Orthogonal Witness Control for Muon Optimization via Sigmoid Spectral Reshaping
Matrix-valued optimizers such as Muon exploit the spectral structure of neural network updates through Newton--Schulz orthogonalization, but their near-flattening of the singular spectrum discards relative magnitude information across gradient modes. We introduce \emph{Soren} (\textbf{S}pectral \textbf{O}rthogonal \textbf{Re}shapi\textbf{n}g), a matrix-valued optimizer that preserves the singular subspaces of the gradient while applying a bounded, monotone sigmoid transformation to its singular values. This smoothly compresses dominant modes without fully flattening the spectrum. We interpret Soren as a positive-definite preconditioned gradient method and establish convergence guarantees ...
| Authors | Dat Phi Van, Ngo Vu Minh, Tuc Nguyen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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