# N-GRPO: Embedding-Level Neighbor Mixing for Enhanced Policy Optimization

arXiv: https://arxiv.org/abs/2606.10768 · HTML: https://mlsanity.com/paper/2606.10768/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation](https://mlsanity.com/paper/2502.21074/) (2025)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Think Silently, Think Fast: Dynamic Latent Compression of LLM Reasoning Chains](https://mlsanity.com/paper/2505.16552/) (2025)
- [Sample More to Think Less: Group Filtered Policy Optimization for Concise Reasoning](https://mlsanity.com/paper/2508.09726/) (2025)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [Soft Tokens, Hard Truths](https://mlsanity.com/paper/2509.19170/) (2025)
- [Hybrid Latent Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2505.18454/) (2025)
- [Online Preference Alignment for Language Models via Count-based Exploration](https://mlsanity.com/paper/2501.12735/) (2025)
- [Measuring Word Significance using Distributed Representations of Words](https://mlsanity.com/paper/1508.02297/) (2015)
- [SofT-GRPO: Surpassing Discrete-Token LLM Reinforcement Learning via Gumbel-Reparameterized Soft-Thinking Policy Optimization](https://mlsanity.com/paper/2511.06411/) (2025)
- [Don't Tell the Answer, Truly Guide the Reasoning During RL Rollouts](https://mlsanity.com/paper/2510.09388/) (2025)
- [SynAdapt: Learning Adaptive Reasoning in Large Language Models via Synthetic Continuous Chain-of-Thought](https://mlsanity.com/paper/2508.00574/) (2025)
- [Semantic Structure in Large Language Model Embeddings](https://mlsanity.com/paper/2508.10003/) (2025)

## Abstract (arXiv)

The success of Large Language Models in mathematical reasoning relies heavily on the generation of diverse and valid solution paths during the rollout phase. However, current rollout techniques face a fundamental trade-off: token-level sampling often yields redundant trajectories that differ only in rephrasing, while embedding-level methods utilizing random noise frequently disrupt semantic consistency. To resolve this, we introduce N-GRPO, a novel exploration strategy integrated into the Group Relative Policy Optimization (GRPO) framework. Rather than relying on token-level sampling or native embedding-level noise, our approach leverages Semantic Neighbor Mixing. This mechanism dynamically constructs input representations by mixing the embeddings of an anchor token and its nearest semantic neighbors, thereby injecting diversity while strictly adhering to the local semantic manifold. Experimental evaluations on the DeepSeek-R1-Distill-Qwen models across different sizes show that N-GRPO not only achieves consistent improvements over strong baselines on math reasoning benchmarks but also exhibits robust generalization capabilities on out-of-distribution tasks.