Beyond the Prompt in Large Language Models: Comprehension, In-Context Learning, and Chain-of-Thought

TL;DR

This paper investigates the theoretical foundations of how large language models understand prompts, perform in-context learning, and utilize chain-of-thought reasoning, revealing mechanisms behind their emergent capabilities.

Contribution

It provides a theoretical analysis explaining how LLMs decode prompt semantics, facilitate in-context learning, and activate reasoning through chain-of-thought prompting, which was previously not well understood.

Findings

LLMs infer token transition probabilities via autoregressive processes

In-Context Learning reduces prompt ambiguity and improves task focus

Chain-of-Thought prompts enable task decomposition and complex reasoning

Abstract

Large Language Models (LLMs) have demonstrated remarkable proficiency across diverse tasks, exhibiting emergent properties such as semantic prompt comprehension, In-Context Learning (ICL), and Chain-of-Thought (CoT) reasoning. Despite their empirical success, the theoretical mechanisms driving these phenomena remain poorly understood. This study dives into the foundations of these observations by addressing three critical questions: (1) How do LLMs accurately decode prompt semantics despite being trained solely on a next-token prediction objective? (2) Through what mechanism does ICL facilitate performance gains without explicit parameter updates? and (3) Why do intermediate reasoning steps in CoT prompting effectively unlock capabilities for complex, multi-step problems? Our results demonstrate that, through the autoregressive process, LLMs are capable of exactly inferring the transition probabilities between tokens across distinct tasks using provided prompts. We show that ICL enhances performance by reducing prompt ambiguity and facilitating posterior concentration on the intended task. Furthermore, we find that CoT prompting activates the model's capacity for task decomposition, breaking complex problems into a sequence of simpler sub-tasks that the model has mastered during the pretraining phase. By comparing their individual error bounds, we provide novel theoretical insights into the statistical superiority of advanced prompt engineering techniques.