  We discuss two solvable grokking (generalisation beyond overfitting) models
in a rule learning scenario. We show that grokking is a phase transition and
find exact analytic expressions for the critical exponents, grokking
probability, and grokking time distribution. Further, we introduce a
tensor-network map that connects the proposed grokking setup with the standard
(perceptron) statistical learning theory and show that grokking is a
consequence of the locality of the teacher model. As an example, we analyse the
cellular automata learning task, numerically determine the critical exponent
and the grokking time distributions and compare them with the prediction of the
proposed grokking model. Finally, we numerically analyse the connection between
structure formation and grokking.
