Muon dynamics are equivalent to gradient flows of spectral Wasserstein distances on parameter-space measures, with the operator norm recovering the Muon geometry.
On the global convergence of gradient descent for over-parameterized models using optimal transport
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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.