MuonGS: Pretraining LLMs with Relaxed Weight-Norm Control

Weight decay and explicit weight-norm constraints improve optimizer performance in language model pretraining, yet a unified understanding of why such control helps and how much is needed remains incomplete. We analyze norm control in Muon over the entire training trajectory using the \emph{accumulated effective learning rate}, $C_T=\sum_{t

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.37647
Primary Topic
Stochastic Gradient Optimization Techniques
Type
preprint
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preprint

MuonGS: Pretraining LLMs with Relaxed Weight-Norm Control

Athanasios Glentis, Mingyi Hong, Dawei Li
arXiv (Cornell University)
Stochastic Gradient Optimization Techniques
preprint

MuonGS: Pretraining LLMs with Relaxed Weight-Norm Control

Athanasios Glentis, Mingyi Hong, Dawei Li
preprint en

Abstract

Weight decay and explicit weight-norm constraints improve optimizer performance in language model pretraining, yet a unified understanding of why such control helps and how much is needed remains incomplete. We analyze norm control in Muon over the entire training trajectory using the \emph{accumulated effective learning rate}, $C_T=\sum_{t

arXiv (Cornell University)
Stochastic Gradient Optimization Techniques
DOIOpen Access PDFOpenAlex
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MuonGS: Pretraining LLMs with Relaxed Weight-Norm Control — Athanasios Glentis, Mingyi Hong, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS