MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration
Orthogonalized-update optimizers such as Muon improve training of matrix-valued parameters, but existing extensions typically either rescale updates after orthogonalization or use heavier whitening-based preconditioners before it. We introduce {\method}, a lightweight family of pre-orthogonalization equilibration schemes for Muon with three forms: two-sided row/column normalization (RC), row normalization (R), and column normalization (C). By rebalancing the momentum matrix before finite-step Newton--Schulz orthogonalization, {\method} improves the geometry seen by orthogonalization. We show that finite-step orthogonalization is governed by the input spectrum, especially stable rank and c...
| Authors | Da Chang, Qiankun Shi, Lvgang Zhang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 March 2026 |
| Last updated at source | 10 May 2026 |
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