# Explore Data Left Behind in Reinforcement Learning for Reasoning Language Models

arXiv: https://arxiv.org/abs/2511.04800 · HTML: https://mlsanity.com/paper/2511.04800/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 44 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Coverage-centric Coreset Selection for High Pruning Rates](https://mlsanity.com/paper/2210.15809/) (2022)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [Sample More to Think Less: Group Filtered Policy Optimization for Concise Reasoning](https://mlsanity.com/paper/2508.09726/) (2025)
- [SRPO: A Cross-Domain Implementation of Large-Scale Reinforcement Learning on LLM](https://mlsanity.com/paper/2504.14286/) (2025)
- [Parallel-R1: Towards Parallel Thinking via Reinforcement Learning](https://mlsanity.com/paper/2509.07980/) (2025)
- [Your Vision-Language Model Itself Is a Strong Filter: Towards High-Quality Instruction Tuning with Data Selection](https://mlsanity.com/paper/2402.12501/) (2024)
- [First Return, Entropy-Eliciting Explore](https://mlsanity.com/paper/2507.07017/) (2025)
- [DCPO: Dynamic Clipping Policy Optimization](https://mlsanity.com/paper/2509.02333/) (2025)

## Built on by (most cited first, 7 of 7)

- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [Learning from Mistakes: Negative Reasoning Samples Enhance Out-of-Domain Generalization](https://mlsanity.com/paper/2601.04992/) (2026)
- [Know What You Know: Metacognitive Entropy Calibration for Verifiable RL Reasoning](https://mlsanity.com/paper/2602.22751/) (2026)
- [CAST: Non-Privileged Clipped Asymmetric Self-Teaching with Advantage Flipping for GRPO](https://mlsanity.com/paper/2606.00172/) (2026)
- [Learning from Self-Debate: Preparing Reasoning Models for Multi-Agent Debate](https://mlsanity.com/paper/2601.22297/) (2026)
- [CuSearch: Curriculum Rollout Sampling via Search Depth for Agentic RAG](https://mlsanity.com/paper/2605.11611/) (2026)
- [Prompts Live on an Arc: Gaussian Curricula in Fisher--Rao Coordinates for Rollout-Efficient GRPO](https://mlsanity.com/paper/2609.38018/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for improving the reasoning abilities of large language models (LLMs). The Group Relative Policy Optimization (GRPO) family has demonstrated strong performance in training LLMs with RLVR. However, as models train longer and scale larger, more training prompts become residual prompts, those with zero variance rewards that provide no training signal. Consequently, fewer prompts contribute to training, reducing diversity and hindering effectiveness. To fully exploit these residual prompts, we propose the Explore Residual Prompts in Policy Optimization (ERPO) framework, which encourages exploration on residual prompts and reactivates their training signals. ERPO maintains a history tracker for each prompt and adaptively increases the sampling temperature for residual prompts that previously produced all correct responses. This encourages the model to generate more diverse reasoning traces, introducing incorrect responses that revive training signals. Empirical results on the Qwen2.5 series demonstrate that ERPO consistently surpasses strong baselines across multiple mathematical reasoning benchmarks.