Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization

arXiv:2602.06880v2 Announce Type: replace Abstract: Adaptive methods like Adam have become the $\textit{de facto}$ standard for large-scale vector and Euclidean optimization due to their coordinate-wise adaptation with a second-order nature. More recently, matrix-based spectral optimizers like Muon (Jordan et al., 2024b) show the power of treating weight matrices as matrices rather than long vectors. Linking these is hard because many natural generalizations are not feasible to implement, and we also cannot simply move the Adam adaptation to the matrix spectrum. To address this, we reformulate

Source: arXiv cs.LG — read the full report at the original publisher.

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