Unverified50% confidenceFactExact time
MuonGS uses Gram-Schmidt projection to remove the radial component in each Muon update without fixing the weight norm.
1
Sources
50%
Confidence
Long-term
Relevance
10/28/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe Muon optimizer replaces the traditional matrix gradient update with an approximate polar factor.71% similarUnverifiedMuon's effectiveness may not be simply attributed to gradient orthogonalization under mean curvature, because that explanation is extremely unstable under general radial distributions.64% similarUnverifiedIn practice, Muon uses approximately 5 steps of Newton-Schulz iteration to approximate the matrix sign function, reducing the computational overhead of exact SVD.59% similarUnverifiedThe Polar-Factor Admissibility Set precisely encodes the geometric conditions under which the Muon update is optimal in terms of gradient shape.56% similarUnverifiedAfter switching embedding models, the ranking results are preserved but the scale of similarity scores changes completely, causing a fixed threshold of 0.8 to break down.55% similar
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