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

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.

Authors 1

Anish Kataria

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Official page: arxiv.org/abs/2609.10657
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh
arXiv id: 2609.10657
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh
Categories: cs.AI, cs.LG
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh
PDF: arxiv.org/pdf/2609.10657
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh
Primary category: cs.AI
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 3 h agohigh

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T19

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3 h ago

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Authors: Anish Kataria

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Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2609.10657	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperQuantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking
New paper: Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking
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arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	1 h ago	1

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