# VL Norm: Rethink Loss Aggregation in RLVR

arXiv: https://arxiv.org/abs/2509.07558 · HTML: https://mlsanity.com/paper/2509.07558/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [GRPO-LEAD: A Difficulty-Aware Reinforcement Learning Approach for Concise Mathematical Reasoning in Language Models](https://mlsanity.com/paper/2504.09696/) (2025)
- [rStar2-Agent: Agentic Reasoning Technical Report](https://mlsanity.com/paper/2508.20722/) (2025)
- [Stable Reinforcement Learning for Efficient Reasoning](https://mlsanity.com/paper/2505.18086/) (2025)
- [Shorten After You're Right: Lazy Length Penalties for Reasoning RL](https://mlsanity.com/paper/2505.12284/) (2025)
- [UloRL:An Ultra-Long Output Reinforcement Learning Approach for Advancing Large Language Models' Reasoning Abilities](https://mlsanity.com/paper/2507.19766/) (2025)

## Built on by (most cited first, 4 of 4)

- [The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View](https://mlsanity.com/paper/2510.04028/) (2025)
- [Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation](https://mlsanity.com/paper/2605.21125/) (2026)
- [Think, then Score: Decoupled Reasoning and Scoring for Video Reward Modeling](https://mlsanity.com/paper/2605.05922/) (2026)
- [Group Pattern Selection Optimization: Let LRMs Pick the Right Pattern for Reasoning](https://mlsanity.com/paper/2601.07238/) (2026)

## Abstract (arXiv)

We propose VL Norm (Variance-reduced Length-dependent Normalization), a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed VL Norm not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Besides, VL Norm is easy to implement with less than 10 lines of code change. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks. When integrated into the state-of-the-art RL algorithm DAPO, it achieves up to 2.67x faster convergence on the CountDown task. Our code is public at https://github.com/zerolllin/Delta-L-Normalization.