On the Diagram of Thought
Authors: name: Yifan Zhang, name: Yang Yuan, name: Andrew Chi-Chih Yao
Organization: math-ai

We introduce Diagram of Thought (DoT), a framework that models iterative
reasoning in large language models (LLMs) as the construction of a directed
acyclic graph (DAG) within a single model. Unlike traditional approaches that
represent reasoning as linear chains or trees, DoT organizes propositions,
critiques, refinements, and verifications into a cohesive DAG structure,
allowing the model to explore complex reasoning pathways while maintaining
logical consistency. Each node in the diagram corresponds to a proposition that
has been proposed, critiqued, refined, or verified, enabling the LLM to
iteratively improve its reasoning through natural language feedback. By
leveraging auto-regressive next-token prediction with role-specific tokens, DoT
facilitates seamless transitions between proposing ideas and critically
evaluating them, providing richer feedback than binary signals. Furthermore, we
formalize the DoT framework using Topos Theory, providing a mathematical
foundation that ensures logical consistency and soundness in the reasoning
process. This approach enhances both the training and inference processes
within a single LLM, eliminating the need for multiple models or external
control mechanisms. DoT offers a conceptual framework for designing
next-generation reasoning-specialized models, emphasizing training efficiency,
robust reasoning capabilities, and theoretical grounding. The code is available
at https://github.com/diagram-of-thought/diagram-of-thought.