OrScale: Orthogonalised Optimization with Layer-Wise Trust-Ratio Scaling
Muon fixes the \emph{direction} of every matrix-valued update at the polar factor of its momentum, while each layer's step \emph{magnitude} is addressed only by a static shape correction. We derive a dynamic per-layer scalar by adapting the LARS/LAMB trust-ratio principle to the orthogonalized setting, where the standard denominator candidates---the raw momentum norm or the polar-factor norm---either live in the wrong unit space or carry no update-scale information. The resulting method, \emph{OrScale}, uses the norm of the parameter-space direction actually applied and anchors each layer's ratio at one via a per-layer calibration, so that the Moonlight recipe (tuned for AdamW, shared wit...
| Authors | Yuxuan Lou, Yang You |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 30 August 2026 |
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