# Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning

arXiv: https://arxiv.org/abs/2502.14768 · HTML: https://mlsanity.com/paper/2502.14768/

## Key facts

- Cited by 262 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 0 of its 24 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Placed in

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

## Built on by (most cited first, 30 of 262)

- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Video-R1: Reinforcing Video Reasoning in MLLMs](https://mlsanity.com/paper/2503.21776/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [WebThinker: Empowering Large Reasoning Models with Deep Research Capability](https://mlsanity.com/paper/2504.21776/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Reinforcement Learning with Rubric Anchors](https://mlsanity.com/paper/2508.12790/) (2025)
- [Agent Lightning: Train ANY AI Agents with Reinforcement Learning](https://mlsanity.com/paper/2508.03680/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [CPPO: Accelerating the Training of Group Relative Policy Optimization-Based Reasoning Models](https://mlsanity.com/paper/2503.22342/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning](https://mlsanity.com/paper/2506.06632/) (2025)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [ReMA: Learning to Meta-think for LLMs with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2503.09501/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)
- [R1-Reward: Training Multimodal Reward Model Through Stable Reinforcement Learning](https://mlsanity.com/paper/2505.02835/) (2025)
- [A Survey on (M)LLM-Based GUI Agents](https://mlsanity.com/paper/2504.13865/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [One Token to Fool LLM-as-a-Judge](https://mlsanity.com/paper/2507.08794/) (2025)
- [UFT: Unifying Supervised and Reinforcement Fine-Tuning](https://mlsanity.com/paper/2505.16984/) (2025)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)

## Abstract (arXiv)

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.