Grokking vs. Learning: Same Features, Different Encodings

TL;DR

This paper compares grokking and steady training in neural networks, revealing they learn similar features but differ in encoding efficiency, with a new compressive regime identified in steady training.

Contribution

It introduces a detailed comparison of grokking and steady training, discovering a novel compressive regime and analyzing the development of features and compressibility during training.

Findings

Grokking and steady training learn the same features.

Steady training exhibits a unique compressive regime with high compression factors.

Models in grokking follow a straight path in information space.

Abstract

Grokking typically achieves similar loss to ordinary, "steady", learning. We ask whether these different learning paths - grokking versus ordinary training - lead to fundamental differences in the learned models. To do so we compare the features, compressibility, and learning dynamics of models trained via each path in two tasks. We find that grokked and steadily trained models learn the same features, but there can be large differences in the efficiency with which these features are encoded. In particular, we find a novel "compressive regime" of steady training in which there emerges a linear trade-off between model loss and compressibility, and which is absent in grokking. In this regime, we can achieve compression factors 25x times the base model, and 5x times the compression achieved in grokking. We then track how model features and compressibility develop through training. We show that model development in grokking is task-dependent, and that peak compressibility is achieved immediately after the grokking plateau. Finally, novel information-geometric measures are introduced which demonstrate that models undergoing grokking follow a straight path in information space.