Why Can Large Language Models Generate Correct Chain-of-Thoughts?

TL;DR

This paper provides a theoretical framework explaining how large language models can generate correct chains of thought, shedding light on their reasoning capabilities and performance improvements in complex tasks.

Contribution

It introduces a hierarchical graphical model and establishes a convergence rate to theoretically justify LLMs' ability to produce accurate reasoning sequences.

Findings

The model explains the likelihood of correct chain-of-thought generation.

A geometrical convergence rate is established for LLM reasoning.

The framework offers a theoretical basis for LLM reasoning performance.

Abstract

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.