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Direct Pass@$k$ Optimization for Thought Pruning: Balancing Quality and Diversity in Test-Time Reasoning

Mahdi Salmani, Adel Javanmard, Devansh Gupta, Meisam Razaviyayn · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31667 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

保持所有候选解决方案到完成可以是计算苛刻的,所以最近的工作在生成仅一个短的前缀后,产生了一个关键的推断策略推理模型,其中一个模型产生了大量的候选解决方案,希望找到至少一个正确的解决方案。运行所有候选解决方案到完成可以是计算苛刻的,所以基于多样性的方法仅根据不同的推理轨迹进行进一步的计算,而在现有的推理策略广泛分为两个类别:基于质量的方法同时分配给每个部分解决方案,并抛弃那些预测最终导致错误的最终解决方案,而基于多样性的方法选择仅次于不同的推理轨迹的部分解决方案,因此可能覆盖不同的最终解决方案。 这些两个目标之间的紧张是探索与分割利用的过程,但没有太多的工作先前进行平衡,

Machine translation (Meta M2M100); the English original follows.

Abstract

Test-time scaling has emerged as a key inference strategy for reasoning models, where a model generates a large number of candidate solutions in the hope of finding at least one correct solution. Running all candidate solutions to completion can be computationally demanding, so recent work prunes the candidate pool after generating only a short prefix, committing further computation only to the surviving candidates. Existing pruning strategies divide broadly into two categories: Quality-based methods assign a score to each partial solution and discard those predicted to ultimately lead to an incorrect final solution, while diversity-based methods select partial solutions that follow different reasoning trajectories and are therefore likely to cover different final solutions. The tension between these two objectives is an instance of exploration versus exploitation, yet little to no prior work on pruning exposes this trade-off directly, let alone optimizes it. In this paper, we introduce a pruning procedure that addresses this trade-off directly by optimizing pass@$k$ over the selected solution pool. In particular, it chooses the pool to maximize the probability that at least one of its partial solutions, when continued to completion, yields a correct answer. Because this objective simultaneously rewards high-quality partial solutions and penalizes redundancy among them, quality and diversity are naturally balanced by the criterion itself rather than through separate ad-hoc design choices. On eight open-weight reasoning models, our method outperforms existing quality-based and diversity-based pruning strategies. The gains are particularly pronounced when the pruning procedure keeps a moderate number of partial solutions for continued generation, highlighting the value of directly balancing quality and diversity during pruning.

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Topics: Pruning, Computer science, Artificial intelligence, Redundancy (engineering), Inference, Machine learning

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