Regularized Muon induces a damped Hamiltonian flow on probability measures over matrix parameters, yielding exponential convergence under gradient dominance assumptions.
arXiv preprint arXiv:2602.08232 , year=
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On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
Muon does not converge on convex Lipschitz functions regardless of learning rate, while error feedback restores theoretical convergence but degrades performance on CIFAR-10 and nanoGPT tasks.
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.
citing papers explorer
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Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer
Regularized Muon induces a damped Hamiltonian flow on probability measures over matrix parameters, yielding exponential convergence under gradient dominance assumptions.
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Phases of Muon: When Muon Eclipses SignSGD
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
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Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
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Muon Does Not Converge on Convex Lipschitz Functions
Muon does not converge on convex Lipschitz functions regardless of learning rate, while error feedback restores theoretical convergence but degrades performance on CIFAR-10 and nanoGPT tasks.
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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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