Optimizer Geometry Changes Scaling Laws: Muon Outperforms AdamW in Hard-Rank Growth

YouJiacheng · x · 2026-08-18

NYU research reveals that realized representation capacity in Transformers emerges from architecture–optimizer interaction, not just architecture alone. Different optimizers (AdamW vs. Muon) yield distinct spectral scaling laws under fixed conditions. Hard-rank scaling sharply differentiates optimizers: AdamW shows weak scaling, while Muon achieves much stronger hard-rank growth, converting added FFN width into dominant usable capacity more efficiently.

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