From Spectral to Frobenius: When Muon Loses Its Spectral Implicit Bias

cs.LG, cs.AI

Submitted: 2026-10-14

Updated: 2026-10-14

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

Sources

• Old Optimizer, New Norm: An Anthology
• Convergence guarantees for Muon: New parameter regimes and generalizations
• Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization
• Muon is Scalable for LLM Training
• In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning
• Convergence of Practical Muon with Finite Newton-Schulz Iterations and Nesterov Momentum
• Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data

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