# L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning

arXiv: https://arxiv.org/abs/2503.04697 · HTML: https://mlsanity.com/paper/2503.04697/

## Key facts

- Cited by 384 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 24 of its 29 references that are in the map.
- First posted on arXiv 6 Mar 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, 24 of 24)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (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)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [A Long Way to Go: Investigating Length Correlations in RLHF](https://mlsanity.com/paper/2310.03716/) (2023)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs](https://mlsanity.com/paper/2501.18585/) (2025)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [C3oT: Generating Shorter Chain-of-Thought without Compromising Effectiveness](https://mlsanity.com/paper/2412.11664/) (2024)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Following Length Constraints in Instructions](https://mlsanity.com/paper/2406.17744/) (2024)
- [Prompt-Based Length Controlled Generation with Reinforcement Learning](https://mlsanity.com/paper/2308.12030/) (2023)
- [Precise Length Control in Large Language Models](https://mlsanity.com/paper/2412.11937/) (2024)

## Built on by (most cited first, 30 of 384)

- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [UI-R1: Enhancing Efficient Action Prediction of GUI Agents by Reinforcement Learning](https://mlsanity.com/paper/2503.21620/) (2025)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning](https://mlsanity.com/paper/2504.07128/) (2025)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [AdaCoT: Pareto-Optimal Adaptive Chain-of-Thought Triggering via Reinforcement Learning](https://mlsanity.com/paper/2505.11896/) (2025)
- [Acting Less is Reasoning More! Teaching Model to Act Efficiently](https://mlsanity.com/paper/2504.14870/) (2025)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [Sample More to Think Less: Group Filtered Policy Optimization for Concise Reasoning](https://mlsanity.com/paper/2508.09726/) (2025)
- [Quantization Hurts Reasoning? An Empirical Study on Quantized Reasoning Models](https://mlsanity.com/paper/2504.04823/) (2025)
- [ShorterBetter: Guiding Reasoning Models to Find Optimal Inference Length for Efficient Reasoning](https://mlsanity.com/paper/2504.21370/) (2025)
- [Effectively Controlling Reasoning Models through Thinking Intervention](https://mlsanity.com/paper/2503.24370/) (2025)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Learning When to Think: Shaping Adaptive Reasoning in R1-Style Models via Multi-Stage RL](https://mlsanity.com/paper/2505.10832/) (2025)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)
- [Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging](https://mlsanity.com/paper/2503.20641/) (2025)
- [Missing Premise exacerbates Overthinking: Are Reasoning Models losing Critical Thinking Skill?](https://mlsanity.com/paper/2504.06514/) (2025)

## Abstract (arXiv)

Reasoning language models have shown an uncanny ability to improve performance at test-time by ``thinking longer''-that is, by generating longer chain-of-thought sequences and hence using more compute. However, the length of their chain-of-thought reasoning is not controllable, making it impossible to allocate test-time compute to achieve a desired level of performance. We introduce Length Controlled Policy Optimization (LCPO), a simple reinforcement learning method that optimizes for accuracy and adherence to user-specified length constraints. We use LCPO to train L1, a reasoning language model that produces outputs satisfying a length constraint given in its prompt. L1's length control allows for smoothly trading off computational cost and accuracy on a wide range of tasks, and outperforms the state-of-the-art S1 method for length control. Furthermore, we uncover an unexpected short chain-of-thought capability in models trained with LCPO. Specifically, using LCPO we derive Short Reasoning Models (SRMs), that exhibit similar reasoning patterns as full-length reasoning models, but can generate CoT lengths comparable to non-reasoning models. They demonstrate significant performance gains, for instance, our 1.5B L1 model surpasses GPT-4o at equal reasoning lengths. Overall, LCPO enables precise control over reasoning length, allowing for fine-grained allocation of test-time compute and accuracy. We release code and models at https://www.cmu-l3.github.io/l1