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.
Scaling laws in linear regression: Compute, parameters, and data
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Derives a novel two-point deterministic equivalence for random matrix resolvents to obtain unified asymptotics for SGD-trained linear regression, kernel regression, and random feature models.
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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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Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models
Derives a novel two-point deterministic equivalence for random matrix resolvents to obtain unified asymptotics for SGD-trained linear regression, kernel regression, and random feature models.