Muon dynamics are equivalent to gradient flows of spectral Wasserstein distances on parameter-space measures, with the operator norm recovering the Muon geometry.
Kantorovich duality for general transport costs and applications.Journal of Functional Analysis, 273(11): 3327–3405
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Muon Dynamics as a Spectral Wasserstein Flow
Muon dynamics are equivalent to gradient flows of spectral Wasserstein distances on parameter-space measures, with the operator norm recovering the Muon geometry.