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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Alex Damian, Eshaan Nichani, and Jason D Lee
13 Pith papers cite this work. Polarity classification is still indexing.
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On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
Rod flow models for Adam and related optimizers track discrete iterates at the edge of stability more accurately than standard stable flows across tested ML architectures.
Mean-square linear stability of two-point ZO methods is governed by the full Hessian spectrum and admits explicit bounds in terms of trace and top eigenvalue; full-batch ZO-GD/GDM/Adam empirically operate at that boundary.
Momentum SGD exhibits two distinct EoSS regimes for batch sharpness, stabilizing at 2(1-β)/η for small batches and 2(1+β)/η for large batches, aligning with linear stability thresholds.
PRISM forms predictions as sparse mixtures of learned prototypes trained with clustering objectives, matching dense model accuracy while enabling ~500x faster data attribution and behavior editing without finetuning.
Lower bounds establish that heavy-ball momentum extends the compute-efficient batch-size window by sqrt(kappa) over SGD in linear regression, with accelerated SGD showing spectrum-dependent CE-serial runtime tradeoffs.
Weight decay slows progressive sharpening at the edge of stability, inducing damped oscillations in CNNs and a phase transition to sub-2/η sharpness in MLPs driven by parameter-sharpness gradient alignment, yielding more stable NTK dynamics.
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.
VRAdam modifies AdamW by shrinking the learning rate when momentum is large and reports lower validation loss than AdamW on several benchmarks.
H2O evicts non-heavy-hitter tokens from the KV cache using a dynamic submodular policy, retaining recent and frequent-co-occurrence tokens to reduce memory while preserving accuracy.
Muon learns more robust and transferable features than Adam and SGD, shown via corruption robustness tests, transfer experiments, layer-wise probes, effective rank measurements, and a theoretical proof on margins in a multi-component classification problem.
GradPower applies sign-power to gradients before optimization and achieves lower terminal loss in language model pre-training across architectures, scales, datasets, and schedules.
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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Phases of Muon: When Muon Eclipses SignSGD
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
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A Rod Flow Model for Adam at the Edge of Stability
Rod flow models for Adam and related optimizers track discrete iterates at the edge of stability more accurately than standard stable flows across tested ML architectures.
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Zeroth-Order Optimization at the Edge of Stability
Mean-square linear stability of two-point ZO methods is governed by the full Hessian spectrum and admits explicit bounds in terms of trace and top eigenvalue; full-batch ZO-GD/GDM/Adam empirically operate at that boundary.
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Momentum Further Constrains Sharpness at the Edge of Stochastic Stability
Momentum SGD exhibits two distinct EoSS regimes for batch sharpness, stabilizing at 2(1-β)/η for small batches and 2(1+β)/η for large batches, aligning with linear stability thresholds.
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Prototype Language Models
PRISM forms predictions as sparse mixtures of learned prototypes trained with clustering objectives, matching dense model accuracy while enabling ~500x faster data attribution and behavior editing without finetuning.
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Compute Efficiency and Serial Runtime Tradeoffs for Stochastic Momentum Methods
Lower bounds establish that heavy-ball momentum extends the compute-efficient batch-size window by sqrt(kappa) over SGD in linear regression, with accelerated SGD showing spectrum-dependent CE-serial runtime tradeoffs.
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Does Weight Decay Enhance Training Stability?
Weight decay slows progressive sharpening at the edge of stability, inducing damped oscillations in CNNs and a phase transition to sub-2/η sharpness in MLPs driven by parameter-sharpness gradient alignment, yielding more stable NTK dynamics.
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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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A Physics-Inspired Optimizer: Velocity Regularized Adam
VRAdam modifies AdamW by shrinking the learning rate when momentum is large and reports lower validation loss than AdamW on several benchmarks.
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H$_2$O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models
H2O evicts non-heavy-hitter tokens from the KV cache using a dynamic submodular policy, retaining recent and frequent-co-occurrence tokens to reduce memory while preserving accuracy.
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Muon Learns More Robust and Transferable Features than Adam
Muon learns more robust and transferable features than Adam and SGD, shown via corruption robustness tests, transfer experiments, layer-wise probes, effective rank measurements, and a theoretical proof on margins in a multi-component classification problem.
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GradPower: Powering Gradients for Faster Language Model Pre-Training
GradPower applies sign-power to gradients before optimization and achieves lower terminal loss in language model pre-training across architectures, scales, datasets, and schedules.