# On the Diagram of Thought

arXiv: https://arxiv.org/abs/2409.10038 · HTML: https://mlsanity.com/paper/2409.10038/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 16 Sep 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [On the Power of Foundation Models](https://mlsanity.com/paper/2211.16327/) (2022)

## Built on by (most cited first, 16 of 16)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Atom of Thoughts for Markov LLM Test-Time Scaling](https://mlsanity.com/paper/2502.12018/) (2025)
- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Mitigating Hallucinations in Large Language Models via Causal Reasoning](https://mlsanity.com/paper/2508.12495/) (2025)
- [Blind Spot Navigation in Large Language Model Reasoning with Thought Space Explorer](https://mlsanity.com/paper/2410.24155/) (2024)
- [How Social is It? A Benchmark for LLMs' Capabilities in Multi-user Multi-turn Social Agent Tasks](https://mlsanity.com/paper/2505.04628/) (2025)
- [Typed Chain-of-Thought: A Curry-Howard Framework for Verifying LLM Reasoning](https://mlsanity.com/paper/2510.01069/) (2025)
- [Adaptive Selection of Symbolic Languages for Improving LLM Logical Reasoning](https://mlsanity.com/paper/2510.10703/) (2025)
- [MOSS: Enabling Code-Driven Evolution and Context Management for AI Agents](https://mlsanity.com/paper/2409.16120/) (2024)
- [Self-controller: Controlling LLMs with Multi-round Step-by-step Self-awareness](https://mlsanity.com/paper/2410.00359/) (2024)
- [Enhancing Cluster Resilience: LLM-agent Based Autonomous Intelligent Cluster Diagnosis System and Evaluation Framework](https://mlsanity.com/paper/2411.05349/) (2024)
- [Reasoning Systems as Structured Processes: Foundations, Failures, and Formal Criteria](https://mlsanity.com/paper/2508.01763/) (2025)
- [Joint Enhancement of Relational Reasoning for Long-Context LLMs](https://mlsanity.com/paper/2508.20351/) (2025)
- [Limit Analysis for Symbolic Multi-step Reasoning Tasks with Information Propagation Rules Based on Transformers](https://mlsanity.com/paper/2509.23178/) (2025)
- [The Neurosymbolic Frontier of Nonuniform Ellipticity: Formalizing Sharp Schauder Theory via Topos-Theoretic Reasoning Models](https://mlsanity.com/paper/2602.10632/) (2026)
- [RouteGoT: Node-Adaptive Routing for Cost-Efficient Graph of Thoughts Reasoning](https://mlsanity.com/paper/2603.05818/) (2026)

## Abstract (arXiv)

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.