Feature Repulsion and Spectral Lock-in: An Empirical Study of Two-Layer Network Grokking

ArXi:2605.08119v1 Announce Type: cross Tian proves a repulsion theorem (Theorem 6) for the matrix $ B = (\widetilde{F}^\top \widetilde{F} + \eta I)^{-1} $ during the interactive feature-learning stage of grokking: similar features have negative off-diagonal entries $ B_{j\ell} $, producing an effective repulsive force that drives them apart. However, the theorem does not specify when this mechanism becomes empirically observable, nor whether it leaves a measurable spectral signature in the parameter updates.