Researchers have analyzed stochastic spectral optimizers, including Muon, in a high-dimensional matrix-valued least squares problem. Their analysis reveals that SignSVD, which Muon approximates, performs a square-root preconditioning with respect to the data covariance spectrum for large batch sizes. In contrast, smaller eigenmodes behave like SGD for small batch sizes, slowing convergence, while SignSGD offers no preconditioning for generic covariance, leading to different optimal learning rates and convergence characteristics. AI
IMPACT Provides theoretical insights into the behavior of optimization algorithms used in machine learning, potentially guiding future algorithm development.
RANK_REASON Academic paper analyzing optimization algorithms. [lever_c_demoted from research: ic=1 ai=1.0]
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