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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

Arabic

وقد تم تشخيص جميع الحلول في وقت الاختبار كخطوة مهمة لتشخيص نموذجي، حيث يتم تشخيص نموذج عدد كبير من الحلول المرشحة في أمل العثور على أقل من الحلول الصحيحة. قد تم تشخيص جميع الحلول المرشحة إلى الانتهاء، وبالتالي فإن العمل الأخير يتم تشخيص القسم المرشح بعد إنتاج قسيمة قصيرة فقط، وتفريغ التحليل الإضافي فقط إلى المرشحين الناجحين، وبالتالي فإن استراتيجيات التخطيط الحالية تنقسم بشكل واسع إلى فئة: طريقة الجودة تخصيص نقطة لكل حل جزئي وتخفيض تلك المتوقعة في النهاية تؤدي إلى حل نهائي خاطئ، في حين أن الأساليب المتعلقة بالثقافة تختار الحلول الجزئية

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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