Unverified50% confidenceOpinionExact time
Muon's effectiveness may not be simply attributed to gradient orthogonalization under mean curvature, because that explanation is extremely unstable under general radial distributions.
1
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50%
Confidence
Long-term
Relevance
10/16/2026
First Seen
Sources
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Related Claims
UnverifiedThe Muon optimizer replaces the traditional matrix gradient update with an approximate polar factor.69% similarUnverifiedVariational inequalities are more difficult to handle than standard convex optimization, mainly because the monotonicity of the operator is not equivalent to a gradient structure of some convex function.65% similarUnverifiedAs long as the radius is no longer a fixed constant, the radial fragility based on the mean-curvature interpretation quickly fails.64% similarUnverifiedThe core conclusion of this study is: the covariate distribution alone being insufficiently smooth is enough to slow down the convergence rate of pointwise CATE estimation, without the treatment effect function or the nuisance function needing to become rougher.62% similarUnverifiedControlled order-statistics baselines (covering bounded, light-tailed, and heavy-tailed distributions) can largely reproduce the observed log-linear geometry, but cannot explain the significant shift in the slope α after training.61% similar
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