Unverified50% confidenceFactExact time
The Muon optimizer replaces the traditional matrix gradient update with an approximate polar factor.
1
Sources
50%
Confidence
Long-term
Relevance
10/16/2026
First Seen
Sources
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Related Claims
UnverifiedThe Polar-Factor Admissibility Set precisely encodes the geometric conditions under which the Muon update is optimal in terms of gradient shape.78% similarUnverifiedMuon's effectiveness may not be simply attributed to gradient orthogonalization under mean curvature, because that explanation is extremely unstable under general radial distributions.69% similarUnverifiedIn practice, Muon uses approximately 5 steps of Newton-Schulz iteration to approximate the matrix sign function, reducing the computational overhead of exact SVD.61% similarUnverifiedWhen the conjugate gradient method solves symmetric positive definite linear systems, the number of iterations required for convergence is closely related to the condition number of the matrix—the larger the condition number, the slower the convergence.59% similarUnverifiedWhen ε ≈ 1, the gradient second-moment term in the denominator is diluted, adaptive scaling has almost no effect, and the optimizer behaves close to pure SGD.59% similar
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