Muon Sublates the Edge of Stability in LLM Pretraining
Muon is increasingly used for language-model pretraining, yet its large-step dynamics are not captured by the classical edge-of-stability (EoS) picture of gradient descent (GD). In GD, loss neutrality, equal-magnitude update reversal, and marginal stability meet at a single learning-rate-dependent edge. We show that Muon breaks this coupling. For stochastic no-momentum Muon, we derive a coherence-corrected conditional loss-neutral boundary $2ρ_b/η$, while temporal alignment follows a separate geometry. Controlled experiments show that loss balance and temporal alignment respond differently to learning rate and batch size. Across our language model experiments, the 130M Llama-like LLM runs...
| Authors | Yanzhe Chen, Qifang Zhao, Xiaoxiao Xu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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