arXiv 2602.167452026-05-31cs.LGcs.AI

PETS：一种面向高效测试时自一致性的最优轨迹分配原则性框架

PETS: A Principled Framework Towards Optimal Trajectory Allocation for Efficient Test-Time Self-Consistency

Stanford University（斯坦福大学）；UNC at Chapel Hill（Chapel Hill 大学）；Yale University（耶鲁大学）；New York University（纽约大学）

Zhangyi Liu, Huaizhi Qu, Xiaowei Yin, He Sun, Yanjun Han, Tianlong Chen, Zhun Deng

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AI总结：

提出PETS框架，通过将轨迹分配建模为优化问题并引入自一致性率度量，在离线（连接众包理论）和在线流式场景下实现样本高效的测试时自一致性，显著降低采样预算。

摘要：

测试时扩展可以通过聚合随机推理轨迹来提高模型性能。然而，在有限预算下实现样本高效的测试时自一致性仍然是一个开放的挑战。我们引入了PETS（原则性且高效的测试时自一致性），它通过一个优化框架启动了对轨迹分配的原则性研究。我们方法的核心是自一致性率，这是一个新定义的度量，即与无限预算多数投票的一致性。这一公式使样本高效的测试时分配在理论上具有坚实基础，并适合严格分析。我们研究了离线和在线两种设置。在离线模式下，所有问题事先已知，我们将轨迹分配与众包（一个经典且成熟的研究领域）联系起来，将推理轨迹建模为工人。这种视角使我们能够利用丰富的现有理论，获得理论保证和一种高效的基于多数投票的分配算法。在在线流式模式下，问题顺序到达且必须实时做出分配，我们提出了一种受离线框架启发的新方法。我们的方法根据问题难度调整预算，同时保持强大的理论保证和计算效率。实验表明，PETS始终优于均匀分配。在GPQA上，PETS在两种设置下均实现了完美的自一致性，同时相对于均匀分配将采样预算减少了高达75%（离线）和55%（在线）。代码可在https://github.com/ZDCSlab/PETS获取。

英文摘要：

Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (Principled and Efficient Test-TimeSelf-Consistency), which initiates a principled study of trajectory allocation through an optimization framework. Central to our approach is the self-consistency rate, a new measure defined as agreement with the infinite-budget majority vote. This formulation makes sample-efficient test-time allocation theoretically grounded and amenable to rigorous analysis. We study both offline and online settings. In the offline regime, where all questions are known in advance, we connect trajectory allocation to crowdsourcing, a classic and well-developed area, by modeling reasoning traces as workers. This perspective allows us to leverage rich existing theory, yielding theoretical guarantees and an efficient majority-voting-based allocation algorithm. In the online streaming regime, where questions arrive sequentially and allocations must be made on the fly, we propose a novel method inspired by the offline framework. Our approach adapts budgets to question difficulty while preserving strong theoretical guarantees and computational efficiency. Experiments show that PETS consistently outperforms uniform allocation. On GPQA, PETS achieves perfect self-consistency in both settings while reducing the sampling budget by up to 75% (offline) and 55% (online) relative to uniform allocation. Code is available at https://github.com/ZDCSlab/PETS.

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