# Learning to Maximize Mutual Information for Chain-of-Thought Distillation

arXiv: https://arxiv.org/abs/2403.03348 · HTML: https://mlsanity.com/paper/2403.03348/

## Key facts

- Cited by 23 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 9 of its 60 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 9 of 9)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [Universal Language Model Fine-tuning for Text Classification](https://mlsanity.com/paper/1801.06146/) (2018)
- [Sci-CoT: Leveraging Large Language Models for Enhanced Knowledge Distillation in Small Models for Scientific QA](https://mlsanity.com/paper/2308.04679/) (2023)

## Built on by (most cited first, 23 of 23)

- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [SciReplicate-Bench: Benchmarking LLMs in Agent-driven Algorithmic Reproduction from Research Papers](https://mlsanity.com/paper/2504.00255/) (2025)
- [Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models](https://mlsanity.com/paper/2503.17523/) (2025)
- [AgentDistill: Training-Free Agent Distillation with Generalizable MCP Boxes](https://mlsanity.com/paper/2506.14728/) (2025)
- [Distilling Reasoning Ability from Large Language Models with Adaptive Thinking](https://mlsanity.com/paper/2404.09170/) (2024)
- [Knowledge Distillation Using Frontier Open-source LLMs: Generalizability and the Role of Synthetic Data](https://mlsanity.com/paper/2410.18588/) (2024)
- [Activation-Guided Consensus Merging for Large Language Models](https://mlsanity.com/paper/2505.14009/) (2025)
- [QCRD: Quality-guided Contrastive Rationale Distillation for Large Language Models](https://mlsanity.com/paper/2405.13014/) (2024)
- [Data-Centric Human Preference with Rationales for Direct Preference Alignment](https://mlsanity.com/paper/2407.14477/) (2024)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [Pedagogically-Inspired Data Synthesis for Language Model Knowledge Distillation](https://mlsanity.com/paper/2602.12172/) (2026)
- [Predicting Through Generation: Why Generation Is Better for Prediction](https://mlsanity.com/paper/2502.17817/) (2025)
- [Kongzi: A Historical Large Language Model with Fact Enhancement](https://mlsanity.com/paper/2504.09488/) (2025)
- [Honey, I Shrunk the Language Model: Impact of Knowledge Distillation Methods on Performance and Explainability](https://mlsanity.com/paper/2504.16056/) (2025)
- [Shorthand for Thought: Compressing LLM Reasoning via Entropy-Guided Supertokens](https://mlsanity.com/paper/2604.26355/) (2026)
- [FALCON: Fine-grained Activation Manipulation by Contrastive Orthogonal Unalignment for Large Language Model](https://mlsanity.com/paper/2502.01472/) (2025)
- [FedCoT: Communication-Efficient Federated Reasoning Enhancement for Large Language Models](https://mlsanity.com/paper/2508.10020/) (2025)
- [What's on My Network? Using Large Language Models to Identify Real-World IoT Devices at Scale](https://mlsanity.com/paper/2510.13817/) (2025)
- [Breaking Memorization Barriers in LLM Code Fine-Tuning via Information Bottleneck for Improved Generalization](https://mlsanity.com/paper/2510.16022/) (2025)
- ["The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Framework](https://mlsanity.com/paper/2601.13992/) (2026)
- [GEM: Generative Entropy-Guided Preference Modeling for Few-shot Alignment of LLMs](https://mlsanity.com/paper/2511.13007/) (2025)
- [Know Thyself, Teach Thyself: Internal Information Flow for Selective Self-Distillation](https://mlsanity.com/paper/2609.36695/) (2026)

## Abstract (arXiv)

Knowledge distillation, the technique of transferring knowledge from large, complex models to smaller ones, marks a pivotal step towards efficient AI deployment. Distilling Step-by-Step~(DSS), a novel method utilizing chain-of-thought~(CoT) distillation, has demonstrated promise by imbuing smaller models with the superior reasoning capabilities of their larger counterparts. In DSS, the distilled model acquires the ability to generate rationales and predict labels concurrently through a multi-task learning framework. However, DSS overlooks the intrinsic relationship between the two training tasks, leading to ineffective integration of CoT knowledge with the task of label prediction. To this end, we investigate the mutual relationship of the two tasks from Information Bottleneck perspective and formulate it as maximizing the mutual information of the representation features of the two tasks. We propose a variational approach to solve this optimization problem using a learning-based method. Our experimental results across four datasets demonstrate that our method outperforms the state-of-the-art DSS. Our findings offer insightful guidance for future research on language model distillation as well as applications involving CoT. Codes are available at urlhttps://github.com/xinchen9/cotdistillationACL2024.