# R^3: Replay, Reflection, and Ranking Rewards for LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2601.19620 · HTML: https://mlsanity.com/paper/2601.19620/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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 Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret](https://mlsanity.com/paper/2503.01491/) (2025)
- [Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't](https://mlsanity.com/paper/2503.16219/) (2025)
- [Skywork R1V2: Multimodal Hybrid Reinforcement Learning for Reasoning](https://mlsanity.com/paper/2504.16656/) (2025)
- [First Return, Entropy-Eliciting Explore](https://mlsanity.com/paper/2507.07017/) (2025)
- [RLEP: Reinforcement Learning with Experience Replay for LLM Reasoning](https://mlsanity.com/paper/2507.07451/) (2025)
- [FastCuRL: Curriculum Reinforcement Learning with Stage-wise Context Scaling for Efficient Training R1-like Reasoning Models](https://mlsanity.com/paper/2503.17287/) (2025)
- [Towards Effective Code-Integrated Reasoning](https://mlsanity.com/paper/2505.24480/) (2025)
- [EFRame: Deeper Reasoning via Exploration-Filter-Replay Reinforcement Learning Framework](https://mlsanity.com/paper/2506.22200/) (2025)
- [Thinker: Learning to Think Fast and Slow](https://mlsanity.com/paper/2505.21097/) (2025)
- [SATURN: SAT-based Reinforcement Learning to Unleash LLMs Reasoning](https://mlsanity.com/paper/2505.16368/) (2025)
- [Relative Entropy Pathwise Policy Optimization](https://mlsanity.com/paper/2507.11019/) (2025)

## Built on by (most cited first, 2 of 2)

- [How Mobile World Model Guides GUI Agents?](https://mlsanity.com/paper/2605.10347/) (2026)
- [AppDeltaWorld: Transition-Grounded Delta Code World Model for Mobile GUI Agents](https://mlsanity.com/paper/2608.05891/) (2026)

## Abstract (arXiv)

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named emphR3 that along three directions: (1) a emphcross-context underlineReplay strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an emphin-context self-underlineReflection mechanism enabling models to refine outputs by leveraging past failures, and (3) a emphstructural entropy underlineRanking reward, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.