"observed_at":"2026-08-06T21:05:46.065197Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.067718Z","title":"The analysis of linear partial differential operators","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.067718Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:5bca1b068018d7ca9cbaa8c7593e4c8f030a8b8836e8d1a11ae84b016d311ede","observation_id":"6d7c19a8-da87-46df-a3fb-08221a56e887","resolution":{"observed_at":"2026-08-06T21:05:46.067718Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.070084Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.070084Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:0cf7c593e8bed2835f3c0978c93a3a51895143efee7ecaf13bd24d5c622b3d93","observation_id":"86ce3d9d-631f-45ae-846c-a538e978bf9f","resolution":{"observed_at":"2026-08-06T21:05:46.070084Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.04620","last_updated":"2021-08-10T12:01:37Z","snapshot_observed_at":"2026-08-16T18:04:07.039785Z","submitted_at":"2021-08-10T12:01:37Z","title":"A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions","version":1},"cited_work":{"arxiv_id":"2108.04620","doi":null,"metadata_source":"pith","pith_arxiv_id":"2108.04620","snapshot_observed_at":"2026-08-06T21:05:46.740717Z","title":"A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions","venue":"math.OC","work_id":"9121f3e6-0539-4c3b-a373-b6fc32f8505c","year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.072617Z"},"links":{"cited_paper":"/paper/2108.04620","citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:e4418a777f749988d6bb01c339a756cc4fbb082991c68165d12f43ee81cb71bd","observation_id":"e2a9b84d-e898-44e5-bced-ef3e07834e7d","resolution":{"observed_at":"2026-08-06T21:05:46.744214Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.075434Z","title":"A mathematical model for automatic differentiation in machine learning , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.075434Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:b6ab32f02dd86227499820a0a4043726b7dbdebc4e46d36d29245115bd88eabd","observation_id":"680be056-bcc0-42d3-b004-40129425f5e3","resolution":{"observed_at":"2026-08-06T21:05:46.075434Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.078144Z","title":"On Correctness of Automatic Differentiation for Non-Differentiable Functions , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.078144Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:1a9df07f51e880036bdf3aaa7895cdb054f1b3f1ba4565b88ff751a66423e293","observation_id":"f35830b2-dd04-4713-9d95-945a6d9c9552","resolution":{"observed_at":"2026-08-06T21:05:46.078144Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.080521Z","title":"NeurIPS , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.080521Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:1bfe8ae9ec3ed6075eb4b658467e65c834c170c8f87f31422073c3833b4df618","observation_id":"596f7fcb-c1d5-4a32-a976-7d55a5353cbb","resolution":{"observed_at":"2026-08-06T21:05:46.080521Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.083006Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.083006Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:7bd73562afc959fdeabf30636cdabfc0ee24e31652fdd6e31945f00df3c34390","observation_id":"65aa3f06-98ac-4417-a44f-6099037da30d","resolution":{"observed_at":"2026-08-06T21:05:46.083006Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.085503Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":99,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.085503Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:6285788b9d3261db0a1da070ba1229d00c5d750c55e242d5c4497956216f47b1","observation_id":"da180ae2-960a-447c-81dd-5d7fbdc7145e","resolution":{"observed_at":"2026-08-06T21:05:46.085503Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10107-020-01501-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T00:03:40.895421Z","title":null,"venue":"Mathematical Programming","work_id":"63a8d153-86e2-4603-8551-5899d434a0a4","year":2021},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.088014Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:bcfd0afaaf361bb211c5e4d6c13293b4d8f7651fb83a727d31be5186c1a998f5","observation_id":"7b525e43-a7ed-479b-bffd-cab009ca7f66","resolution":{"observed_at":"2026-08-06T21:05:46.443906Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:05:46.090449Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations","version":1},"reference_index":101,"source":"arxiv_source","source_observed_at":"2026-08-06T21:05:46.090449Z"},"links":{"citing_paper":"/paper/2608.04607"},"observation_digest":"sha256:bb6a6d67b1cd03d3c67856d861672abd6fc60cf03577432440817db03d3d590c","observation_id":"35cabb40-1329-4f68-9982-ce269dd0d7cc","resolution":{"observed_at":"2026-08-06T21:05:46.090449Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.04607","last_updated":"2026-08-05T09:14:22Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-19T08:22:55.066034Z","submitted_at":"2026-08-05T09:14:22Z","title":"On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":7,"parse_uncertain":0,"unresolved":83,"verified_exact":10,"verified_fuzzy":0},"total_outbound_references":194},"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 100 of 194 outbound references and 0 inbound Pith citation observations for arXiv:2608.04607."}