AMO: Operator-level Adaptive Muon Orthogonalization
Muon has recently emerged as a competitive alternative to AdamW for large-scale pre-training, with orthogonalization via Newton-Schulz (NS) iteration as its core operation. Standard Muon applies a uniform NS schedule to all parameter matrices, overlooking possible differences in orthogonalization difficulty and its impact on performance. Through a systematic empirical study, we show that this per-matrix heterogeneity is pervasive and strongly associated with matrix geometry, which evolves dynamically across operator types, training stages, and network depths. Therefore, uniform NS schedules can lead to uneven orthogonalization quality across the model. Motivated by these findings, we prop...
| Authors | Xinlin Zhuang, Panyi Ouyang, Yichen Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 18 May 2026 |
| Last updated at source | 27 September 2026 |
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