# Noisy Data is Destructive to Reinforcement Learning with Verifiable Rewards

arXiv: https://arxiv.org/abs/2603.16140 · HTML: https://mlsanity.com/paper/2603.16140/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 25 of 25)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Are we done with ImageNet?](https://mlsanity.com/paper/2006.07159/) (2020)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [SWE-RL: Advancing LLM Reasoning via Reinforcement Learning on Open Software Evolution](https://mlsanity.com/paper/2502.18449/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [Soft Adaptive Policy Optimization](https://mlsanity.com/paper/2511.20347/) (2025)
- [UTBoost: Rigorous Evaluation of Coding Agents on SWE-Bench](https://mlsanity.com/paper/2506.09289/) (2025)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Understanding the Effects of Noise in Text-to-SQL: An Examination of the BIRD-Bench Benchmark](https://mlsanity.com/paper/2402.12243/) (2024)
- [NL2SQL-BUGs: A Benchmark for Detecting Semantic Errors in NL2SQL Translation](https://mlsanity.com/paper/2503.11984/) (2025)
- [Evaluating Cross-Domain Text-to-SQL Models and Benchmarks](https://mlsanity.com/paper/2310.18538/) (2023)
- [Noise-corrected GRPO: From Noisy Rewards to Unbiased Gradients](https://mlsanity.com/paper/2510.18924/) (2025)
- [Pervasive Annotation Errors Break Text-to-SQL Benchmarks and Leaderboards](https://mlsanity.com/paper/2601.08778/) (2026)
- [The Climb Carves Wisdom Deeper Than the Summit: On the Noisy Rewards in Learning to Reason](https://mlsanity.com/paper/2505.22653/) (2025)
- [Clip-Low Increases Entropy and Clip-High Decreases Entropy in Reinforcement Learning of Large Language Models](https://mlsanity.com/paper/2509.26114/) (2025)

## Built on by (most cited first, 5 of 5)

- [An Imperfect Verifier is Good Enough: Learning with Noisy Rewards](https://mlsanity.com/paper/2604.07666/) (2026)
- [Delay, Plateau, or Collapse: Evaluating the Impact of Systematic Verification Error on RLVR](https://mlsanity.com/paper/2605.02909/) (2026)
- [Scaling Large Reasoning Models beyond Human Supervision: A Path toward Superintelligence](https://mlsanity.com/paper/2608.31075/) (2026)
- [Multilingual Verifier Bias in RLVR: Benchmark, Rollout Diagnosis, and the Cross-Lingual Selection Bottleneck](https://mlsanity.com/paper/2608.20362/) (2026)
- [Checking the Checkers: A Synthesis of Verifier Noise and Robustness in RLVR](https://mlsanity.com/paper/2610.17824/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has driven recent capability advances of large language models across various domains. Recent studies suggest that improved RLVR algorithms allow models to learn effectively from incorrect annotations, achieving performance comparable to learning from clean data. In this work, we show that these findings are invalid because the claimed 100% noisy training data is "contaminated" with clean data. After rectifying the dataset with a rigorous re-verification pipeline, we demonstrate that noise is destructive to RLVR. We show that existing RLVR algorithm improvements fail to mitigate the impact of noise, achieving similar performance to that of the basic GRPO. Furthermore, we find that the model trained on truly incorrect annotations performs 8-10% worse than the model trained on clean data across mathematical reasoning benchmarks. Finally, we show that these findings hold for real-world noise in Text2SQL tasks, where training on real-world, human annotation errors cause 5-12% lower accuracy than clean data. Our results show that current RLVR methods cannot yet compensate for poor data quality. High-quality data remains essential.