Explaining grokking through circuit efficiency

TL;DR

This paper explains the grokking phenomenon in neural networks by proposing that it results from the interplay of more efficient generalising circuits and less efficient memorising circuits, with implications for dataset size and training dynamics.

Contribution

It introduces a novel explanation for grokking based on circuit efficiency, predicts new behaviors like ungrokking and semi-grokking, and provides empirical evidence supporting this theory.

Findings

Grokking occurs when generalising circuits are more efficient than memorising ones.

A critical dataset size exists where memorisation and generalisation are equally efficient.

Discovered phenomena include ungrokking and semi-grokking behaviors.

Abstract

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking occurs when the task admits a generalising solution and a memorising solution, where the generalising solution is slower to learn but more efficient, producing larger logits with the same parameter norm. We hypothesise that memorising circuits become more inefficient with larger training datasets while generalising circuits do not, suggesting there is a critical dataset size at which memorisation and generalisation are equally efficient. We make and confirm four novel predictions about grokking, providing significant evidence in favour of our explanation. Most strikingly, we demonstrate two novel and surprising behaviours: ungrokking, in which a network regresses from perfect to low test accuracy, and semi-grokking, in which a network shows delayed generalisation to partial rather than perfect test accuracy.