mlsanityData to 14 Oct 2026

Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning

arXiv 2506.02867 ↗First posted 3 Jun 2025cs.AI cs.CLcited by 51

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

Key facts. Cited by 51 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 51 of its 67 references that are in the map. First posted on arXiv 3 Jun 2025.

Builds on

51 of 67 references.

Closest ancestors · 6

Same direction, newest first

  1. 2025Beyond Exponential Decay: Rethinking Error Accumulation in Large Language Models30 May
  2. 2025s1: Simple test-time scaling31 Jan
  3. 2025Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning26 Jan
  4. 2024Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability29 Nov
  5. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  6. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May

Other references · 45

  1. 2017Attention Is All You Needcited by 60,361
  2. 2024The Llama 3 Herd of Modelscited by 14,715
  3. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  4. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  5. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  6. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  8. 2024Qwen2.5 Technical Reportcited by 4,942
  9. 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
  10. 2023Let's Verify Step by Stepcited by 3,789
  11. 2023Universal and Transferable Adversarial Attacks on Aligned Language Modelscited by 3,104
  12. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,879
33 more
  1. 2022Least-to-Most Prompting Enables Complex Reasoning in Large Language Modelscited by 1,407
  2. 2020What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Examscited by 1,356
  3. 2023Representation Engineering: A Top-Down Approach to AI Transparencycited by 1,336
  4. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,210
  5. 2024Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvementcited by 1,090
  6. 2023Steering Llama 2 via Contrastive Activation Additioncited by 1,085
  7. 2022Discovering Latent Knowledge in Language Models Without Supervisioncited by 767
  8. 2022Towards Reasoning in Large Language Models: A Surveycited by 596
  9. 2019On Variational Bounds of Mutual Informationcited by 559
  10. 2022Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Spacecited by 532
  11. 2024Safety Alignment Should Be Made More Than Just a Few Tokens Deepcited by 472
  12. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 384
  13. 2025Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Modelscited by 293
  14. 2023The Unlocking Spell on Base LLMs: Rethinking Alignment via In-Context Learningcited by 257
  15. 2025When More is Less: Understanding Chain-of-Thought Length in LLMscited by 183
  16. 2025Multimodal Chain-of-Thought Reasoning: A Comprehensive Surveycited by 182
  17. 2024Do Large Language Models Latently Perform Multi-Hop Reasoning?cited by 169
  18. 2024From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Modelscited by 137
  19. 2024Rho-1: Not All Tokens Are What You Needcited by 133
  20. 2019The HSIC Bottleneck: Deep Learning without Back-Propagationcited by 77
  21. 2024Explainable and Interpretable Multimodal Large Language Models: A Comprehensive Surveycited by 52
  22. 2024TokenSHAP: Interpreting Large Language Models with Monte Carlo Shapley Value Estimationcited by 42
  23. 2024Understanding Chain-of-Thought in LLMs through Information Theorycited by 37
  24. 2024Learning to Maximize Mutual Information for Chain-of-Thought Distillationcited by 23
  25. 2024Towards Tracing Trustworthiness Dynamics: Revisiting Pre-training Period of Large Language Modelscited by 18
  26. 2024Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspectivecited by 15
  27. 2025Understanding LLM Behaviors via Compression: Data Generation, Knowledge Acquisition and Scaling Lawscited by 15
  28. 2025L2M: Mutual Information Scaling Law for Long-Context Language Modelingcited by 9
  29. 2025Saliency-driven Dynamic Token Pruning for Large Language Modelscited by 5
  30. 2024NormXLogit: The Head-on-Top Never Liescited by 4
  31. 2025Reasoning Can Hurt the Inductive Abilities of Large Language Modelscited by 4
  32. 2024Information-Theoretic Foundations for Machine Learningcited by 2
  33. 2025Revisiting Transformers through the Lens of Low Entropy and Dynamic Sparsitycited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 14; 2026: 37.

51 papers.

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  1. 2025Reasoning with Exploration: An Entropy Perspectivecited by 281
  2. 2025Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Rewardcited by 25
  3. 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signalscited by 24
  4. 2025On Predictability of Reinforcement Learning Dynamics for Large Language Modelscited by 23
  5. 2025Early Stopping Chain-of-thoughts in Large Language Modelscited by 20
  6. 2025Plan Then Action:High-Level Planning Guidance Reinforcement Learning for LLM Reasoningcited by 19
  7. 2025Trace Length is a Simple Uncertainty Signal in Reasoning Modelscited by 19
  8. 2025Do Thinking Tokens Help or Trap? Towards More Efficient Large Reasoning Modelcited by 14
  9. 2025The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic Viewcited by 13
  10. 2026On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitationcited by 13
  11. 2026Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decodingcited by 12
  12. 2025Quantile Advantage Estimation: Stabilizing RLVR for LLM Reasoningcited by 11
38 more
  1. 2026Large Reasoning Models Are (Not Yet) Multilingual Latent Reasonerscited by 9
  2. 2026Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertaintycited by 9
  3. 2026Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Modelscited by 8
  4. 2026ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spacescited by 8
  5. 2026How to Fine-Tune a Reasoning Model? A Teacher-Student Cooperation Framework to Synthesize Student-Consistent SFT Datacited by 8
  6. 2026Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoningcited by 8
  7. 2026TERMINATOR: Learning Optimal Exit Points for Early Stopping in Chain-of-Thought Reasoningcited by 6
  8. 2026Neglected Free Lunch from Post-training: Progress Advantage for LLM Agentscited by 6
  9. 2025Less is More: Improving LLM Reasoning with Minimal Test-Time Interventioncited by 5
  10. 2025From "Aha Moments" to Controllable Thinking: Toward Meta-Cognitive Reasoning in Large Reasoning Models via Decoupled Reasoning and Controlcited by 4
  11. 2025Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Modelscited by 4
  12. 2026Identifying and Transferring Reasoning-Critical Neurons: Improving LLM Inference Reliability via Activation Steeringcited by 4
  13. 2025Self-Reflective Generation at Test Timecited by 3
  14. 2025ThinkPilot: Steering Reasoning Models via Automated Think-prefixes Optimizationcited by 3
  15. 2026Limited Reasoning Space: The cage of long-horizon reasoning in LLMscited by 3
  16. 2026The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?cited by 3
  17. 2026The Truth Lies Somewhere in the Middle (of the Generated Tokens)cited by 3
  18. 2026How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMscited by 3
  19. 2026When Reasoning Leaks Membership: Membership Inference Attack on Black-box Large Reasoning Modelscited by 2
  20. 2026From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Modelscited by 2
  21. 2026Echoes as Anchors: Probabilistic Costs and Attention Refocusing in LLM Reasoningcited by 2
  22. 2026Process Supervision of Confidence Margin for Calibrated LLM Reasoningcited by 2
  23. 2026The Tell-Tale Norm: ℓ2 Magnitude as a Signal for Reasoning Dynamics in Large Language Modelscited by 2
  24. 2026PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVRcited by 2
  25. 2026Two Pathways to Truthfulness: On the Intrinsic Encoding of LLM Hallucinationscited by 1
  26. 2026"The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Frameworkcited by 1
  27. 2026Oops, Wait: Discourse Tokens Matter in Reasoning Modelcited by 1
  28. 2026Thinking Seeds: Leveraging Historical Diversity for Position-Aware RL in LLMscited by 1
  29. 2026REFINE: Real-world Exploration of Interactive Feedback and Student Behaviourcited by 1
  30. 2026Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Modelscited by 1
  31. 2026InfoMem: Training Long-Context Memory Agents with Answer-Conditioned Information Gaincited by 1
  32. 2026Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoningcited by 1
  33. 2026Attention Degradation, Function Token Anchoring, and the Limits of Attention-Based Intervention in Large Language Modelscited by 1
  34. 2026Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoningcited by 1
  35. 2026TokenSeek: Memory Efficient Fine Tuning via Instance-Aware Token Ditchingcited by 0
  36. 2026Attention-Guided Reward for Reinforcement Learning-based Jailbreak against Large Reasoning Modelscited by 0
  37. 2026PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoningcited by 0
  38. 2026Preference Tuning as Spectral Update Reorganizationcited by 0

50 most cited of 51 All 51 (JSON)

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  1. 2025The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity
  2. 2025The Evolution of Thought: Tracking LLM Overthinking via Reasoning Dynamics Analysis
  3. 2025Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens
  4. 2026Reasoning as State Transition: A Representational Analysis of Reasoning Evolution in Large Language Models
  5. 2025Scaling Competence, Shrinking Reasoning: Cognitive Signatures in Language Model Learning
  6. 2026PRISM: A Dual View of LLM Reasoning through Semantic Flow and Latent Computation
  7. 2025State over Tokens: Characterizing the Role of Reasoning Tokens
  8. 2026LLM Reasoning Is Latent, Not the Chain of Thought