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.
Universality laws for high-dimensional learning with random features.IEEE Transactions on Information Theory, 69(3):1932–1964
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Derives via two-site cavity method that nonlinear RNN covariance matrix equals that of linear equivalent network at large N for typical random couplings.
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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.