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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

Korean

테스트 타임 스케일링은 논리 모델에 대한 핵심 추론 전략으로 나타났으며, 모델은 적어도 하나의 올바른 솔루션을 찾는 희망으로 많은 수의 후보 솔루션을 생성합니다. 완료하기 위해 모든 후보 솔루션을 실행하는 것은 계산적으로 어려울 수 있으므로 최근 작업은 단지 짧은 사전을 생성 한 후에 후보 폴을 스케일하고, 생존 후보에게만 추가 계산을 맡고 있습니다. 기존 스케일링 전략은 두 가지 범주로 넓게 나누어집니다. 품질 기반 방법은 각 부분 솔루션에 동시에 점수를 부여하고 예측 된 것을 제거하여 최종적으로 잘못된 최종 솔루션으로 이어질 수 있습니다. 다양성 기반 방법은 다른 논리 트레일러를 따르는 부분적 솔루

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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