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

arXiv: https://arxiv.org/abs/2506.02867 · HTML: https://mlsanity.com/paper/2506.02867/

## 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.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [The Unlocking Spell on Base LLMs: Rethinking Alignment via In-Context Learning](https://mlsanity.com/paper/2312.01552/) (2023)
- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)

## Built on by (most cited first, 30 of 51)

- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2510.03222/) (2025)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [On Predictability of Reinforcement Learning Dynamics for Large Language Models](https://mlsanity.com/paper/2510.00553/) (2025)
- [Early Stopping Chain-of-thoughts in Large Language Models](https://mlsanity.com/paper/2509.14004/) (2025)
- [Plan Then Action:High-Level Planning Guidance Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2510.01833/) (2025)
- [Trace Length is a Simple Uncertainty Signal in Reasoning Models](https://mlsanity.com/paper/2510.10409/) (2025)
- [Do Thinking Tokens Help or Trap? Towards More Efficient Large Reasoning Model](https://mlsanity.com/paper/2506.23840/) (2025)
- [The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View](https://mlsanity.com/paper/2510.04028/) (2025)
- [On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation](https://mlsanity.com/paper/2603.22117/) (2026)
- [Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decoding](https://mlsanity.com/paper/2603.13366/) (2026)
- [Quantile Advantage Estimation: Stabilizing RLVR for LLM Reasoning](https://mlsanity.com/paper/2509.22611/) (2025)
- [Large Reasoning Models Are (Not Yet) Multilingual Latent Reasoners](https://mlsanity.com/paper/2601.02996/) (2026)
- [Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertainty](https://mlsanity.com/paper/2603.15500/) (2026)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces](https://mlsanity.com/paper/2602.11683/) (2026)
- [How to Fine-Tune a Reasoning Model? A Teacher-Student Cooperation Framework to Synthesize Student-Consistent SFT Data](https://mlsanity.com/paper/2604.14164/) (2026)
- [Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning](https://mlsanity.com/paper/2604.18419/) (2026)
- [TERMINATOR: Learning Optimal Exit Points for Early Stopping in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2603.12529/) (2026)
- [Neglected Free Lunch from Post-training: Progress Advantage for LLM Agents](https://mlsanity.com/paper/2606.26080/) (2026)
- [Less is More: Improving LLM Reasoning with Minimal Test-Time Intervention](https://mlsanity.com/paper/2510.13940/) (2025)
- [From "Aha Moments" to Controllable Thinking: Toward Meta-Cognitive Reasoning in Large Reasoning Models via Decoupled Reasoning and Control](https://mlsanity.com/paper/2508.04460/) (2025)
- [Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Models](https://mlsanity.com/paper/2509.24711/) (2025)
- [Identifying and Transferring Reasoning-Critical Neurons: Improving LLM Inference Reliability via Activation Steering](https://mlsanity.com/paper/2601.19847/) (2026)
- [Self-Reflective Generation at Test Time](https://mlsanity.com/paper/2510.02919/) (2025)
- [ThinkPilot: Steering Reasoning Models via Automated Think-prefixes Optimization](https://mlsanity.com/paper/2510.12063/) (2025)
- [Limited Reasoning Space: The cage of long-horizon reasoning in LLMs](https://mlsanity.com/paper/2602.19281/) (2026)
- [The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?](https://mlsanity.com/paper/2604.06192/) (2026)
- [The Truth Lies Somewhere in the Middle (of the Generated Tokens)](https://mlsanity.com/paper/2605.09969/) (2026)
- [How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMs](https://mlsanity.com/paper/2606.10646/) (2026)

## 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.