Adapted optimal transport on filtered Gaussian processes reduces to a constrained Procrustes problem between Cholesky factors, yielding explicit martingale projections and asymptotic equivalence among bicausal couplings.
On the Bures–Wasserstein distance between positive definite matrices.Expositiones Mathematicae, 37(2):165–191
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Muon dynamics are equivalent to gradient flows of spectral Wasserstein distances on parameter-space measures, with the operator norm recovering the Muon geometry.
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Adapted Optimal Transport between Filtered Gaussian Processes
Adapted optimal transport on filtered Gaussian processes reduces to a constrained Procrustes problem between Cholesky factors, yielding explicit martingale projections and asymptotic equivalence among bicausal couplings.
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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.