Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking
arXiv:2609.10657v1 Announce Type: new Abstract: Neural networks trained past memorization frequently undergo a delayed transition to generalization, a phenomenon known as grokking. Despite theoretical progress on emph{why} this transition occurs, the quantitative structure of emph{when} it occurs in hyperparameter space remains uncharacterized. We map the memorization-to-generalization boundary across 384 configurations of two-hidden-layer MLPs on modular arithmetic, fitting a power-law scaling relation for generalization onset time: T_{mathrm{grok}} propto H^{-0.27}, D^{-2.04}, eta^{-0.50}, lambda^{-0.64} (R^2 = 0.732; 0.821 with interactions). The exponent hierarchy reveals that data complexity (D^{-2.04}) is the dominant driver of regime transition, not model capacity (H^{-0.27}): doubling data accelerates generalization by {sim}4times, while doubling width yields only {sim}1.2times. A sharp phase boundary at weight decay lambda gtrsim 1.0 separates grokking from non-grokking configurations, and weight norm trajectories show monotonic compression during the transition, consistent with implicit regularization selecting low-complexity solutions. These results provide a quantitative foundation for predicting and controlling regime transitions in overparameterized networks.