Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking

arXiv cs.AISeptember 12, 2026en

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

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