This paper delves into the capabilities of large language models (LLMs), specifically focusing on advancing the theoretical comprehension of chain-of-thought prompting. We investigate how LLMs can be effectively induced to generate a coherent chain of thoughts. To achieve this, we introduce a two-level hierarchical graphical model tailored for natural language generation. Within this framework, we establish a compelling geometrical convergence rate that gauges the likelihood of an LLM-generated chain of thoughts compared to those originating from the true language. Our findings provide a theoretical justification for the ability of LLMs to produce the correct sequence of thoughts (potentially) explaining performance gains in tasks demanding reasoning skills.

翻译：本文深入探讨大型语言模型（LLMs）的能力，特别聚焦于推进对思维链提示的理论理解。我们研究如何有效引导LLMs生成连贯的思维链。为此，我们引入了一个专为自然语言生成设计的两层层次化图模型。在此框架内，我们建立了一个具有说服力的几何收敛速率，用于衡量LLM生成的思维链相对于源自真实语言的思维链的似然度。我们的研究结果为LLMs生成正确思维序列的能力提供了理论依据，这（可能）解释了在需要推理能力的任务中观察到的性能提升。