On the Diagram of Thought

Current large language models (LLMs) demonstrate impressive capabilities but struggle with complex, multi-step reasoning tasks. Existing methods often tackle this by requiring external control mechanisms or multi-model orchestration, which introduces system complexity and typically lacks formal guarantees of reasoning soundness. We introduce the Diagram of Thought (DoT), a framework wherein a single auto-regressive LLM internally constructs and navigates a Directed Acyclic Graph (DAG). This DAG represents the iterative reasoning process, encompassing steps like proposing ideas, critiquing them, refining based on feedback, and synthesizing conclusions. This self-orchestrated, self-contained process is guided by learned role-specific tokens (e.g., <proposer>, <critic>, <summarizer>) embedded within the standard generation loop, thereby eliminating external dependencies. Crucially, we establish a rigorous mathematical foundation for DoT using Topos Theory. We formalize the reasoning DAG as a diagram within a suitable topos and prove that the final synthesis step, aggregating validated information, corresponds semantically to computing the colimit of the relevant sub-diagram. This formalization provides theoretical guarantees concerning the logical consistency and robustness of the synthesized outcome. DoT thus offers a unified, self-contained, interpretable, efficient, and formally grounded approach designed to significantly advance the complex reasoning capabilities of LLMs.