Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization
Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in general norm geometries and develop three complementary algorithms. For smooth non-convex objectives, we introduce Distance-Adaptive Muon, whose trust-region radius is set from the radius explored by the trajectory, and prove a stationarity guarantee under a bounded-trajectory assumption. We then turn to star-convex objectives, a tractable model of the favorable global geometry often used to reason about the empirical loss landscapes of deep neural net...
| Authors | Yury Demidovich, Abhishek Chakraborty, Grigory Malinovsky et al. |
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| Primary category | cs.LG |
| Published | 18 May 2026 |
| Last updated at source | 18 May 2026 |
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