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.
arXiv preprint arXiv:2512.22768 , year=
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A framework quantifies hyperparameter transfer via scaling-law fit quality, extrapolation robustness, and loss penalty, with ablations showing that μP's advantage over standard parameterization stems from maximizing the embedding layer learning rate to avoid bottlenecks and instabilities in AdamW.
A two-level DMFT tracks bulk and outlier spectral dynamics in wide networks, predicting width-consistent outlier growth and hyperparameter transfer under muP scaling for deep linear nets while noting bulk restructuring for large-output tasks.
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
citing papers explorer
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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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Quantifying Hyperparameter Transfer and the Importance of Embedding Layer Learning Rate
A framework quantifies hyperparameter transfer via scaling-law fit quality, extrapolation robustness, and loss penalty, with ablations showing that μP's advantage over standard parameterization stems from maximizing the embedding layer learning rate to avoid bottlenecks and instabilities in AdamW.
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Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer
A two-level DMFT tracks bulk and outlier spectral dynamics in wide networks, predicting width-consistent outlier growth and hyperparameter transfer under muP scaling for deep linear nets while noting bulk restructuring for large-output tasks.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.