The Active Ingredient in Muon's Grokking
The Muon optimizer reaches the grokking threshold on modular arithmetic faster than AdamW. Prior work attributes this to "spectral-norm constraints plus orthogonalized momentum" but does not isolate which mechanism matters. To better understand Moun's behavior, we run multi-seed and multi-learning-rate sweeps to decompose and stress-test the effect. First, an ablation shows the speedup comes from orthogonalization (the Newton-Schulz iteration): orthogonalize-only matches full Muon, whereas spectral-only is no faster than AdamW and is unreliable, and this verdict holds across learning rates. Second, a mechanistic analysis finds that orthogonalizing optimizers reach generalization at roughl...
| Authors | Yufeng Wang |
|---|---|
| Primary category | cs.LG |
| Published | 6 July 2026 |
| Last updated at source | 6 July 2026 |
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