Grokking as Dimensional Phase Transition in Neural Networks
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914448730488832 |
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| author | Wang, Ping |
| author_facet | Wang, Ping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04655 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grokking as Dimensional Phase Transition in Neural Networks Wang, Ping Machine Learning Disordered Systems and Neural Networks Artificial Intelligence Adaptation and Self-Organizing Systems 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. |
| title | Grokking as Dimensional Phase Transition in Neural Networks |
| topic | Machine Learning Disordered Systems and Neural Networks Artificial Intelligence Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2604.04655 |