A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
Emergence and scaling laws in sgd learning of shallow neural networks
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The authors derive a Maximally Scale-Stable Parameterization (MSSP) for MoE models that achieves robust learning-rate transfer and monotonic performance gains with scale across co-scaling regimes of width, experts, and sparsity.
In extensive-width networks, features are recovered sequentially through sharp phase transitions, yielding an effective width k_c that unifies Bayes-optimal generalization error scaling as Θ(k_c d / n).
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.
citing papers explorer
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Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
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How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization
The authors derive a Maximally Scale-Stable Parameterization (MSSP) for MoE models that achieves robust learning-rate transfer and monotonic performance gains with scale across co-scaling regimes of width, experts, and sparsity.
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Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks
In extensive-width networks, features are recovered sequentially through sharp phase transitions, yielding an effective width k_c that unifies Bayes-optimal generalization error scaling as Θ(k_c d / n).
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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.