  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.
