Grokking in the Ising Model

Abstract: Delayed generalization, termed grokking, in a machine learning calculation occurs when the training accuracy approaches its maximum value long before the test accuracy. This paper examines grokking in the context of a neural network trained to classify 2D Ising model configurations.. We find, partially with the aid of novel PCA-based network layer analysis techniques, that the grokking behavior can be qualitatively interpreted as a phase transition in the neural network in which the fully connected network transforms into a relatively sparse subnetwork. This in turn reduces the confusion associated with a multiplicity of paths. The network can then identify the common features of the input classes and hence generalize to the recognition of previously unseen patterns.