# When Sharpening Becomes Collapse: Sampling Bias and Semantic Coupling in RL with Verifiable Rewards

arXiv: https://arxiv.org/abs/2601.15609 · HTML: https://mlsanity.com/paper/2601.15609/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (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)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Online Difficulty Filtering for Reasoning Oriented Reinforcement Learning](https://mlsanity.com/paper/2504.03380/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [Escaping Collapse: The Strength of Weak Data for Large Language Model Training](https://mlsanity.com/paper/2502.08924/) (2025)
- [Quantile Advantage Estimation: Stabilizing RLVR for LLM Reasoning](https://mlsanity.com/paper/2509.22611/) (2025)
- [Exploring Multi-Temperature Strategies for Token- and Rollout-Level Control in RLVR](https://mlsanity.com/paper/2510.08892/) (2025)

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

- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [OctoLong: Mid-Training On Cross-Repository Code Contexts Enhances Long-Context Modeling](https://mlsanity.com/paper/2608.05141/) (2026)
- [RLVR is a Kernel, Not a Function: Statistical Inference for pass@k Crossovers](https://mlsanity.com/paper/2609.22547/) (2026)
- [Beyond Distribution Sharpening: The Importance of Task Rewards](https://mlsanity.com/paper/2604.16259/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) is a central paradigm for turning large language models (LLMs) into reliable problem solvers, especially in logic-heavy domains. Despite its empirical success, it remains unclear whether RLVR elicits novel capabilities or merely sharpens the distribution over existing knowledge. We study this by formalizing over-sharpening, a phenomenon where the policy collapses onto limited modes, suppressing valid alternatives. At a high level, we discover finite-batch updates intrinsically bias learning toward sampled modes, triggering a collapse that propagates globally via semantic coupling. To mitigate this, we propose inverse-success advantage calibration to prioritize difficult queries and distribution-level calibration to diversify sampling via a memory network. Empirical evaluations validate that our strategies can effectively improve generalization.