The Stiefel Muon linear minimization oracle has an exact closed-form solution, obtainable from the polar factor of a skew-symmetric matrix.
https://leloykun.github.io/ponder/steepest-descent-stiefel/
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Muon on the Stiefel Manifold Admits an Exact Closed-Form Update
The Stiefel Muon linear minimization oracle has an exact closed-form solution, obtainable from the polar factor of a skew-symmetric matrix.