# Pass@k Metric for RLVR: A Diagnostic Tool of Exploration, But Not an Objective

arXiv: https://arxiv.org/abs/2511.16231 · HTML: https://mlsanity.com/paper/2511.16231/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 16 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [Beyond the Sampled Token: Preserving Candidate Support in RLVR](https://mlsanity.com/paper/2510.14807/) (2025)

## Built on by (most cited first, 12 of 12)

- [InT: Self-Proposed Interventions Enable Credit Assignment in LLM Reasoning](https://mlsanity.com/paper/2601.14209/) (2026)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [Why Pass@k Optimization Can Degrade Pass@1: Prompt Interference in LLM Post-training](https://mlsanity.com/paper/2602.21189/) (2026)
- [ResRL: Boosting LLM Reasoning via Negative Sample Projection Residual Reinforcement Learning](https://mlsanity.com/paper/2605.00380/) (2026)
- [TopoCurate:Modeling Interaction Topology for Tool-Use Agent Training](https://mlsanity.com/paper/2603.01714/) (2026)
- [Distribution-Aware Reward Estimation for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2601.21804/) (2026)
- [Beyond Token-level Supervision: Unlocking the Potential of Decoding-based Regression via Reinforcement Learning](https://mlsanity.com/paper/2512.06533/) (2025)
- [Discovering Novel LLM Experts via Task-Capability Coevolution](https://mlsanity.com/paper/2604.14969/) (2026)
- [When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer](https://mlsanity.com/paper/2605.29190/) (2026)
- [Annealed Softmax Greedy in Many-Armed Bayesian Bandits](https://mlsanity.com/paper/2605.31034/) (2026)
- [Locked at the Entrance, Open Inside: Where RLVR Narrows the Solution Space](https://mlsanity.com/paper/2608.29188/) (2026)
- [SERA: Scale-Equalized Rollout Allocation for Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2609.36552/) (2026)

## Abstract (arXiv)

The ability of Large Language Models (LLMs) to perform complex, multi-step reasoning is a central focus of modern AI research. To evaluate and enhance this capability, the pass@k metric, which measures the probability of obtaining at least one correct solution in k independent samples, has received significant attention. Its intuitive appeal has led to its adoption not only as an evaluation standard but also as a direct optimization objective in reinforcement learning. In this paper, we analyze the pass@k objective, derive its gradient, and demonstrate that it is fundamentally a per-example positive reweighting of the simpler pass@1 objective. Our analysis reveals that the pass@k objective provides a vanishing learning signal in regimes where exploration is most critical. We further analyze the dynamics of "exploration collapse", showing that as the policy concentrates probability mass, the gap between pass@k and pass@1 diminishes. We conclude that while pass@k is a useful diagnostic tool, it may be an unsuitable direct objective for optimization. Instead, mechanisms explicitly encouraging efficient exploration could offer a more effective path forward for reinforcement learning in reasoning tasks.