# NGRPO: Negative-enhanced Group Relative Policy Optimization

arXiv: https://arxiv.org/abs/2509.18851 · HTML: https://mlsanity.com/paper/2509.18851/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 25 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (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)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)

## Built on by (most cited first, 30 of 32)

- [Reinforce-Ada: An Adaptive Sampling Framework under Non-linear RL Objectives](https://mlsanity.com/paper/2510.04996/) (2025)
- [Don't Waste Mistakes: Leveraging Negative RL-Groups via Confidence Reweighting](https://mlsanity.com/paper/2510.08696/) (2025)
- [R3L: Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification](https://mlsanity.com/paper/2601.03715/) (2026)
- [Learning to Hint for Reinforcement Learning](https://mlsanity.com/paper/2604.00698/) (2026)
- [Robust Tool Use via Fission-GRPO: Learning to Recover from Execution Errors](https://mlsanity.com/paper/2601.15625/) (2026)
- [Progress-conditioned Group Policy Optimization for Long-Horizon Agentic Tasks](https://mlsanity.com/paper/2607.22724/) (2026)
- [Auditing Data Membership in Reinforcement Learning With Verifiable Rewards](https://mlsanity.com/paper/2511.14045/) (2025)
- [Unveiling Implicit Advantage Symmetry: Why GRPO Struggles with Exploration and Difficulty Adaptation](https://mlsanity.com/paper/2602.05548/) (2026)
- [Mid-Think: Training-Free Intermediate-Budget Reasoning via Token-Level Triggers](https://mlsanity.com/paper/2601.07036/) (2026)
- [Composition-RL: Compose Your Verifiable Prompts for Reinforcement Learning of Large Language Models](https://mlsanity.com/paper/2602.12036/) (2026)
- [Learning from Mistakes: Negative Reasoning Samples Enhance Out-of-Domain Generalization](https://mlsanity.com/paper/2601.04992/) (2026)
- [When Domains Interact: Asymmetric and Order-Sensitive Cross-Domain Effects in Reinforcement Learning for Reasoning](https://mlsanity.com/paper/2602.01365/) (2026)
- [TaoSR-AGRL: Adaptive Guided Reinforcement Learning Framework for E-commerce Search Relevance](https://mlsanity.com/paper/2510.08048/) (2025)
- [AMIR-GRPO: Inducing Implicit Preference Signals into GRPO](https://mlsanity.com/paper/2601.03661/) (2026)
- [HeaPA: Difficulty-Aware Heap Sampling and On-Policy Query Augmentation for LLM Reinforcement Learning](https://mlsanity.com/paper/2601.22448/) (2026)
- [Leveraging Error Diversity in Group Rollouts for Reinforcement Learning](https://mlsanity.com/paper/2605.17333/) (2026)
- [MMR-GRPO: Accelerating GRPO-Style Training through Diversity-Aware Reward Reweighting](https://mlsanity.com/paper/2601.09085/) (2026)
- [MDP-GRPO: Stabilized Group Relative Policy Optimization for Multi-Constraint Instruction Following](https://mlsanity.com/paper/2606.06058/) (2026)
- [RLVP: Penalize the Path, Reward the Outcome](https://mlsanity.com/paper/2607.07435/) (2026)
- [UCPO: Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2601.22648/) (2026)
- [Making Expert Reasoning Learnable with Self-Distillation](https://mlsanity.com/paper/2602.02405/) (2026)
- [MCPO: Mastery-Consolidated Policy Optimization for Large Reasoning Models](https://mlsanity.com/paper/2604.16972/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [Advantage Scale Calibration Imbalance in Group-Relative Optimization under Low-Variance Rewards: Diagnosis and Bounded Recovery](https://mlsanity.com/paper/2609.19164/) (2026)
- [MHPO: Modulated Hazard-aware Policy Optimization for Stable Reinforcement Learning](https://mlsanity.com/paper/2603.16929/) (2026)
- [CRPO: Character-centric Group Relative Policy Optimization for Role-aware Reasoning in Role-playing Agents](https://mlsanity.com/paper/2605.25511/) (2026)
- [Right Makes Might: Aligning Verified Hidden States Empowers RL Reasoning](https://mlsanity.com/paper/2606.03234/) (2026)
- [HarmTrace: Anchor-Calibrated Decoupled Optimization for Fine-Grained Target Identification in Harmful Memes](https://mlsanity.com/paper/2608.16622/) (2026)
- [Spurious Advantage Hidden in GRPO](https://mlsanity.com/paper/2609.04063/) (2026)
- [Hill Sampling for Test-Time Scaling: A Simple and Better Alternative to Repeated Sampling, Evolution, and Training](https://mlsanity.com/paper/2609.25510/) (2026)

## Abstract (arXiv)

RLVR has enhanced the reasoning capabilities of Large Language Models (LLMs) across various tasks. However, GRPO, a representative RLVR algorithm, suffers from a critical limitation: when all responses within a group are either entirely correct or entirely incorrect, the model fails to learn from these homogeneous responses. This is particularly problematic for homogeneously incorrect groups, where GRPO's advantage function yields a value of zero, leading to null gradients and the loss of valuable learning signals. To overcome this issue, we propose NGRPO (Negative-enhanced Group Relative Policy Optimization), an algorithm designed to convert homogeneous errors into robust learning signals. First, NGRPO introduces Advantage Calibration. This mechanism hypothesizes the existence of a virtual maximum-reward sample during advantage calculation, thereby altering the mean and variance of rewards within a group and ensuring that the advantages for homogeneously incorrect samples are no longer zero. Second, NGRPO employs Asymmetric Clipping, which relaxes the update magnitude for positive samples while imposing stricter constraints on that of negative samples. This serves to stabilize the exploration pressure introduced by the advantage calibration. Our experiments on Qwen2.5-Math-7B demonstrate that NGRPO significantly outperforms baselines such as PPO, GRPO, DAPO, and PSR-NSR on mathematical benchmarks including MATH500, AMC23, and AIME2025. These results validate NGRPO's ability to learn from homogeneous errors, leading to stable and substantial improvements in mathematical reasoning. Our code is available at https://github.com/nangongrui-ngr/NGRPO.