Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature
GO-MUON claims an exact weighted spectral-oracle update under any positive-definite left and right maps.
Tong Che’s note frames Muon’s polar update as exact only in an unweighted spectral geometry, then introduces GO-MUON as the matched, data-dependent version. The paper says the raw update remains exact regardless of how those geometry maps are estimated or how stale they are. It also analyzes when softmax cross-entropy’s observed-label backward factor approaches the model Fisher and generalized Gauss-Newton factor. A four-step refresh is presented as a compute-statistics tradeoff, not a denoising trick. ArXiv · AI/CL/LG's note
Tong Che’s note frames Muon’s polar update as exact only in an unweighted spectral geometry, then introduces GO-MUON as the matched, data-dependent version. The paper says the raw update remains exact regardless of how those geometry maps are estimated or how stale they are. It also analyzes when softmax cross-entropy’s observed-label backward factor approaches the model Fisher and generalized Gauss-Newton factor. A four-step refresh is presented as a compute-statistics tradeoff, not a denoising trick. ArXiv · AI/CL/LG's note
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