arXiv Computation and Language By Esther Xin

Tune the Baseline First: Most of Muon's Scaled Weight Decay Gain Is a Tuning Gap, but Its Small Real Advantage Grows With Model Size

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The study re‑examines scaled weight decay (Muon‑SW) versus constant decoupled weight decay for language models, tuning learning‑rate and weight‑decay jointly across a range of model sizes. It finds that most of the reported performance gain is due to a tuning gap, with the tuned advantage shrinking to only 0.0026 BPB. However, the remaining advantage grows with model size, rising from 0.0036 to 0.0051 BPB over an eight‑fold increase in active parameters, and the optimal LR‑WD product shifts faster for Muon‑SW.

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