Effective cascade dimension D(t) crosses D=1 at the grokking transition in MLPs and Transformers, with opposite directions for modular addition versus XOR, consistent with attraction to a shared critical manifold.
Goldenfeld,Lectures on phase transitions and the renormalization group(Addison-Wesley, 1992)
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Grokking occurs as the effective dimensionality of the gradient field transitions from sub-diffusive to super-diffusive at the onset of generalization, exhibiting self-organized criticality.
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Dimensional Criticality at Grokking Across MLPs and Transformers
Effective cascade dimension D(t) crosses D=1 at the grokking transition in MLPs and Transformers, with opposite directions for modular addition versus XOR, consistent with attraction to a shared critical manifold.
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Grokking as Dimensional Phase Transition in Neural Networks
Grokking occurs as the effective dimensionality of the gradient field transitions from sub-diffusive to super-diffusive at the onset of generalization, exhibiting self-organized criticality.