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 the highly structured representations in both phases; and discuss the learnt algorithm.

翻译：大型语言模型能够解决训练集中未出现的任务。这种能力被认为源于上下文学习与技能组合。在本研究中，我们探究了模块化算术任务集合中上下文学习与技能组合的涌现现象。具体而言，我们考虑由向量 $(a, b) \in \mathbb{Z}_p^2$ 标记的有限线性模函数集合 $z = a \, x + b \, y \;\mathrm{mod}\; p$。我们使用部分任务进行预训练，其余任务用于分布外测试。实验表明，随着预训练任务数量的增加，GPT风格的Transformer模型呈现出从分布内泛化到分布外泛化的转变。我们发现，能够实现分布外泛化的最小模型需要两个Transformer模块，而对于更深层的模型，分布外泛化阶段具有\emph{瞬态性}，需要采用早停策略。最后，我们对预训练模型进行了可解释性研究，揭示了两个阶段中高度结构化的表征方式，并讨论了所学到的算法。