Convergence of Practical Muon with Finite Newton-Schulz Iterations and Nesterov Momentum

cs.LG

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 26 pages

Code: https://github.com/KellerJordan/Muon

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Sources

• Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition
• Training Compute-Optimal Large Language Models
• Depth Dependence of $\mu$P Learning Rates in ReLU MLPs
• Scaling Laws for Neural Language Models
• IKnow: Instruction-Knowledge-Aware Continual Pretraining for Effective Domain Adaptation
• Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization
• Muon is Scalable for LLM Training
• Training Deep Learning Models with Norm-Constrained LMOs
• Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)
• Practical Efficiency of Muon for Pretraining
• On the Convergence Analysis of Muon
• Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer

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