Learning to grok: Emergence of in-context learning and skill composition in modular arithmetic tasks

TL;DR

This paper investigates how large language models, specifically GPT-style transformers, develop in-context learning and skill composition abilities on modular arithmetic tasks, revealing the emergence of structured representations and algorithmic shifts with training.

Contribution

It demonstrates the transition from in-distribution to out-of-distribution generalization in transformers and identifies the minimal model depth needed for out-of-distribution skills.

Findings

Transformers show a transition to out-of-distribution generalization with more pre-training tasks.

Two transformer blocks are sufficient for out-of-distribution generalization.

Deeper models exhibit transient out-of-distribution capabilities requiring early stopping.

Abstract

Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill composition in a collection of modular arithmetic tasks. Specifically, we consider a finite collection of linear modular functions $z = a \, x + b \, y \;\mathrm{mod}\; p$ labeled by the vector $(a, b) \in \mathbb{Z}_p^2$. We use some of these tasks for pre-training and the rest for out-of-distribution testing. We empirically show that a GPT-style transformer exhibits a transition from in-distribution to out-of-distribution generalization as the number of pre-training tasks increases. We find that the smallest model capable of out-of-distribution generalization requires two transformer blocks, while for deeper models, the out-of-distribution generalization phase is \emph{transient}, necessitating early stopping. Finally, we perform an interpretability study of the pre-trained models, revealing highly structured representations in both attention heads and MLPs; and discuss the learned algorithms. Notably, we find an algorithmic shift in deeper models, as we go from few to many in-context examples.