{"paper":{"title":"MuCon: Clipped Muon Updates for LLM Training","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Albert Yi","submitted_at":"2026-05-26T02:16:17Z","abstract_excerpt":"Muon-style optimizers take a matrix-valued momentum or preconditioned update $B = U \\operatorname{diag}(\\sigma_1,\\ldots,\\sigma_r) V^\\top$ and replace it with its canonical partial polar factor $\\operatorname{Pol}(B) = U V^\\top$. This maps every nonzero singular value to one. MuCon is the clipped-Muon variant studied here: it applies singular-value clipping to the same Muon matrix, $D^{\\mathrm{MuCon}}\\_\\tau(B) = \\operatorname{MClip}\\_\\tau(B) = U \\operatorname{diag}\\bigl(\\min\\{\\sigma\\_i,\\tau\\}\\bigr) V^\\top, \\qquad \\tau > 0$. Thus, $\\operatorname{MClip}\\_\\tau$ denotes the mathematical clipping op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26459","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26459/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}