{"as_of":"2026-08-19T14:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e59ba72649d258aa22b0a99e8b2948bdd5cc5efbbaceeab350462d7721848f68","coverage":[{"denominator":119,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T04:23:03.940072Z","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":"2026-08-19T06:32:44.657259+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/2607.13246/citation-record","integrity":"/paper/2607.13246/integrity","json":"/paper/2607.13246/citation-record.json","paper":"/paper/2607.13246"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T04:22:53.302904Z","title":"2024 , note =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:53.302904Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:20417077f8efa4b450fce4121da695ef0a3b3c7a9315439a13814581b0692f7d","observation_id":"38b6a5e6-757d-4e21-94b6-79f274befad4","resolution":{"observed_at":"2026-08-04T04:22:53.302904Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.16982","last_updated":"2025-02-24T09:12:29Z","snapshot_observed_at":"2026-08-16T22:48:15.725816Z","submitted_at":"2025-02-24T09:12:29Z","title":"Muon is Scalable for LLM Training","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.16982","snapshot_observed_at":"2026-08-04T04:22:53.413089Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:53.413089Z"},"links":{"cited_paper":"/paper/2502.16982","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:0f0664f354c34f750b9ff5c527700cd06ce3f7964f4a0146e2dd9295500969f8","observation_id":"9fed5329-ed6b-47d3-ab31-73f7ff3ba867","resolution":{"observed_at":"2026-08-04T04:22:53.413089Z","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":"2026-08-04T04:22:53.549064Z","title":"Improved Convergence Rates of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:53.549064Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:5b34af9ae99b53c8480660a4f48471cb4bb143b0aa544d9c1c5835523de1ca16","observation_id":"b81b85b6-5eff-4ce1-b6fc-0fea4ef56c88","resolution":{"observed_at":"2026-08-04T04:22:53.549064Z","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":"2026-08-04T04:22:53.622202Z","title":"Training Deep Learning Models with Norm-Constrained LMOs , booktitle =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:53.622202Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:35c2e9d556f7e19c8cc4b6ef935874fc864406aab0fce98144830747aa763690","observation_id":"5e56627c-ae2f-4f13-8157-f39aa7a7c76d","resolution":{"observed_at":"2026-08-04T04:22:53.622202Z","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":"2026-08-04T04:22:53.856109Z","title":"2022 , eprint=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:53.856109Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:e2ba17ba574f2cc6046e93bbd473df5debf081378861c106e698861cdb4429f5","observation_id":"3959e2e7-34d7-42e3-8f5a-3a172062483b","resolution":{"observed_at":"2026-08-04T04:22:53.856109Z","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":"2026-08-04T04:22:54.004505Z","title":"Proceedings of the 35th International Conference on Machine Learning,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.004505Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:fb8afac6067c08618b46b0b74e008ae6da1d94156129dc5f98a08a41a8d494b0","observation_id":"6e05e01b-ae55-426d-853d-4c271fa74a34","resolution":{"observed_at":"2026-08-04T04:22:54.004505Z","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":"2026-08-04T04:22:54.115982Z","title":"Preconditioning Benefits of Spectral Orthogonalization in","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.115982Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:fc3d6e9bee712799f0628bee3afb541b7e558c4fd93ff405bedb68d20f4d8cc0","observation_id":"67de6294-c29f-420c-8aa5-1b7b080a877c","resolution":{"observed_at":"2026-08-04T04:22:54.115982Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.04356","last_updated":"2026-04-06T02:08:09Z","snapshot_observed_at":"2026-08-11T06:34:19.697476Z","submitted_at":"2026-04-06T02:08:09Z","title":"REAM: Merging Improves Pruning of Experts in LLMs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.04356","snapshot_observed_at":"2026-08-04T04:22:54.309035Z","title":"arXiv preprint arXiv:2604.04356 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.309035Z"},"links":{"cited_paper":"/paper/2604.04356","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:86ea55f2a4d3b5d5547ac18aae3251c4e66d83db2784a68726c3b2858b762da5","observation_id":"b211665c-e344-49fd-a601-177160bd99f4","resolution":{"observed_at":"2026-08-04T04:22:54.309035Z","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":"2026-08-04T04:22:54.434401Z","title":"New Perspectives in Graph Machine Learning , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.434401Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:9f15eb86e2115d3b521884c2587f63c4b4f1f659ee4c29bfedffa7d63a562ac1","observation_id":"460cb6f9-e883-47d5-81ec-5083e7aa9c7f","resolution":{"observed_at":"2026-08-04T04:22:54.434401Z","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":"2026-08-04T04:22:54.630407Z","title":"International conference on machine learning , pages=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.630407Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ef59a1e8214473f640c8d6224a6abb45382e6e1f9770e660d0f265e37b9c0362","observation_id":"9e516bb9-43bb-487f-b30c-c36496448720","resolution":{"observed_at":"2026-08-04T04:22:54.630407Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.00811","last_updated":"2018-02-07T21:43:25Z","snapshot_observed_at":"2026-08-14T20:17:35.789825Z","submitted_at":"2017-11-02T16:49:19Z","title":"Expressive power of recurrent neural networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.00811","snapshot_observed_at":"2026-08-04T04:22:54.780874Z","title":"arXiv preprint arXiv:1711.00811 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.780874Z"},"links":{"cited_paper":"/paper/1711.00811","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:394f258e4f05a625a41c48e38dd9047e50b570b742f1ded68a88a1d0e39beddb","observation_id":"95192450-50da-42f0-859e-d1a086ab72c3","resolution":{"observed_at":"2026-08-04T04:22:54.780874Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.19943","last_updated":"2026-05-19T15:00:38Z","snapshot_observed_at":"2026-08-16T18:34:25.395005Z","submitted_at":"2026-05-19T15:00:38Z","title":"Probabilistic Tiny Recursive Model","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.19943","snapshot_observed_at":"2026-08-04T04:22:54.948927Z","title":"arXiv preprint arXiv:2605.19943 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:54.948927Z"},"links":{"cited_paper":"/paper/2605.19943","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:00de5b6bb7e05fa8c834177b1c04819f26f2ce17c55f62ac3c6377a45f3d0325","observation_id":"1e664831-5642-4d49-b59b-3d9d1f4502dd","resolution":{"observed_at":"2026-08-04T04:22:54.948927Z","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":"2026-08-04T04:22:55.186883Z","title":"Conference on learning theory , pages=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:55.186883Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:1587472c43123b9f2b18d9b410a053b95920d7fe101f880c72d56164c84f4fbd","observation_id":"24776180-9905-48de-a3fb-f4244503ce11","resolution":{"observed_at":"2026-08-04T04:22:55.186883Z","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":"2026-08-04T04:22:55.419670Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:55.419670Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:e346233222fcee01d3d9a6d2b61d6956258a886e8ac4a95b71247dda41e7809f","observation_id":"cc3c7ae8-aca8-40c1-9e17-61cc046db777","resolution":{"observed_at":"2026-08-04T04:22:55.419670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.02900","last_updated":"2025-06-01T18:46:31Z","snapshot_observed_at":"2026-08-09T10:38:54.874245Z","submitted_at":"2025-02-05T05:44:22Z","title":"A Note on the Convergence of Muon","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.02900","snapshot_observed_at":"2026-08-04T04:22:55.629450Z","title":"A Note on the Convergence of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:55.629450Z"},"links":{"cited_paper":"/paper/2502.02900","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:f97251ffe7ffd808e2de2a90e4aca7bd971ed2fcddf3fe191289a4054e2aa7d2","observation_id":"f15dc13a-07e9-4edb-ba90-ff5c91a74823","resolution":{"observed_at":"2026-08-04T04:22:55.629450Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.13416","last_updated":"2025-05-19T17:50:45Z","snapshot_observed_at":"2026-08-17T21:25:27.735163Z","submitted_at":"2025-05-19T17:50:45Z","title":"Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.13416","snapshot_observed_at":"2026-08-04T04:22:55.756619Z","title":"Gluon: Making","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:55.756619Z"},"links":{"cited_paper":"/paper/2505.13416","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:621351b028107916c83a3f227b993ed4b645cbd3402568f842a92cf151e3fa20","observation_id":"2942369d-0b12-4d62-b9fb-938b1af576fd","resolution":{"observed_at":"2026-08-04T04:22:55.756619Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.23737","last_updated":"2026-07-28T01:40:23Z","snapshot_observed_at":"2026-08-17T04:14:11.630903Z","submitted_at":"2025-05-29T17:58:01Z","title":"On the Convergence Analysis of Muon","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.23737","snapshot_observed_at":"2026-08-04T04:22:55.826713Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:55.826713Z"},"links":{"cited_paper":"/paper/2505.23737","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:298df45a307d66721d3e9532962152966332835a487edd6c16f71b034527480a","observation_id":"a2631f6a-5480-4151-9a89-e0d1a62c0bb9","resolution":{"observed_at":"2026-08-04T04:22:55.826713Z","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":"2026-08-04T04:22:55.947955Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:55.947955Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:58f2716267c844dd4340feb00de69dee35b1e5ec9b67c9b30aaaa99e324cec06","observation_id":"a2eddc23-d574-4744-acf2-311491f98d8c","resolution":{"observed_at":"2026-08-04T04:22:55.947955Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.01598","last_updated":"2026-06-08T02:38:54Z","snapshot_observed_at":"2026-08-16T23:33:31.313167Z","submitted_at":"2025-07-02T11:03:13Z","title":"Convergence Bound and Critical Batch Size of Muon Optimizer","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.01598","snapshot_observed_at":"2026-08-04T04:22:56.093779Z","title":"Convergence Bound and Critical Batch Size of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.093779Z"},"links":{"cited_paper":"/paper/2507.01598","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:4a20316a03244c50f55db98bc04bc099af78d4b6dbb719116a3e947107e16433","observation_id":"0280ecb4-bc47-4bba-a6a4-cd6b3a378448","resolution":{"observed_at":"2026-08-04T04:22:56.093779Z","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":"2026-08-04T04:22:56.237036Z","title":"Journal of Machine Learning Research , year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.237036Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:1b5f9433fb72d7815e29dc514ddeaf8c746bb1e10383ceb0b8886fd90d316df0","observation_id":"80e8d635-8e9e-4c9a-9e4f-c2b752cd2a76","resolution":{"observed_at":"2026-08-04T04:22:56.237036Z","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":"2026-08-04T04:22:56.337910Z","title":"Proceedings of the 36th International Conference on Machine Learning , pages =","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.337910Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:f308d8ee7853d9f78dbe56bf5e2713bd8e37d2d3f077a72cb008620ff31e33af","observation_id":"81d0fd97-a1dd-46e0-88c6-30656c12a409","resolution":{"observed_at":"2026-08-04T04:22:56.337910Z","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":"2026-08-04T04:22:56.418573Z","title":"Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond , journal =","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.418573Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:6d9cd2abd99ff45c57570bc5147b883a1d13aa137ac0abcdb0d47cd990cfe3a9","observation_id":"9c27d578-07c6-479a-ab6b-aa00fd2b2b8d","resolution":{"observed_at":"2026-08-04T04:22:56.418573Z","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":"2026-08-04T04:22:56.526077Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.526077Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:06e28d6a8db749c5473fdf26ab10a97c39958871094f3503afdcd3c0713e3ed9","observation_id":"f057273a-0350-4fb9-a502-a10d62edda46","resolution":{"observed_at":"2026-08-04T04:22:56.526077Z","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":"2026-08-04T04:22:56.560132Z","title":"Investigating the Overlooked Hessian Structure: From","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.560132Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ec88e1bf25714ee1172fbd318d51a724b0a74ef6275c5f14fdb034f9d6bed33b","observation_id":"d7d0365f-9144-4f47-8fa8-041ac59290fd","resolution":{"observed_at":"2026-08-04T04:22:56.560132Z","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":"2026-08-04T04:22:56.618431Z","title":"2022 , isbn =","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.618431Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:925ec9e4ba9d8c46270d0ed5a3191a43c2bedf0e4731dbd5bb5082f620834c27","observation_id":"861f62df-3cc8-4a10-9378-00c9ed57f30b","resolution":{"observed_at":"2026-08-04T04:22:56.618431Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.02222","last_updated":"2025-05-20T01:04:35Z","snapshot_observed_at":"2026-08-17T11:38:13.930266Z","submitted_at":"2025-05-04T19:14:43Z","title":"Practical Efficiency of Muon for Pretraining","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.02222","snapshot_observed_at":"2026-08-04T04:22:56.743147Z","title":"Polloreno and Karl Stratos and Philip Monk and Adarsh Chaluvaraju and Andrew Hojel and Andrew Ma and Anil Thomas and Ashish Tanwer and Darsh J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.743147Z"},"links":{"cited_paper":"/paper/2505.02222","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:08799280d85329c851e8e74669cb5c058d212455ebebe4af800c37719664aa9f","observation_id":"366f1d69-2de7-4786-ac7d-149cc0e6f122","resolution":{"observed_at":"2026-08-04T04:22:56.743147Z","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":"2026-08-04T04:22:56.816857Z","title":"Proceedings of the 39th International Conference on Machine Learning , pages =","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.816857Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:71dbfa612bcac225bd974c73b18f9b446053cc965bc507938a6e9e3d170bfaf2","observation_id":"94be6f5c-afb2-43ff-97e2-c6cc3843ea86","resolution":{"observed_at":"2026-08-04T04:22:56.816857Z","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":"2026-08-04T04:22:56.879221Z","title":"2019 , eprint=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.879221Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:525a8cd9c378a2408c49e1e9e2f5daa3f9171ad03f1f85a97463899dc5d6d236","observation_id":"8b3a73b9-27e8-42ab-b7a1-c0027cbaedcd","resolution":{"observed_at":"2026-08-04T04:22:56.879221Z","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":"2026-08-04T04:22:56.929280Z","title":"2019 , url=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:56.929280Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:aefb57db164c4fcf4bd57eeb86b9d9bb9705624c3be6af20f9972791472e82e6","observation_id":"e8b9cd1c-11f8-4186-8e61-5a8a3c433fe3","resolution":{"observed_at":"2026-08-04T04:22:56.929280Z","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":"2026-08-04T04:22:57.006485Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.006485Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:48c256826a89085c32c2d5586d08d1ec6d463f033ccfd7765b2ebc39dea939cd","observation_id":"373ed4fd-cc35-49b9-b686-84bbfaeb7440","resolution":{"observed_at":"2026-08-04T04:22:57.006485Z","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":"2026-08-04T04:22:57.057453Z","title":"Proceedings of the 37th International Conference on Machine Learning , pages =","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.057453Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:a5abed2cd738b18d0d988f63ac1f06dd66cebac61c222567faa5a7ce19af75bf","observation_id":"50e67e58-b241-47ad-9e4c-7c91ac017a4e","resolution":{"observed_at":"2026-08-04T04:22:57.057453Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.12645","last_updated":"2025-04-08T16:47:42Z","snapshot_observed_at":"2026-08-18T11:39:27.990371Z","submitted_at":"2025-03-16T20:49:34Z","title":"Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.12645","snapshot_observed_at":"2026-08-04T04:22:57.127991Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.127991Z"},"links":{"cited_paper":"/paper/2503.12645","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:d84ee5134c9985e3b8003563f048fe7e1c4ae4c959a2147447b01c33c040d0fd","observation_id":"f121ad90-f4bb-4347-be89-68b31afbfc2e","resolution":{"observed_at":"2026-08-04T04:22:57.127991Z","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":"2026-08-04T04:22:57.298997Z","title":"Beyond the Ideal: Analyzing the Inexact","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.298997Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:4c618afd6eb26ed7332d79db85dfc0e673d4cb6fca33c510ad2813fc2ffa01a9","observation_id":"47739ee0-c892-4918-9a90-720c0bb8b096","resolution":{"observed_at":"2026-08-04T04:22:57.298997Z","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":"2026-08-04T04:22:57.362762Z","title":"Error Feedback for","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.362762Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:d55f3ae9d366cbcf88ac20b38b6b6a1b0f81c0c133cc52d822da452fda3041f7","observation_id":"fb69b566-ca00-400b-9912-099931afa979","resolution":{"observed_at":"2026-08-04T04:22:57.362762Z","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":"2026-08-04T04:22:57.420794Z","title":"Convergence of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.420794Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:1618f396a999a67489d05c6ae0d27542d546739d0506fe0fa189daf09191633a","observation_id":"90404c75-b755-4459-9822-7bb14045d95e","resolution":{"observed_at":"2026-08-04T04:22:57.420794Z","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":"2026-08-04T04:22:57.485371Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.485371Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:351ab8d7cad97e87793a1f619f34fe5e08cb3ee97de199636faebd60a67bc175","observation_id":"a45c0958-5649-417b-aa54-0ac4ec0cd651","resolution":{"observed_at":"2026-08-04T04:22:57.485371Z","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":"2026-08-04T04:22:57.595496Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.595496Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ca51a8242063c27ebe3db3bbceed0980a4019c840361984ac5b3c2e8d78471b2","observation_id":"183e12a4-2cae-477a-b8fc-aa82d8831c78","resolution":{"observed_at":"2026-08-04T04:22:57.595496Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16932","last_updated":"2026-05-04T23:23:45Z","snapshot_observed_at":"2026-08-14T07:16:28.974722Z","submitted_at":"2025-05-22T17:23:14Z","title":"The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16932","snapshot_observed_at":"2026-08-04T04:22:57.687506Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.687506Z"},"links":{"cited_paper":"/paper/2505.16932","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:b9cfff55f82b3bc7431c4bdf9cf59d95b84c23d49500e571ddd1d2b0febdba90","observation_id":"42a2f19b-773b-4556-8d13-880fdb8b5a2c","resolution":{"observed_at":"2026-08-04T04:22:57.687506Z","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":"2026-08-04T04:22:57.795925Z","title":"2025 , eprint=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.795925Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:72fabb055ae8af8199b55fad59da2114bfbf20feb0220d7d894072330226f850","observation_id":"08bc8301-34a7-4d07-a9bc-0da6fedb2f65","resolution":{"observed_at":"2026-08-04T04:22:57.795925Z","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":"2026-08-04T04:22:57.862618Z","title":"2024 , url =","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.862618Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:8fa4c3d8c54dd945aec11c08fe3d950ba351b936242219a3dbd457a78dee06ad","observation_id":"8a02e517-45c4-46ff-ae6f-0be70f56ff32","resolution":{"observed_at":"2026-08-04T04:22:57.862618Z","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":"2026-08-04T04:22:57.930307Z","title":"Rakhuba , title =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.930307Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:5e1455663227a1c583efbde7678050d4b95bedb9d7be2103a415776d23b8615a","observation_id":"b61f662c-926f-4581-b059-06b77a36ceba","resolution":{"observed_at":"2026-08-04T04:22:57.930307Z","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":"2026-08-04T04:22:57.967373Z","title":"2025 , month =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:57.967373Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:365bd596bcf373a99c54f7c1d9c63cf12a41812767cb1025ac2321ad3dbc684b","observation_id":"caa8a6de-8622-4312-969f-591e0a73e203","resolution":{"observed_at":"2026-08-04T04:22:57.967373Z","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":"2026-08-04T04:22:58.041231Z","title":"PolarGrad:","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.041231Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:4f694f4566afc5214dbe68b7b75498c9c8833191438284695074f19ab5256125","observation_id":"10bead1b-be19-45db-a86c-54d59591580b","resolution":{"observed_at":"2026-08-04T04:22:58.041231Z","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":"2026-08-04T04:22:58.097696Z","title":"2025 , url =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.097696Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:e786127b739fb3d37bbf67cf6590f1e4d759192bef427c998a89a466e68dec52","observation_id":"facbeb86-2c83-460e-954b-101bc074d3a6","resolution":{"observed_at":"2026-08-04T04:22:58.097696Z","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":"2026-08-04T04:22:58.216141Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.216141Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:24f8a379138e47259626d5155da3c4f95aa2b5bdf62fbb7201dcca24cd37cf86","observation_id":"7c28d257-6701-4708-9ad4-85941e3c8418","resolution":{"observed_at":"2026-08-04T04:22:58.216141Z","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":"2026-08-04T04:22:58.277077Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.277077Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:519eb393634f3de82f631dbabb27ae3edea14044c0f974785b0ca8fa29c5369c","observation_id":"184d7e0e-f226-4909-988a-83d4f3e7645b","resolution":{"observed_at":"2026-08-04T04:22:58.277077Z","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":"2026-08-04T04:22:58.391684Z","title":"2025 , eprint=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.391684Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:adacb87b4e2b015a7358e3fc0c1bf4adcc7d6f7e368f6cf742a5a95595144a82","observation_id":"eaed8ff4-ec13-4adb-bfc3-5d9fa67d84e4","resolution":{"observed_at":"2026-08-04T04:22:58.391684Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2509.11983","last_updated":"2026-04-19T16:56:37Z","snapshot_observed_at":"2026-08-13T05:15:24.130541Z","submitted_at":"2025-09-15T14:28:53Z","title":"Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.11983","snapshot_observed_at":"2026-08-04T04:22:58.527258Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.527258Z"},"links":{"cited_paper":"/paper/2509.11983","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:733d8c6067eb0bc1701dc9634d7d3cf9ccea1b5416f72e2919a88d8e00f7603f","observation_id":"c25b7eca-9696-466d-aec6-9679815edb44","resolution":{"observed_at":"2026-08-04T04:22:58.527258Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2509.14562","last_updated":"2026-07-24T13:07:17Z","snapshot_observed_at":"2026-08-16T22:35:10.348502Z","submitted_at":"2025-09-18T02:49:27Z","title":"LiMuon: Light and Fast Muon Optimizer for Large Models","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.14562","snapshot_observed_at":"2026-08-04T04:22:58.655166Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.655166Z"},"links":{"cited_paper":"/paper/2509.14562","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:aac053e4ae3a3fd75ad7947a4183e6ef8b855f48f492171c10b0bb63c7ab917b","observation_id":"4dc5550f-2909-4632-a1d0-3168a7edb678","resolution":{"observed_at":"2026-08-04T04:22:58.655166Z","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":"2026-08-04T04:22:58.799965Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.799965Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:62af7b8ac7a84108c3bffd55ea1d409b12ebc21d074942ef94d55a5c721fe1c9","observation_id":"53fb57a2-8496-442b-84c6-c721e546838d","resolution":{"observed_at":"2026-08-04T04:22:58.799965Z","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":"2026-08-04T04:22:58.886599Z","title":"CoRR , volume =","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.886599Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:7a15fa1d1dcf21184d3a919e10de6f4c1cb28f33675280394d6ba197e2df073b","observation_id":"74eb4fc5-552f-4a0d-9c89-36ff3a6e970f","resolution":{"observed_at":"2026-08-04T04:22:58.886599Z","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":"2026-08-04T04:22:58.929432Z","title":"Why transformers need","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:58.929432Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:e45a23a00764b38a7851dd3853c89a79b2452425838618b7ad2381522b263625","observation_id":"5f0d1b9b-152d-4663-95b5-c84ed6698fde","resolution":{"observed_at":"2026-08-04T04:22:58.929432Z","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":"2026-08-04T04:22:59.073864Z","title":"Provable acceleration of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.073864Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:9f9d5a78a6aedb26659f2412536c7b4bcac5acde9100cabe5b3c5dc502c147b4","observation_id":"c534ce25-b153-4d56-b4ba-c0a8fa801c6c","resolution":{"observed_at":"2026-08-04T04:22:59.073864Z","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":"2026-08-04T04:22:59.178666Z","title":"Conference On Learning Theory , pages=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.178666Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:530b107bd2f7409412a9be76234b5cc038755e538d27de578bdd5b5787e8ab45","observation_id":"ff2e0f2d-8dcf-4c3a-ada9-1161ebc7988f","resolution":{"observed_at":"2026-08-04T04:22:59.178666Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.20325","last_updated":"2024-12-06T14:09:22Z","snapshot_observed_at":"2026-08-12T12:26:45.359430Z","submitted_at":"2024-09-30T14:26:12Z","title":"Old Optimizer, New Norm: An Anthology","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.20325","snapshot_observed_at":"2026-08-04T04:22:59.385571Z","title":"arXiv preprint arXiv:2409.20325 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.385571Z"},"links":{"cited_paper":"/paper/2409.20325","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:6545f005e088c11627f99d82b5ac9293e6631fc71250f88f2c5df29a5e11471a","observation_id":"86d2a74d-508f-4c13-a673-e5c2d70968b0","resolution":{"observed_at":"2026-08-04T04:22:59.385571Z","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":"2026-08-04T04:22:59.470850Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.470850Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:bbd6da79461900d193b2026dfcb433a0eb33bfbe6acee656a6da9c2b21024036","observation_id":"3a38f9a8-894b-486e-91fc-d6197668abab","resolution":{"observed_at":"2026-08-04T04:22:59.470850Z","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":"2026-08-04T04:22:59.581391Z","title":"Training deep learning models with norm-constrained","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.581391Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ae79fdd978680c25d2d85f248e4688a7bfb3b5b1e677091a677f7b4824f5e2b2","observation_id":"c0e8e19b-fd47-4c3e-ae8c-a3a0a36d81a1","resolution":{"observed_at":"2026-08-04T04:22:59.581391Z","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":"2026-08-04T04:22:59.685113Z","title":"BIT Numerical Mathematics , volume=","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.685113Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ad9aedbdca8a809e926878af9a16b7513bb97a39ee0c69b04e81a80a6de5d524","observation_id":"0c29f86f-0a71-49a2-9fd7-4a87276d0e3e","resolution":{"observed_at":"2026-08-04T04:22:59.685113Z","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":"2026-08-04T04:22:59.785451Z","title":"Proceedings of the International Congress of Mathematicians 2010 , pages=","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.785451Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:7f20f0045e212e94f59b406fe4465f616f1d1ffb0fce1563e2c3632dbb721903","observation_id":"ca4848b5-1a75-49d6-b4d5-6f6f3facacc0","resolution":{"observed_at":"2026-08-04T04:22:59.785451Z","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":"2026-08-04T04:22:59.845639Z","title":"Numerical Linear Algebra with Applications , volume=","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.845639Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:e32077fa9864ff075f589da0f27806a675d945de016c5dd2b2514688685ae2e6","observation_id":"2ba82fc1-340d-4ea6-957f-a9d7c37a26ad","resolution":{"observed_at":"2026-08-04T04:22:59.845639Z","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":"2026-08-04T04:22:59.945747Z","title":"International Conference on Machine Learning , pages=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-04T04:22:59.945747Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:f268e0299c607a3355182bb05907038f1791d12c2d3483ae6122fc7dbdb93db2","observation_id":"03a36047-7038-4b16-a93e-c03551b76e45","resolution":{"observed_at":"2026-08-04T04:22:59.945747Z","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":"2026-08-04T04:23:00.002688Z","title":"2018 , organization=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.002688Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:5a8d811b2cdf492b595ba940df9486f484a0229920fae2e0e56410ab5aa9e7c7","observation_id":"490d03bf-38a2-4557-b10d-e575f7facb21","resolution":{"observed_at":"2026-08-04T04:23:00.002688Z","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":"2026-08-04T04:23:00.161269Z","title":"Stat , volume=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.161269Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:3c1b9d9f9e1d6665d986403dd542a2f73b0ccb758dc1b1c57db84f48df5e4168","observation_id":"74ac2714-614b-403b-87c6-357045a00c62","resolution":{"observed_at":"2026-08-04T04:23:00.161269Z","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":"2026-08-04T04:23:00.319579Z","title":"SIAM journal on Matrix Analysis and Applications , volume=","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.319579Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:d12b975905c7b45971ce44e46c370a3af5c4379d16b3ffd202d54d14c599bf59","observation_id":"c3779ddc-d005-450f-9dd5-d186689178cb","resolution":{"observed_at":"2026-08-04T04:23:00.319579Z","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":"2026-08-04T04:23:00.460540Z","title":"2013 , publisher=","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.460540Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:5a21207ddb5ec974de622f9d1abf60a6963fada776d6c4762681e721c75a9771","observation_id":"c31e415c-2e00-49bb-bd58-0e6cd8d859cc","resolution":{"observed_at":"2026-08-04T04:23:00.460540Z","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":"2026-08-04T04:23:00.581048Z","title":"SIAM Journal on Matrix Analysis and Applications , volume=","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.581048Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:8688b505d76ec4788c51d5f5a1b65bb25adca6d0ff34c38d0b82fee74d4a1a25","observation_id":"3d4e1a48-13fa-4285-8e92-33ef1b319b1d","resolution":{"observed_at":"2026-08-04T04:23:00.581048Z","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":"2026-08-04T04:23:00.656399Z","title":"SIAM journal on matrix analysis and applications , volume=","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.656399Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:6d3dcac5618d8b42ae9d416509f29b7ae996b86c4e59da0b9b471d9a490912b5","observation_id":"3f1cc495-5a10-4c77-b3ec-2ff5a421f1bc","resolution":{"observed_at":"2026-08-04T04:23:00.656399Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.21265","last_updated":"2024-12-06T17:02:28Z","snapshot_observed_at":"2026-08-16T13:05:17.001660Z","submitted_at":"2024-10-28T17:57:31Z","title":"Modular Duality in Deep Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.21265","snapshot_observed_at":"2026-08-04T04:23:00.756777Z","title":"arXiv preprint arXiv:2410.21265 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.756777Z"},"links":{"cited_paper":"/paper/2410.21265","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:4dfbcfc2e0d8636564554d2ab6e3b09748091b5938214083d35115860b4c05e8","observation_id":"3773977a-28d1-4cee-b341-83bd46971ade","resolution":{"observed_at":"2026-08-04T04:23:00.756777Z","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":"2026-08-04T04:23:00.857005Z","title":"IEEE Journal of Selected Topics in Signal Processing , volume=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.857005Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:9e1bd75ad7d96936736b57793eb6e2eb5365b16d66100fccb9b76d06fa6e128b","observation_id":"3b13c636-ac56-4651-8bf8-1504220bc28a","resolution":{"observed_at":"2026-08-04T04:23:00.857005Z","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":"2026-08-04T04:23:00.939373Z","title":"Transformers are","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:00.939373Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:52c77dabf0a65ce601b2cb1f75be509b3d9a0ba498fa1d3b0df68822e7c05f88","observation_id":"98bbe20b-8ff0-416d-bf16-418d06236184","resolution":{"observed_at":"2026-08-04T04:23:00.939373Z","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":"2026-08-04T04:23:01.010264Z","title":"2008 , publisher=","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.010264Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ce6c393f876a06c47732fc5ba9d429980ab8e54d4b8a092f7d1e9ba87867f351","observation_id":"d93a480c-6577-49ba-b856-b5bad0bc7a6b","resolution":{"observed_at":"2026-08-04T04:23:01.010264Z","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":"2026-08-04T04:23:01.110173Z","title":"Stochastic spectral descent for restricted","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.110173Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:99d8b902a2d62f5124985669ddd7abafdaae27428c21f8809442cfbc0304da1c","observation_id":"9026f80f-0a4e-4d51-97d3-0f37cc695cd3","resolution":{"observed_at":"2026-08-04T04:23:01.110173Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2202.07052","last_updated":"2022-02-14T21:46:07Z","snapshot_observed_at":"2026-08-16T17:21:20.573906Z","submitted_at":"2022-02-14T21:46:07Z","title":"Orthogonalising gradients to speed up neural network optimisation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.07052","snapshot_observed_at":"2026-08-04T04:23:01.225267Z","title":"arXiv preprint arXiv:2202.07052 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.225267Z"},"links":{"cited_paper":"/paper/2202.07052","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:4612ea6cfc1c68b772df8cc213180c9fa2b93645c9840b096c187f1dfb62ae5e","observation_id":"255b4c59-575c-4ab9-801a-983a749a9932","resolution":{"observed_at":"2026-08-04T04:23:01.225267Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.16041","last_updated":"2025-04-22T17:08:09Z","snapshot_observed_at":"2026-08-17T22:11:05.813214Z","submitted_at":"2025-04-22T17:08:09Z","title":"Muon Optimizer Accelerates Grokking","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.16041","snapshot_observed_at":"2026-08-04T04:23:01.281987Z","title":"arXiv preprint arXiv:2504.16041 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.281987Z"},"links":{"cited_paper":"/paper/2504.16041","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:9514e67e449381ca1eb7bc35e4d29c2518cead32cec9a8656a4c41ad6b90b6ae","observation_id":"d7aeb7f8-b799-4088-b80f-36f79f4ad905","resolution":{"observed_at":"2026-08-04T04:23:01.281987Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.01769","last_updated":"2023-11-24T18:08:25Z","snapshot_observed_at":"2026-08-18T05:04:49.424808Z","submitted_at":"2023-10-03T03:34:22Z","title":"How Over-Parameterization Slows Down Gradient Descent in Matrix Sensing: The Curses of Symmetry and Initialization","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.01769","snapshot_observed_at":"2026-08-04T04:23:01.340425Z","title":"arXiv preprint arXiv:2310.01769 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.340425Z"},"links":{"cited_paper":"/paper/2310.01769","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:f6dc5e51c75b419f7d1a0c9184e53f8ffb7e79ab9c1c442ba0e50b83426743e9","observation_id":"08815c80-51c8-4df3-9cc8-3b0ddb268db1","resolution":{"observed_at":"2026-08-04T04:23:01.340425Z","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":"2026-08-04T04:23:01.494017Z","title":"The Polar Express: Optimal Matrix Sign Methods and Their Application to the","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.494017Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:810c23b3805af6d753cfc80ce4ebeb9f7bf7c7014cd3dad99a691bf2e9b6feba","observation_id":"dfef4bc6-4f27-4987-9a6b-06a1c3654fe8","resolution":{"observed_at":"2026-08-04T04:23:01.494017Z","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":"2026-08-04T04:23:01.626731Z","title":"Practical efficiency of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.626731Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:2a1efbeb9e43dc70e73f74744a4f29b36ed0a1a9591967b46afc5528e568f3e5","observation_id":"4d8264af-5831-4483-ba98-2c7794ab893e","resolution":{"observed_at":"2026-08-04T04:23:01.626731Z","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":"2026-08-04T04:23:01.753049Z","title":"Understanding","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.753049Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:929f59beaa92290c2c57d00bee61202bb281ebf166b07394895c7164f707000a","observation_id":"260f1e34-85a4-4c36-a1e1-cc4082c07b81","resolution":{"observed_at":"2026-08-04T04:23:01.753049Z","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":"2026-08-04T04:23:01.905231Z","title":"Towards quantifying the preconditioning effect of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:01.905231Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:120235e54689d92f3bff6e155d5f781a1107d805aa2bf9912109f16ba13af321","observation_id":"5a38254d-df8d-4ee6-9b9a-76e4210bf952","resolution":{"observed_at":"2026-08-04T04:23:01.905231Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.01763","last_updated":"2025-02-03T19:08:32Z","snapshot_observed_at":"2026-08-18T05:28:06.282520Z","submitted_at":"2025-02-03T19:08:32Z","title":"On The Concurrence of Layer-wise Preconditioning Methods and Provable Feature Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.01763","snapshot_observed_at":"2026-08-04T04:23:02.017903Z","title":"arXiv preprint arXiv:2502.01763 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.017903Z"},"links":{"cited_paper":"/paper/2502.01763","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:5c7e56805f321b977c51c36b8c8fc3568d30b858fa3c0bedae58d96a7c6b2ca3","observation_id":"5512bc06-639e-46bb-ac2b-6717516fa8eb","resolution":{"observed_at":"2026-08-04T04:23:02.017903Z","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":"2026-08-04T04:23:02.197418Z","title":"Muon is scalable for","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.197418Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:f66411b3de57065f89dc892277172bcbe5fa695b755fb698a33121e8d509113d","observation_id":"33390da9-92a2-4598-ba2d-821b3992b6be","resolution":{"observed_at":"2026-08-04T04:23:02.197418Z","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":"2026-08-04T04:23:02.338644Z","title":"Implicit Bias of Spectral Descent and","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.338644Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:c204bca004fc8c029008da4cd78d088c8cf684fa9f7ee3392a68485d49dc76c1","observation_id":"45f06328-8132-443f-ab00-ce6a4d07b68c","resolution":{"observed_at":"2026-08-04T04:23:02.338644Z","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":"2026-08-04T04:23:02.525034Z","title":"2013 , publisher =","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.525034Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:0b89ca3ea3bbbb5d1d73578479e87475b76eb182a5f43d518ad82f02b8817c55","observation_id":"39978922-e125-4481-b72d-8c382f120f1a","resolution":{"observed_at":"2026-08-04T04:23:02.525034Z","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":"2026-08-04T04:23:02.638016Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.638016Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:a84f214c38ef99babe4c9d61c0dc9df665875ca58f3760c60333be011fe7cfc6","observation_id":"8d8da7b8-9376-445c-a052-e1ad659b0f49","resolution":{"observed_at":"2026-08-04T04:23:02.638016Z","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":"2026-08-04T04:23:02.703921Z","title":"A Note on the Convergence of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.703921Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:41f4c4e95689d926480693d8014b951dc607129b5637df6205614ea4eb7edaba","observation_id":"c373292c-8249-4bae-b590-8fb48ae8aa21","resolution":{"observed_at":"2026-08-04T04:23:02.703921Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.09059","last_updated":"2020-12-25T08:33:40Z","snapshot_observed_at":"2026-08-14T21:53:38.814552Z","submitted_at":"2020-06-16T10:36:06Z","title":"Explicit formulas for the joint third and fourth central moments of the multinomial distribution","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.09059","snapshot_observed_at":"2026-08-04T04:23:02.750219Z","title":"arXiv preprint arXiv:2006.09059 , year=","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.750219Z"},"links":{"cited_paper":"/paper/2006.09059","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:9f49e88c1a634af582c765362c1a5cfcba312dcfa46a93dc68464ed18ae05569","observation_id":"792b5982-dd80-40c4-8939-421e585312a9","resolution":{"observed_at":"2026-08-04T04:23:02.750219Z","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":"2026-08-04T04:23:02.815687Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.815687Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:4a6d0d89f74305407b5ba54353a45ea0496063db4c90c524ba4ebd52e7a1906f","observation_id":"74587072-55dc-4bdd-bcbd-020ea1988ba9","resolution":{"observed_at":"2026-08-04T04:23:02.815687Z","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":"2026-08-04T04:23:02.891419Z","title":"Beyond the ideal: Analyzing the inexact","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.891419Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:fe42b6b3c84d71c6f0783dd773b038045125c4bab0b51e0f2fc630ae525b6dbf","observation_id":"6101aed4-3c26-4585-8596-2141eb04a82f","resolution":{"observed_at":"2026-08-04T04:23:02.891419Z","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":"2026-08-04T04:23:02.941251Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:02.941251Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:ba137c8a87f6b453f437d90c837e562f551670e5a32d82d99102871c2285d2ec","observation_id":"7a1596c5-31af-4dd9-835b-aa74941ad6e4","resolution":{"observed_at":"2026-08-04T04:23:02.941251Z","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":"2026-08-04T04:23:03.022859Z","title":"Foundations and Trends","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.022859Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:c3122bcca9a9f2f48490a5417dd7cb3f3421330868ae4e87f0cab79f0d48ff9d","observation_id":"9234cfad-e1e0-42dc-86da-46187649c222","resolution":{"observed_at":"2026-08-04T04:23:03.022859Z","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":"2026-08-04T04:23:03.081134Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.081134Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:09d262acf43b551816e1d95d7cd67eadae901d3ea297bbabd1c8fb83eef565da","observation_id":"8bd8ae9b-8e44-4c1c-815a-43fff40e359f","resolution":{"observed_at":"2026-08-04T04:23:03.081134Z","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":"2026-08-04T04:23:03.139804Z","title":"International Conference on Machine Learning , pages=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.139804Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:155a0ff41280e9675497d2da2905faed4ea77e72ab10f9374f16d10612a5fcb9","observation_id":"8fc85e8e-26e8-4417-a118-75e7c21e4ac5","resolution":{"observed_at":"2026-08-04T04:23:03.139804Z","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":"2026-08-04T04:23:03.156467Z","title":"Preconditioned Gradient Descent for Overparameterized Nonconvex","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.156467Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:1720da8f1d4853e7ced4204e0e2ce2f345858eedd79aab9278a422f010f57280","observation_id":"39600799-4841-4264-b290-db9ebead926c","resolution":{"observed_at":"2026-08-04T04:23:03.156467Z","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":"2026-08-04T04:23:03.254148Z","title":"Foundations and Trends","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.254148Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:56b75c6e666b68e0ec0623be729e55ba528d28fea9e354c4a6ccd32baf5ebf74","observation_id":"bd7908ed-202a-4103-a369-88c0583970cb","resolution":{"observed_at":"2026-08-04T04:23:03.254148Z","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":"2026-08-04T04:23:03.336738Z","title":"On the convergence analysis of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.336738Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:2cd320495645613c8913f5fc2fe76d89ef6201c77eaae9c73aae6d51c4ebf117","observation_id":"8aa0eb89-8d6a-445b-8229-c8967bc1fe97","resolution":{"observed_at":"2026-08-04T04:23:03.336738Z","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":"2026-08-04T04:23:03.444556Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.444556Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:2c5e5499c98971c8b673a621a14f7c7ab7875f94f6d98a79fbfe2bf0c3e62c91","observation_id":"d0e54ab4-6298-41d2-8b46-75ed0b78e37b","resolution":{"observed_at":"2026-08-04T04:23:03.444556Z","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":"2026-08-04T04:23:03.593521Z","title":"Muon Outperforms","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.593521Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:41baeb72b39cd012dfcae32dddd71807d1213bdbc1d46bb5e8656e663d11b934","observation_id":"41f7b3af-5a79-492f-af10-580119fc1b55","resolution":{"observed_at":"2026-08-04T04:23:03.593521Z","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":"2026-08-04T04:23:03.698675Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.698675Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:9ba4d39e0b1f3350309a49753d07a6f303e1da30bdc639c3d0595fb9c9ea59e1","observation_id":"d727a142-70b1-462e-bb2a-86b784208e97","resolution":{"observed_at":"2026-08-04T04:23:03.698675Z","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":"2026-08-04T04:23:03.810614Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":99,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.810614Z"},"links":{"citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:5b8e02e95ec84daac66ad17c0cf3502e8e79b495985d81674b20876dc35361ab","observation_id":"a2979013-462b-4a66-8a7f-add67d5af168","resolution":{"observed_at":"2026-08-04T04:23:03.810614Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.12645","last_updated":"2025-04-08T16:47:42Z","snapshot_observed_at":"2026-08-18T11:39:27.990371Z","submitted_at":"2025-03-16T20:49:34Z","title":"Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.12645","snapshot_observed_at":"2026-08-04T04:23:03.940072Z","title":"arXiv preprint arXiv:2503.12645 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization","version":2},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-08-04T04:23:03.940072Z"},"links":{"cited_paper":"/paper/2503.12645","citing_paper":"/paper/2607.13246"},"observation_digest":"sha256:1e3d78b9b80a3aabbb0cd2bb4da140a4e5f4b98d03f0aff6dd5c197ecc45da56","observation_id":"ce417a14-eb4d-400d-8945-4f731974707c","resolution":{"observed_at":"2026-08-04T04:23:03.940072Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.13246","last_updated":"2026-08-01T19:18:42Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-17T22:30:33.654823Z","submitted_at":"2026-07-14T20:21:38Z","title":"Reassessing Muon for Matrix Factorization"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":100,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":119},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 100 of 119 outbound references and 0 inbound Pith citation observations for arXiv:2607.13246."}