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

Abstract: While test-time scaling can boost model performance by combining stochastic reasoning paths, ensuring sample-efficient test-time self-consistency within constrained budgets remains a significant hurdle. To address this, we present PETS (Principled and Efficient Test-Time Self-Consistency), an optimization-based framework that establishes a rigorous foundation for trajectory allocation. The core of our method is the self-consistency rate, a novel metric defined by agreement with a hypothetical majority vote under infinite budget. This definition provides a theoretically sound basis for efficient allocation, enabling rigorous analysis. We examine both offline and online environments. In the offline scenario, where the full set of questions is available beforehand, we draw parallels between trajectory allocation and crowdsourcing by treating reasoning traces as workers. This analogy allows us to apply established theories to derive theoretical guarantees and develop an efficient algorithm based on majority voting. For the online streaming setting, where questions appear sequentially and decisions must be made in real-time, we introduce a new method derived from our offline insights. This technique dynamically adjusts budgets according to question difficulty while maintaining strong theoretical assurances and computational speed. Our experiments demonstrate that PETS consistently surpasses uniform allocation strategies. Specifically, on the GPQA benchmark, PETS reaches perfect self-consistency in both scenarios, cutting the sampling budget by as much as 75% in the offline case and 55% in the online case compared to uniform allocation. The code can be accessed at https://github.com/ZDCSlab/PETS.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC