Demonstrations, CoT, and Prompting: A Theoretical Analysis of ICL

TL;DR

This paper provides a theoretical framework for understanding in-context learning (ICL) in large language models, analyzing how demonstration quality, chain-of-thought prompting, and prompt templates influence generalization to new tasks.

Contribution

It introduces a theoretical analysis of ICL that connects practical design choices to model performance, including the effects of demonstration selection, CoT prompting, and prompt templates.

Findings

Performance depends on demonstration quality and model capability.

Chain-of-thought prompting helps decompose tasks into easier subtasks.

Prompt sensitivity varies with the number of demonstrations.

Abstract

In-Context Learning (ICL) enables pretrained LLMs to adapt to downstream tasks by conditioning on a small set of input-output demonstrations, without any parameter updates. Although there have been many theoretical efforts to explain how ICL works, most either rely on strong architectural or data assumptions, or fail to capture the impact of key practical factors such as demonstration selection, Chain-of-Thought (CoT) prompting, the number of demonstrations, and prompt templates. We address this gap by establishing a theoretical analysis of ICL under mild assumptions that links these design choices to generalization behavior. We derive an upper bound on the ICL test loss, showing that performance is governed by (i) the quality of selected demonstrations, quantified by Lipschitz constants of the ICL loss along paths connecting test prompts to pretraining samples, (ii) an intrinsic ICL capability of the pretrained model, and (iii) the degree of distribution shift. Within the same framework, we analyze CoT prompting as inducing a task decomposition and show that it is beneficial when demonstrations are well chosen at each substep and the resulting subtasks are easier to learn. Finally, we characterize how ICL performance sensitivity to prompt templates varies with the number of demonstrations. Together, our study shows that pretraining equips the model with the ability to generalize beyond observed tasks, while CoT enables the model to compose simpler subtasks into more complex ones, and demonstrations and instructions enable it to retrieve similar or complex tasks, including those that can be composed into more complex ones, jointly supporting generalization to unseen tasks. All theoretical insights are corroborated by experiments.