Towards Understanding Grokking: An Effective Theory of Representation Learning

TL;DR

This paper investigates the grokking phenomenon in deep learning, providing a theoretical framework and phase diagrams to explain how models generalize after overfitting, with insights into representation learning and phase transitions.

Contribution

It introduces an effective theory and phase diagram analysis to understand grokking, revealing the conditions for representation learning and the phases of learning in neural networks.

Findings

Grokking arises from structured representations predicted by the effective theory.

Four learning phases identified: comprehension, grokking, memorization, and confusion.

Representation learning occurs only within a specific 'Goldilocks zone' between memorization and confusion.

Abstract

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.