Muon in matrix factorization avoids saddle-to-saddle dynamics, learns top modes simultaneously, conserves sqrt(P^TP) - sqrt(Q^TQ), and reaches balanced solutions from small initialization with a two-step alignment schedule.
Spectralgradientdescentmitigatesanisotropy-driven misalignment: A case study in phase retrieval.arXiv preprint arXiv:2601.22652, 2026
3 Pith papers cite this work. Polarity classification is still indexing.
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Momentum in Muon functions as a spectral filter on signal-plus-perturbation gradients, enlarging the gap to stabilize singular subspaces before orthogonalization and outperforming the reverse order.
Proves linear convergence of Spectral Descent (SD) and Truncated SD for non-smooth convex problems under stated conditions, sublinear rates for regularized versions via Frank-Wolfe, and recovery guarantees for robust low-rank matrix recovery.
citing papers explorer
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Muon learns balanced solutions in matrix factorization without slow saddle-to-saddle dynamics
Muon in matrix factorization avoids saddle-to-saddle dynamics, learns top modes simultaneously, conserves sqrt(P^TP) - sqrt(Q^TQ), and reaches balanced solutions from small initialization with a two-step alignment schedule.
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Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering
Momentum in Muon functions as a spectral filter on signal-plus-perturbation gradients, enlarging the gap to stabilize singular subspaces before orthogonalization and outperforming the reverse order.
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Convergence of Spectral Descent for Non-smooth Optimization
Proves linear convergence of Spectral Descent (SD) and Truncated SD for non-smooth convex problems under stated conditions, sublinear rates for regularized versions via Frank-Wolfe, and recovery guarantees for robust low-rank matrix recovery.