# Understanding Chain-of-Thought in LLMs through Information Theory

arXiv: https://arxiv.org/abs/2411.11984 · HTML: https://mlsanity.com/paper/2411.11984/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 16 of 16)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [Impact of Pretraining Term Frequencies on Few-Shot Reasoning](https://mlsanity.com/paper/2202.07206/) (2022)
- [LogiQA: A Challenge Dataset for Machine Reading Comprehension with Logical Reasoning](https://mlsanity.com/paper/2007.08124/) (2020)
- [Multi-step Problem Solving Through a Verifier: An Empirical Analysis on Model-induced Process Supervision](https://mlsanity.com/paper/2402.02658/) (2024)
- [Beyond Words: A Mathematical Framework for Interpreting Large Language Models](https://mlsanity.com/paper/2311.03033/) (2023)

## Built on by (most cited first, 30 of 37)

- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning](https://mlsanity.com/paper/2501.15602/) (2025)
- [Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens](https://mlsanity.com/paper/2505.18237/) (2025)
- [Benchmarking Reasoning Robustness in Large Language Models](https://mlsanity.com/paper/2503.04550/) (2025)
- [Entropy-based Exploration Conduction for Multi-step Reasoning](https://mlsanity.com/paper/2503.15848/) (2025)
- [Understanding Agent Scaling in LLM-Based Multi-Agent Systems via Diversity](https://mlsanity.com/paper/2602.03794/) (2026)
- [Landscape of Thoughts: Visualizing the Reasoning Process of Large Language Models](https://mlsanity.com/paper/2503.22165/) (2025)
- [Entropy After </Think> for reasoning model early exiting](https://mlsanity.com/paper/2509.26522/) (2025)
- [Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.09853/) (2025)
- [Unlocking the Power of Multi-Agent LLM for Reasoning: From Lazy Agents to Deliberation](https://mlsanity.com/paper/2511.02303/) (2025)
- [PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains](https://mlsanity.com/paper/2508.21787/) (2025)
- [Analyzing and Improving Chain-of-Thought Monitorability Through Information Theory](https://mlsanity.com/paper/2602.18297/) (2026)
- [Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertainty](https://mlsanity.com/paper/2603.15500/) (2026)
- [Translate Policy to Language: Flow Matching Generated Rewards for LLM Explanations](https://mlsanity.com/paper/2502.12530/) (2025)
- [Reasoning or Overthinking: Evaluating Large Language Models on Financial Sentiment Analysis](https://mlsanity.com/paper/2506.04574/) (2025)
- [Beyond In-Distribution Success: Scaling Curves of CoT Granularity for Language Model Generalization](https://mlsanity.com/paper/2502.18273/) (2025)
- [Decoupling Knowledge and Reasoning in LLMs: An Exploration Using Cognitive Dual-System Theory](https://mlsanity.com/paper/2507.18178/) (2025)
- [PRInTS: Reward Modeling for Long-Horizon Information Seeking](https://mlsanity.com/paper/2511.19314/) (2025)
- [Reasoning Can Hurt the Inductive Abilities of Large Language Models](https://mlsanity.com/paper/2505.24225/) (2025)
- [Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought](https://mlsanity.com/paper/2509.04027/) (2025)
- [Pinpointing crucial steps: Attribution-based Credit Assignment for Verifiable Reinforcement Learning](https://mlsanity.com/paper/2510.08899/) (2025)
- [The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?](https://mlsanity.com/paper/2604.06192/) (2026)
- [How Far Ahead Do LLMs Plan? Uncovering the Latent Horizon in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.02103/) (2026)
- [GRACE: Step-Level Benchmark for Faithful Reasoning over Context](https://mlsanity.com/paper/2606.16151/) (2026)
- [Understanding Generalization in Role-Playing Models via Information Theory](https://mlsanity.com/paper/2512.17270/) (2025)
- [SCA: Segment-Wise CoT Compression with Answer Alignment](https://mlsanity.com/paper/2603.07598/) (2026)
- [Reasoning as Compression: Unifying Budget Forcing via the Conditional Information Bottleneck](https://mlsanity.com/paper/2603.08462/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have shown impressive performance in complex reasoning tasks through the use of Chain-of-Thought (CoT) reasoning, allowing models to break down problems into manageable sub-tasks. However, existing CoT evaluation techniques either require annotated CoT data or fall short in accurately assessing intermediate reasoning steps, leading to high rates of false positives. In this paper, we formalize CoT reasoning in LLMs through an information-theoretic lens. Specifically, our framework quantifies the `information-gain' at each reasoning step, enabling the identification of failure modes in LLMs without the need for expensive annotated datasets. We demonstrate the efficacy of our approach through extensive experiments on toy arithmetic, GSM8K and PRM800k datasets, where it significantly outperforms existing outcome-based methods by providing more accurate insights into model performance on individual subtasks.