Muon succeeds by guaranteeing local step-size optimality rather than by tracking any ideal global geometry, as random-spectrum and quasi-norm variants match its performance on language models.
Understanding gradient orthogonalization for deep learning via non-euclidean trust-region optimization
8 Pith papers cite this work. Polarity classification is still indexing.
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Muon with Nesterov momentum and inexact polar decomposition achieves optimal convergence rates of O(ε^(-(3α-2)/(α-1))) under heavy-tailed noise for ε-stationary points in non-convex settings.
Muon achieves faster convergence and larger stable learning rates by flattening the singular value spectrum of the momentum buffer through orthogonalization, scaling step size with average rather than maximum singular values.
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.
Proving stability of Leon's preconditioner enables the first tuning-free Nesterov-accelerated projection-free adaptive SGD variant with improved non-smooth non-convex rates.
Proximal stochastic spectral preconditioning converges for nonconvex constrained objectives under heavy-tailed noise, with a variance-reduced version achieving faster rates and a refined analysis of Muon iterations.
Compressed Gluon variants using unbiased/contraction compressors and SARAH-style variance reduction achieve convergence guarantees and lower communication costs in federated learning under layer-wise smoothness.
Constraining fine-tuning updates with LoRA mitigates performance degradation when switching from Adam to Muon on pretrained models.
citing papers explorer
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Muon is Not That Special: Random or Inverted Spectra Work Just as Well
Muon succeeds by guaranteeing local step-size optimality rather than by tracking any ideal global geometry, as random-spectrum and quasi-norm variants match its performance on language models.
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Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition
Muon with Nesterov momentum and inexact polar decomposition achieves optimal convergence rates of O(ε^(-(3α-2)/(α-1))) under heavy-tailed noise for ε-stationary points in non-convex settings.
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Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergence
Muon achieves faster convergence and larger stable learning rates by flattening the singular value spectrum of the momentum buffer through orthogonalization, scaling step size with average rather than maximum singular values.
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Dimension-Free Saddle-Point Escape in Muon
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.
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Optimal Projection-Free Adaptive SGD for Matrix Optimization
Proving stability of Leon's preconditioner enables the first tuning-free Nesterov-accelerated projection-free adaptive SGD variant with improved non-smooth non-convex rates.
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Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives
Proximal stochastic spectral preconditioning converges for nonconvex constrained objectives under heavy-tailed noise, with a variance-reduced version achieving faster rates and a refined analysis of Muon iterations.
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Communication-Efficient Gluon in Federated Learning
Compressed Gluon variants using unbiased/contraction compressors and SARAH-style variance reduction achieve convergence guarantees and lower communication costs in federated learning under layer-wise smoothness.
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Can Muon Fine-tune Adam-Pretrained Models?
Constraining fine-tuning updates with LoRA mitigates performance degradation when switching from Adam to Muon on pretrained models.