On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
Since ˆY= Σ out1/2 ˆZ, this is − 1 B2 RΣout1/2 ˆZdiag(X ⊤G⊤ t+1RY D) ˆZ⊤, an (B.2) sandwich
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Phases of Muon: When Muon Eclipses SignSGD
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.