Grokking as Dimensional Phase Transition in Neural Networks

Ping Wang

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arXiv · 2604.04655

Grokking as Dimensional Phase Transition in Neural Networks

Ping Wang

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Abstract

Neural network grokking -- the abrupt memorization-to-generalization transition -- challenges our understanding of learning dynamics. Through finite-size scaling of gradient avalanche dynamics across eight model scales, we find that grokking is a \textit{dimensional phase transition}: effective dimensionality~$D$ crosses from sub-diffusive (subcritical, $D < 1$) to super-diffusive (supercritical, $D > 1$) at generalization onset, exhibiting self-organized criticality (SOC). Crucially, $D$ reflects \textbf{gradient field geometry}, not network architecture: synthetic i.i.d.\ Gaussian gradients maintain $D \approx 1$ regardless of graph topology, while real training exhibits dimensional excess from backpropagation correlations. The grokking-localized $D(t)$ crossing -- robust across topologies -- offers new insight into the trainability of overparameterized networks.

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Ping Wang. 2026-04-06. Grokking as Dimensional Phase Transition in Neural Networks. https://arxiv.org/abs/2604.04655

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