mlsanityData to 7 Oct 2026

Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties

arXiv 2506.05744 ↗First posted 6 Jun 2025cs.AIcited by 28

On the map: LLM reasoning → Knowledge- and tool-augmented reasoning

Abstract (arXiv)

Recent large-scale reasoning models have achieved state-of-the-art performance on challenging mathematical benchmarks, yet the internal mechanisms underlying their success remain poorly understood. In this work, we introduce the notion of a reasoning graph, extracted by clustering hidden-state representations at each reasoning step, and systematically analyze three key graph-theoretic properties: cyclicity, diameter, and small-world index, across multiple tasks (GSM8K, MATH500, AIME 2024). Our findings reveal that distilled reasoning models (e.g., DeepSeek-R1-Distill-Qwen-32B) exhibit significantly more recurrent cycles (about 5 per sample), substantially larger graph diameters, and pronounced small-world characteristics (about 6x) compared to their base counterparts. Notably, these structural advantages grow with task difficulty and model capacity, with cycle detection peaking at the 14B scale and exploration diameter maximized in the 32B variant, correlating positively with accuracy. Furthermore, we show that supervised fine-tuning on an improved dataset systematically expands reasoning graph diameters in tandem with performance gains, offering concrete guidelines for dataset design aimed at boosting reasoning capabilities. By bridging theoretical insights into reasoning graph structures with practical recommendations for data construction, our work advances both the interpretability and the efficacy of large reasoning models.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning. Builds on 32 of its 75 references that are in the map. First posted on arXiv 6 Jun 2025.

Builds on

32 of 75 references.

References · 32

  1. 2017Proximal Policy Optimization Algorithmscited by 14,441
  2. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  3. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
  4. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
  5. 2024GPT-4o System Cardcited by 4,467
  6. 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,970
  7. 2024OpenAI o1 System Cardcited by 1,220
  8. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 946
  9. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 895
  10. 2025LIMO: Less is More for Reasoningcited by 488
  11. 2025Process Reinforcement through Implicit Rewardscited by 478
  12. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Modelscited by 456
20 more
  1. 2024Training Language Models to Self-Correct via Reinforcement Learningcited by 405
  2. 2024Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2cited by 381
  3. 2025Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRscited by 373
  4. 2025Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approachcited by 372
  5. 2025Demystifying Long Chain-of-Thought Reasoning in LLMscited by 323
  6. 2024VinePPO: Refining Credit Assignment in RL Training of LLMscited by 168
  7. 2025Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMscited by 162
  8. 2025The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Taskscited by 150
  9. 2025LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!cited by 132
  10. 2025Small Models Struggle to Learn from Strong Reasonerscited by 109
  11. 2024Common 7B Language Models Already Possess Strong Math Capabilitiescited by 108
  12. 2025Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thoughtcited by 108
  13. 2025OverThink: Slowdown Attacks on Reasoning LLMscited by 94
  14. 2023Strategic Reasoning with Language Modelscited by 64
  15. 2025Missing Premise exacerbates Overthinking: Are Reasoning Models losing Critical Thinking Skill?cited by 58
  16. 2024Physics of Language Models: Part 2.2, How to Learn From Mistakes on Grade-School Math Problemscited by 49
  17. 2025Understanding Aha Moments: from External Observations to Internal Mechanismscited by 48
  18. 2024Self-Explore: Enhancing Mathematical Reasoning in Language Models with Fine-grained Rewardscited by 31
  19. 2025Metastable Dynamics of Chain-of-Thought Reasoning: Provable Benefits of Search, RL and Distillationcited by 25
  20. 2025Thinking Preference Optimizationcited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 12; 2026: 16.

28 papers.

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  1. 2025RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMscited by 32
  2. 2025What Characterizes Effective Reasoning? Revisiting Length, Review, and Structure of CoTcited by 24
  3. 2025Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimizationcited by 23
  4. 2025The Geometry of Reasoning: Flowing Logics in Representation Spacecited by 21
  5. 2025Reasoning or Retrieval? A Study of Answer Attribution on Large Reasoning Modelscited by 9
  6. 2025The Shape of Reasoning: Topological Analysis of Reasoning Traces in Large Language Modelscited by 9
  7. 2026DAGGER: Distractor-Aware Graph Generation for Executable Reasoning in Math Problemscited by 9
  8. 2025Emergent Slow Thinking in LLMs as Inverse Tree Freezingcited by 8
  9. 2025ReJump: A Tree-Jump Representation for Analyzing and Improving LLM Reasoningcited by 5
  10. 2026Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failurescited by 5
  11. 2026Characterizing, Evaluating, and Optimizing Complex Reasoningcited by 5
  12. 2025Modeling Hierarchical Thinking in Large Reasoning Modelscited by 3
16 more
  1. 2026Student Guides Teacher: Weak-to-Strong Inference via Spectral Orthogonal Explorationcited by 3
  2. 2026How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMscited by 3
  3. 2026Transformers in the Dark: Navigating Unknown Search Spaces via Bandit Feedbackcited by 2
  4. 2026SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topologycited by 2
  5. 2026Dynamic Thinking-Token Selection for Efficient Reasoning in Large Reasoning Modelscited by 1
  6. 2026Boule or Baguette? A Study on Task Topology, Length Generalization, and the Benefit of Reasoning Tracescited by 1
  7. 2026Reasoning Models Know What's Important, and Encode It in Their Activationscited by 1
  8. 2026ThoughtFold: Folding Reasoning Chains via Introspective Preference Learningcited by 1
  9. 2026Diverse Thinking Schemata Elicit Better Reasoning in Large Language Modelscited by 1
  10. 2025GSM-Agent: Understanding Agentic Reasoning Using Controllable Environmentscited by 0
  11. 2025Soundness-Aware Level: A Microscopic Signature that Predicts LLM Reasoning Potentialcited by 0
  12. 2025Step-Tagging: Toward controlling the generation of Language Reasoning Models through step monitoringcited by 0
  13. 2026Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answeringcited by 0
  14. 2026Quantifying and Understanding Uncertainty in Large Reasoning Modelscited by 0
  15. 2026TRACES: Tagging Reasoning Steps for Adaptive Cost-Efficient Early-Stoppingcited by 0
  16. 2026Selecting Diverse SFT Traces Improves Post-RL Generalizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Exposing Weaknesses of Large Reasoning Models through Graph Algorithm Problems
  2. 2026From Chains to DAGs: Probing the Graph Structure of Reasoning in LLMs
  3. 2023Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning
  4. 2025Improving LLMs' Generalized Reasoning Abilities by Graph Problems
  5. 2025Rethinking and Benchmarking Large Language Models for Graph Reasoning
  6. 2026Reasoning Topology Matters: Network-of-Thought for Complex Reasoning Tasks
  7. 2025Grounding LLM Reasoning with Knowledge Graphs
  8. 2026GTA: Graph Theory Agent and Benchmark for Algorithmic Graph Reasoning with LLMs