The Polar Express: Optimal Matrix Sign Methods and their Application to the Muon Algorithm

Computes the matrix polar decomposition used by Muon. Minimax-designed polynomial iterations use GPU-friendly matrix multiplications, with analysis of approximation error and finite-precision behavior.

Computes the matrix polar decomposition used by Muon. Minimax-designed polynomial iterations use GPU-friendly matrix multiplications, with analysis of approximation error and finite-precision behavior.

When reading the original paper, identify its problem, inputs, outputs, and methodological assumptions.

Computes the matrix polar decomposition used by Muon. Minimax-designed polynomial iterations use GPU-friendly matrix multiplications, with analysis of approximation error and finite-precision behavior.

Check the baselines, datasets, evaluation protocol, and ablations in the original paper. This directory overview does not provide an independent evaluation or experimental results table.