Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking

TL;DR

This paper provides a theoretical explanation for the grokking phenomenon, showing how early and late phase implicit biases in neural networks lead to a sudden transition from memorization to generalization.

Contribution

It introduces a theoretical framework demonstrating how a dichotomy of implicit biases causes the grokking transition in neural network training.

Findings

Training gets trapped at a kernel predictor solution for a long period.

A sharp transition to min-norm/max-margin predictors occurs, improving test accuracy.

The phenomenon is provably induced by specific training conditions and biases.

Abstract

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy. This paper studies the grokking phenomenon in theoretical setups and shows that it can be induced by a dichotomy of early and late phase implicit biases. Specifically, when training homogeneous neural nets with large initialization and small weight decay on both classification and regression tasks, we prove that the training process gets trapped at a solution corresponding to a kernel predictor for a long time, and then a very sharp transition to min-norm/max-margin predictors occurs, leading to a dramatic change in test accuracy.