On the Diagram of Thought

TL;DR

The paper introduces the Diagram of Thought (DoT), a framework enabling LLMs to build and navigate structured reasoning diagrams, improving multi-step problem-solving without external search algorithms.

Contribution

It presents a novel diagram-based reasoning framework grounded in category theory, allowing LLMs to generate auditable, step-by-step reasoning traces with formal guarantees.

Findings

DoT improves LLM reasoning on complex tasks.

Formalism provides auditable and reliable reasoning traces.

Framework is grounded in category theory for semantic guarantees.

Abstract

Large Language Models (LLMs) excel at many tasks but often falter on complex problems that require structured, multi-step reasoning. We introduce the Diagram of Thought (DoT), a framework that enables a single LLM to build and navigate a mental map of its reasoning. Instead of thinking in a straight line, the model constructs a dynamic diagram of ideas, where it can propose different lines of thought, critique its own steps, and synthesize validated insights into a final conclusion. This process is controller-light: it does not require an external search algorithm or planner, but it does use a deterministic online validator for grammar-constrained typed traces, register constraints, and optional solver checks. To clarify the reliability target of this process, we ground DoT in a mathematical framework from category theory. We interpret accepted typed reasoning records as diagrams in a slice topos and model synthesis of the selected proposer subdiagram as a finite limit. In the predicate fragment, this same object is equivalently a variance-reversed colimit in the opposite information order. The resulting formalism gives an auditable, step-by-step trace of the LLM's typed reasoning and separates semantic guarantees for the typed subtrace from unconstrained natural-language text and uncertified operational edges.