Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View 文章

arXiv:2606.04405v1 Announce Type: cross Abstract: Modern Transformer architectures frequently employ normalization mechanisms such as RMSNorm and Query-Key Normalization, making parts of the model approximately scale-invariant with respect to weight magnitudes. In this regime, standard Frobenius-norm weight decay acts purely along the radial direction of the weight space and cannot directly simplify the function represented by the normalized layer. We study grokking in small algorithmic tasks through this lens and propose \emph{Low-Rank Decay} (LRD), a nuclear-norm-like spectral regularizer whose subgradient -- the polar factor $UV^\top$ -- retains a tangential component even in the scale-invariant setting. This distinction has a concrete dynamical consequence: after the model memorizes the training set and task gradients vanish, L2 decay can no longer reshape the weight spectrum, whereas LRD continues to compress singular values in an $\ell_1$-like fashion.