[Submitted on 9 Sep 2026]
Title:Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking
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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 ${\sim}4\times$, while doubling width yields only ${\sim}1.2\times$. 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.
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
Cite as: arXiv:2609.10657 [cs.AI]
(or arXiv:2609.10657v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.10657
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Anish Kataria [view email] [v1] Wed, 9 Sep 2026 16:47:03 UTC (223 KB)
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