Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization
cs.LG, math.OC, stat.ML
Submitted: 2026-08-26
Updated: 2026-08-26
Comments: 37 pages, 3 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition
- When do spectral gradient updates help in deep learning?
- Muon$^p$: Muon with Fractional Spectral Powers
- GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models
- Insights on Muon from Simple Quadratics
- Kimi K2: Open Agentic Intelligence
- Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization
- A Note on the Convergence of Muon
- Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering
- Muon is Scalable for LLM Training
- Preconditioning Benefits of Spectral Orthogonalization in Muon
- Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer
- Muon Does Not Converge on Convex Lipschitz Functions
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