Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
The sharpness disparity principle in transformers for accelerating language model pre-training.arXiv preprint arXiv:2502.19002, 2025a
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MoLS scales Adam updates using module-level SNR estimates to correct gradient noise imbalance and improve LLM training convergence and generalization.
LLR uses heavy-tailed self-regularization theory to set per-layer learning rates in Transformers, yielding faster convergence and higher zero-shot accuracy than uniform rates across model scales.
HTMuon modifies Muon to produce heavier-tailed updates and weight spectra via HT-SR theory, yielding up to 0.98 lower perplexity on LLaMA pretraining and serving as a plug-in for other Muon variants.
GradPower applies sign-power to gradients before optimization and achieves lower terminal loss in language model pre-training across architectures, scales, datasets, and schedules.
FOAM adaptively controls damping and update frequency in Shampoo based on staleness-oriented error approximation to cut wall-clock time while preserving convergence.
citing papers explorer
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Why Muon Outperforms Adam: A Curvature Perspective
Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
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Revealing Modular Gradient Noise Imbalance in LLMs: Calibrating Adam via Signal-to-Noise Ratio
MoLS scales Adam updates using module-level SNR estimates to correct gradient noise imbalance and improve LLM training convergence and generalization.
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One LR Doesn't Fit All: Heavy-Tail Guided Layerwise Learning Rates for LLMs
LLR uses heavy-tailed self-regularization theory to set per-layer learning rates in Transformers, yielding faster convergence and higher zero-shot accuracy than uniform rates across model scales.
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HTMuon: Improving Muon via Heavy-Tailed Spectral Correction
HTMuon modifies Muon to produce heavier-tailed updates and weight spectra via HT-SR theory, yielding up to 0.98 lower perplexity on LLaMA pretraining and serving as a plug-in for other Muon variants.
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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.
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FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo
FOAM adaptively controls damping and update frequency in Shampoo based on staleness-oriented error approximation to cut wall-clock time while preserving convergence.