Does Muon Need Fine-Grained Spectral Shaping?
Muon combines current and past gradients into matrix momentum. For $M=UΣV^\top$, the idealized polar update $Q=UV^\top$ gives every singular direction the same weight. We refer to this as the flat profile. Several recent optimizers replace this flat profile with fine-grained spectral maps that give each direction its own gain. We ask how much of this spectral detail a Muon update needs. Our spectral diagnostics show that approximately $94$--$97\%$ of measured singular modes lie below an estimated noise edge, yet collectively align positively with a reference gradient. We introduce BulkBoost, a two-band spectral reweighting framework with fixed-rank and noise-calibrated variants. The latte...
| Authors | Meher Chaitanya, Tianyi Zhou, Aristides Gionis |
|---|---|
| Primary category | cs.AI |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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