Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning
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
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- 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
- 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May
Other references · 45
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- 2019The HSIC Bottleneck: Deep Learning without Back-Propagationcited by 77
- 2024Explainable and Interpretable Multimodal Large Language Models: A Comprehensive Surveycited by 52
- 2024TokenSHAP: Interpreting Large Language Models with Monte Carlo Shapley Value Estimationcited by 42
- 2024Understanding Chain-of-Thought in LLMs through Information Theorycited by 37
- 2024Learning to Maximize Mutual Information for Chain-of-Thought Distillationcited by 23
- 2024Towards Tracing Trustworthiness Dynamics: Revisiting Pre-training Period of Large Language Modelscited by 18
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Citing papers per year: 2025: 14; 2026: 37.
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- 2025Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Modelscited by 4
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- 2026The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?cited by 3
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- 2026"The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Frameworkcited by 1
- 2026Oops, Wait: Discourse Tokens Matter in Reasoning Modelcited by 1
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- 2026REFINE: Real-world Exploration of Interactive Feedback and Student Behaviourcited by 1
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- 2026Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning8 Sep 2026
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- 2026Attention Degradation, Function Token Anchoring, and the Limits of Attention-Based Intervention in Large Language Models9 Jul 2026
- 2026Neglected Free Lunch from Post-training: Progress Advantage for LLM Agents24 Jun 2026
- 2026Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning18 Jun 2026
- 2026How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMs9 Jun 2026
- 2026PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVR7 Jun 2026
- 2026The Tell-Tale Norm: ℓ2 Magnitude as a Signal for Reasoning Dynamics in Large Language Models4 Jun 2026
- 2026InfoMem: Training Long-Context Memory Agents with Answer-Conditioned Information Gain2 Jun 2026
- 2026PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoning21 May 2026
- 2026Attention-Guided Reward for Reinforcement Learning-based Jailbreak against Large Reasoning Models19 May 2026
- 2026Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Models18 May 2026
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- 2026Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning20 Apr 2026
- 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals7 Apr 2026
- 2026REFINE: Real-world Exploration of Interactive Feedback and Student Behaviour31 Mar 2026
- 2026How to Fine-Tune a Reasoning Model? A Teacher-Student Cooperation Framework to Synthesize Student-Consistent SFT Data23 Mar 2026
- 2026On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation23 Mar 2026
- 2026Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertainty16 Mar 2026
- 2026TERMINATOR: Learning Optimal Exit Points for Early Stopping in Chain-of-Thought Reasoning13 Mar 2026
- 2026The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?11 Mar 2026
- 2026Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decoding9 Mar 2026
- 2026Limited Reasoning Space: The cage of long-horizon reasoning in LLMs22 Feb 2026
- 2026ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces12 Feb 2026
- 2026Echoes as Anchors: Probabilistic Costs and Attention Refocusing in LLM Reasoning6 Feb 2026
- 2026Thinking Seeds: Leveraging Historical Diversity for Position-Aware RL in LLMs29 Jan 2026
- 2026Identifying and Transferring Reasoning-Critical Neurons: Improving LLM Inference Reliability via Activation Steering27 Jan 2026
- 2026TokenSeek: Memory Efficient Fine Tuning via Instance-Aware Token Ditching27 Jan 2026
- 2026Oops, Wait: Discourse Tokens Matter in Reasoning Model24 Jan 2026
- 2026From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Models22 Jan 2026
- 2026"The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Framework20 Jan 2026
- 2026When Reasoning Leaks Membership: Membership Inference Attack on Black-box Large Reasoning Models20 Jan 2026
- 2026Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models16 Jan 2026
- 2026Two Pathways to Truthfulness: On the Intrinsic Encoding of LLM Hallucinations12 Jan 2026
- 2026Large Reasoning Models Are (Not Yet) Multilingual Latent Reasoners6 Jan 2026
- 2025Less is More: Improving LLM Reasoning with Minimal Test-Time Intervention15 Oct 2025
- 2025ThinkPilot: Steering Reasoning Models via Automated Think-prefixes Optimization14 Oct 2025
- 2025Trace Length is a Simple Uncertainty Signal in Reasoning Models12 Oct 2025
- 2025The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View5 Oct 2025
- 2025Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward3 Oct 2025
- 2025Self-Reflective Generation at Test Time3 Oct 2025
- 2025Plan Then Action:High-Level Planning Guidance Reinforcement Learning for LLM Reasoning2 Oct 2025
- 2025On Predictability of Reinforcement Learning Dynamics for Large Language Models1 Oct 2025
- 2025Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Models29 Sep 2025
- 2025Quantile Advantage Estimation: Stabilizing RLVR for LLM Reasoning26 Sep 2025
- 2025Early Stopping Chain-of-thoughts in Large Language Models17 Sep 2025
- 2025From "Aha Moments" to Controllable Thinking: Toward Meta-Cognitive Reasoning in Large Reasoning Models via Decoupled Reasoning and Control6 Aug 2025
- 2025Do Thinking Tokens Help or Trap? Towards More Efficient Large Reasoning Model30 Jun 2025
50 newest of 51 All 51 (JSON)
- 2025Reasoning with Exploration: An Entropy Perspectivecited by 281
- 2025Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Rewardcited by 25
- 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signalscited by 24
- 2025On Predictability of Reinforcement Learning Dynamics for Large Language Modelscited by 23
- 2025Early Stopping Chain-of-thoughts in Large Language Modelscited by 20
- 2025Plan Then Action:High-Level Planning Guidance Reinforcement Learning for LLM Reasoningcited by 19
- 2025Trace Length is a Simple Uncertainty Signal in Reasoning Modelscited by 19
- 2025Do Thinking Tokens Help or Trap? Towards More Efficient Large Reasoning Modelcited by 14
- 2025The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic Viewcited by 13
- 2026On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitationcited by 13
- 2026Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decodingcited by 12
- 2025Quantile Advantage Estimation: Stabilizing RLVR for LLM Reasoningcited by 11
12 most cited of 42 All 42 (JSON)
- 2026Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning8 Sep 2026
- 2026RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer6 Aug 2026
- 2026Neglected Free Lunch from Post-training: Progress Advantage for LLM Agents24 Jun 2026
- 2026Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning18 Jun 2026
- 2026How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMs9 Jun 2026
- 2026PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVR7 Jun 2026
- 2026The Tell-Tale Norm: ℓ2 Magnitude as a Signal for Reasoning Dynamics in Large Language Models4 Jun 2026
- 2026PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoning21 May 2026
- 2026Attention-Guided Reward for Reinforcement Learning-based Jailbreak against Large Reasoning Models19 May 2026
- 2026Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Models18 May 2026
- 2026Process Supervision of Confidence Margin for Calibrated LLM Reasoning25 Apr 2026
- 2026Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning20 Apr 2026
12 newest of 42 All 42 (JSON)
- 2026The Truth Lies Somewhere in the Middle (of the Generated Tokens)cited by 3
- 2026From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Modelscited by 2
- 2026Two Pathways to Truthfulness: On the Intrinsic Encoding of LLM Hallucinationscited by 1
- 2026REFINE: Real-world Exploration of Interactive Feedback and Student Behaviourcited by 1
- 2026Attention Degradation, Function Token Anchoring, and the Limits of Attention-Based Intervention in Large Language Modelscited by 1
- 2026TokenSeek: Memory Efficient Fine Tuning via Instance-Aware Token Ditchingcited by 0
- 2026Preference Tuning as Spectral Update Reorganizationcited by 0
- 2026Attention Degradation, Function Token Anchoring, and the Limits of Attention-Based Intervention in Large Language Models9 Jul 2026
- 2026Preference Tuning as Spectral Update Reorganization12 May 2026
- 2026The Truth Lies Somewhere in the Middle (of the Generated Tokens)11 May 2026
- 2026REFINE: Real-world Exploration of Interactive Feedback and Student Behaviour31 Mar 2026
- 2026TokenSeek: Memory Efficient Fine Tuning via Instance-Aware Token Ditching27 Jan 2026
- 2026From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Models22 Jan 2026
- 2026Two Pathways to Truthfulness: On the Intrinsic Encoding of LLM Hallucinations12 Jan 2026
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- 2025Scaling Competence, Shrinking Reasoning: Cognitive Signatures in Language Model Learning
- 2026PRISM: A Dual View of LLM Reasoning through Semantic Flow and Latent Computation
- 2025State over Tokens: Characterizing the Role of Reasoning Tokens
- 2026LLM Reasoning Is Latent, Not the Chain of Thought