  Scaling large language models (LLMs) leads to an emergent capacity to learn
in-context from example demonstrations. Despite progress, theoretical
understanding of this phenomenon remains limited. We argue that in-context
learning relies on recombination of compositional operations found in natural
language data. We derive an information-theoretic bound showing how in-context
learning abilities arise from generic next-token prediction when the
pretraining distribution has sufficient amounts of compositional structure,
under linguistically motivated assumptions. A second bound provides a
theoretical justification for the empirical success of prompting LLMs to output
intermediate steps towards an answer. To validate theoretical predictions, we
introduce a controlled setup for inducing in-context learning; unlike previous
approaches, it accounts for the compositional nature of language. Trained
transformers can perform in-context learning for a range of tasks, in a manner
consistent with the theoretical results. Mirroring real-world LLMs in a
miniature setup, in-context learning emerges when scaling parameters and data,
and models perform better when prompted to output intermediate steps. Probing
shows that in-context learning is supported by a representation of the input's
compositional structure. Taken together, these results provide a step towards
theoretical understanding of emergent behavior in large language models.
