Introduces Distance-Adaptive Muon, Scale-Calibrated Muon, and Distance-Free Muon with stationarity and O(1/T) objective-gap guarantees, shown to match or improve fixed-scale Muon on GPT-124M and ViT-Tiny models.
Fork=s+j, we have kX i=1 ¯ri ≥ kX i=s+1 ¯ri = jX ℓ=1 aℓ,¯r k+1 =a j+1
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Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization
Introduces Distance-Adaptive Muon, Scale-Calibrated Muon, and Distance-Free Muon with stationarity and O(1/T) objective-gap guarantees, shown to match or improve fixed-scale Muon on GPT-124M and ViT-Tiny models.