# REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards

arXiv: https://arxiv.org/abs/2505.24760 · HTML: https://mlsanity.com/paper/2505.24760/

## Key facts

- Cited by 130 papers in the map (data through 14 Oct 2026).
- Builds on 66 of its 92 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 30 of 66)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)

## Built on by (most cited first, 30 of 130)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments](https://mlsanity.com/paper/2511.07317/) (2025)
- [Nemotron 3 Super: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2604.12374/) (2026)
- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [OptimalThinkingBench: Evaluating Over and Underthinking in LLMs](https://mlsanity.com/paper/2508.13141/) (2025)
- [Evolution Strategies at Scale: LLM Fine-Tuning Beyond Reinforcement Learning](https://mlsanity.com/paper/2509.24372/) (2025)
- [BroRL: Scaling Reinforcement Learning via Broadened Exploration](https://mlsanity.com/paper/2510.01180/) (2025)
- [MedAgentGym: A Scalable Agentic Training Environment for Code-Centric Reasoning in Biomedical Data Science](https://mlsanity.com/paper/2506.04405/) (2025)
- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [GEM: A Gym for Agentic LLMs](https://mlsanity.com/paper/2510.01051/) (2025)
- [Differential Smoothing Mitigates Sharpening and Improves LLM Reasoning](https://mlsanity.com/paper/2511.19942/) (2025)
- [Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum](https://mlsanity.com/paper/2510.00526/) (2025)
- [A Comedy of Estimators: On KL Regularization in RL Training of LLMs](https://mlsanity.com/paper/2512.21852/) (2025)
- [Scaling Agentic Reinforcement Learning for Tool-Integrated Reasoning in VLMs](https://mlsanity.com/paper/2511.19773/) (2025)
- [MemoHarness: Agent Harnesses That Learn from Experience](https://mlsanity.com/paper/2607.14159/) (2026)
- [From Code Foundation Models to Agents and Applications: A Comprehensive Survey and Practical Guide to Code Intelligence](https://mlsanity.com/paper/2511.18538/) (2025)
- [On-Policy Delta Distillation](https://mlsanity.com/paper/2607.15161/) (2026)
- [Multi-Task GRPO: Reliable LLM Reasoning Across Tasks](https://mlsanity.com/paper/2602.05547/) (2026)
- [Output Supervision Can Obfuscate the Chain of Thought](https://mlsanity.com/paper/2511.11584/) (2025)
- [SETA: Scaling Environments for Terminal Agents](https://mlsanity.com/paper/2607.10891/) (2026)
- [VisGym: Diverse, Customizable, Scalable Environments for Multimodal Agents](https://mlsanity.com/paper/2601.16973/) (2026)
- [Stable Asynchrony: Variance-Controlled Off-Policy RL for LLMs](https://mlsanity.com/paper/2602.17616/) (2026)
- [Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR](https://mlsanity.com/paper/2609.04108/) (2026)
- [Golden Goose: A Simple Trick to Synthesize Unlimited RLVR Tasks from Unverifiable Internet Text](https://mlsanity.com/paper/2601.22975/) (2026)
- [Analyzing and Improving Chain-of-Thought Monitorability Through Information Theory](https://mlsanity.com/paper/2602.18297/) (2026)
- [Seemingly Simple Planning Problems are Computationally Challenging: The Countdown Game](https://mlsanity.com/paper/2508.02900/) (2025)
- [h1: Bootstrapping LLMs to Reason over Longer Horizons via Reinforcement Learning](https://mlsanity.com/paper/2510.07312/) (2025)

## Abstract (arXiv)

We introduce Reasoning Gym (RG), a library of reasoning environments for reinforcement learning with verifiable rewards. It provides over 100 data generators and verifiers spanning multiple domains including algebra, arithmetic, computation, cognition, geometry, graph theory, logic, and various common games. Its key innovation is the ability to generate virtually infinite training data with adjustable complexity, unlike most previous reasoning datasets, which are typically fixed. This procedural generation approach allows for continuous evaluation across varying difficulty levels. Our experimental results demonstrate the efficacy of RG in both evaluating and reinforcement learning of reasoning models.