DGA-Muon: Decoupled Geometry-Aligned Adaptive Scaling for Muon· DGA-Muon: 解耦几何对齐自适应缩放

While NorMuon has achieved strong empirical performance in large-scale pretraining by enhancing Muon with row-wise adaptive scaling, its underlying adaptive mechanism remains poorly understood. In this work, we provide the first systematic analysis of NorMuon's adaptivity, revealing that it originates primarily from orthogonalization-induced geometry rather than genuine optimization-relevant information. Under exact orthogonalization, the adaptive scaling factors degenerate into a single global scalar for square and wide matrices, while for tall matrices their variation arises from the non-uniform distribution of row energy after orthogonalization. Under approximate orthogonalization, the orthogonality residual introduces additional variation into the scaling factors, leading to the \texti