# Learning to Think: Information-Theoretic Reinforcement Fine-Tuning for LLMs

arXiv: https://arxiv.org/abs/2505.10425 · HTML: https://mlsanity.com/paper/2505.10425/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 67 references that are in the map.
- First posted on arXiv 15 May 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 15 of 15)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [CodeXGLUE: A Machine Learning Benchmark Dataset for Code Understanding and Generation](https://mlsanity.com/paper/2102.04664/) (2021)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [The relationship between reasoning and performance in large language models--o3 (mini) thinks harder, not longer](https://mlsanity.com/paper/2502.15631/) (2025)
- [On the Emergence of Thinking in LLMs I: Searching for the Right Intuition](https://mlsanity.com/paper/2502.06773/) (2025)

## Built on by (most cited first, 16 of 16)

- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [Thinking Beyond Tokens: From Brain-Inspired Intelligence to Cognitive Foundations for Artificial General Intelligence and its Societal Impact](https://mlsanity.com/paper/2507.00951/) (2025)
- [Rectifying LLM Thought from Lens of Optimization](https://mlsanity.com/paper/2512.01925/) (2025)
- [On the Plasticity and Stability for Post-Training Large Language Models](https://mlsanity.com/paper/2602.06453/) (2026)
- [CogniSQL-R1-Zero: Lightweight Reinforced Reasoning for Efficient SQL Generation](https://mlsanity.com/paper/2507.06013/) (2025)
- [Concept than Document: Context Compression via AMR-based Conceptual Entropy](https://mlsanity.com/paper/2511.18832/) (2025)
- [Efficient Paths and Dense Rewards: Probabilistic Flow Reasoning for Large Language Models](https://mlsanity.com/paper/2601.09260/) (2026)
- [From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2601.15690/) (2026)
- [SAT: Balancing Reasoning Accuracy and Efficiency with Stepwise Adaptive Thinking](https://mlsanity.com/paper/2604.07922/) (2026)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [Towards Generalizable Reasoning: Group Causal Counterfactual Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2602.06475/) (2026)
- [Design-MLLM: A Reinforcement Alignment Framework for Verifiable and Aesthetic Interior Design](https://mlsanity.com/paper/2603.13312/) (2026)
- [CAMD: Coverage-Aware Multimodal Decoding for Efficient Reasoning of Multimodal Large Language Models](https://mlsanity.com/paper/2603.14745/) (2026)
- [A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions](https://mlsanity.com/paper/2604.17312/) (2026)
- [When Less is Enough: Efficient Inference via Collaborative Reasoning](https://mlsanity.com/paper/2605.01111/) (2026)
- [Pareto-Guided Optimal Transport for Multi-Reward Alignment](https://mlsanity.com/paper/2605.13155/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel at complex tasks thanks to advances in their reasoning abilities. However, existing methods overlook the trade-off between reasoning effectiveness and efficiency, often encouraging unnecessarily long reasoning chains and wasting tokens. To address this, we propose Learning to Think (L2T), an information-theoretic reinforcement fine-tuning framework for LLMs to make the models achieve optimal reasoning with fewer tokens. Specifically, L2T treats each query-response interaction as a hierarchical session of multiple episodes and proposes a universal dense process reward, i.e., quantifies the episode-wise information gain in parameters, requiring no extra annotations or task-specific evaluators. We propose a method to quickly estimate this reward based on PAC-Bayes bounds and the Fisher information matrix. Theoretical analyses show that it significantly reduces computational complexity with high estimation accuracy. By immediately rewarding each episode's contribution and penalizing excessive updates, L2T optimizes the model via reinforcement learning to maximize the use of each episode and achieve effective updates. Empirical results on various reasoning benchmarks and base models demonstrate the advantage of L2T across different tasks, boosting both reasoning effectiveness and efficiency.