Dimension-Free Saddle-Point Escape in Muon
Modern Large Language Model (LLM) training is fundamentally bottlenecked by pathologically flat saddle points in extreme high-dimensional landscapes. Motivated by this challenge, we analyze the saddle-point escape dynamics of the emerging Muon optimizer, demonstrating its resilience against the $\mathcal{O}(D)$ dimensional curse that severely traps element-wise adaptive optimizers like AdamW. By extending generalized matrix perturbation theory, we develop a theoretical framework to capture Muon's non-equilibrium optimization trajectories. This theoretical machinery mathematically proves that Muon elegantly bypasses the dimensional curse via a non-linear spectral shaping mechanism. By leve...
| Authors | Yanlin Long, Yufei Gu, Zeke Xie |
|---|---|
| Primary category | cs.LG |
| Published | 10 May 2026 |
| Last updated at source | 10 May 2026 |
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