# Less Noise, More Voice: Reinforcement Learning for Reasoning via Instruction Purification

arXiv: https://arxiv.org/abs/2601.21244 · HTML: https://mlsanity.com/paper/2601.21244/

## 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 30 of its 42 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

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

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

- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (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)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [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)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [Dense Reward for Free in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2402.00782/) (2024)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping](https://mlsanity.com/paper/2509.21880/) (2025)
- [Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration](https://mlsanity.com/paper/2508.13755/) (2025)
- [Dealing with Sparse Rewards in Reinforcement Learning](https://mlsanity.com/paper/1910.09281/) (2019)
- [Reinforce-Ada: An Adaptive Sampling Framework under Non-linear RL Objectives](https://mlsanity.com/paper/2510.04996/) (2025)
- [Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimization](https://mlsanity.com/paper/2510.13554/) (2025)
- [GTPO and GRPO-S: Token and Sequence-Level Reward Shaping with Policy Entropy](https://mlsanity.com/paper/2508.04349/) (2025)
- [MA-RLHF: Reinforcement Learning from Human Feedback with Macro Actions](https://mlsanity.com/paper/2410.02743/) (2024)
- [Mitigating Reward Over-Optimization in RLHF via Behavior-Supported Regularization](https://mlsanity.com/paper/2503.18130/) (2025)
- [Learning to Focus: Causal Attention Distillation via Gradient-Guided Token Pruning](https://mlsanity.com/paper/2506.07851/) (2025)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced LLM reasoning, but remains constrained by inefficient exploration under limited rollout budgets, leading to low sampling success and unstable training in complex tasks. We find that many exploration failures arise not from problem difficulty, but from a small number of prompt tokens that introduce interference. Building on this insight, we propose the Less Noise Sampling Framework (LENS), which first prompts by identifying and removing interference tokens. then transfers successful rollouts from the purification process to supervise policy optimization on the original noisy prompts, enabling the model to learn to ignore interference in the real-world, noisy prompting settings. Experimental results show that LENS significantly outperforms GRPO, delivering higher performance and faster convergence, with a 3.88% average gain and over 1.6× speedup on math reasoning, and a 1.83% gain on scientific and general reasoning. Our work highlights the critical role of pruning interference tokens in improving rollout efficiency, offering a new perspective for RLVR research.