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

arXiv: https://arxiv.org/abs/2602.16745 · HTML: https://mlsanity.com/paper/2602.16745/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 27 of 27)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [O1-Pruner: Length-Harmonizing Fine-Tuning for O1-Like Reasoning Pruning](https://mlsanity.com/paper/2501.12570/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning](https://mlsanity.com/paper/2408.13457/) (2024)
- [Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling](https://mlsanity.com/paper/2408.17017/) (2024)
- [Efficiently Scaling LLM Reasoning with Certaindex](https://mlsanity.com/paper/2412.20993/) (2024)
- [Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models](https://mlsanity.com/paper/2505.16122/) (2025)
- [QwenLong-L1.5: Post-Training Recipe for Long-Context Reasoning and Memory Management](https://mlsanity.com/paper/2512.12967/) (2025)
- [Bayesian Calibration of Win Rate Estimation with LLM Evaluators](https://mlsanity.com/paper/2411.04424/) (2024)
- [Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling](https://mlsanity.com/paper/2506.15707/) (2025)
- [The Quest for Efficient Reasoning: A Data-Centric Benchmark to CoT Distillation](https://mlsanity.com/paper/2505.18759/) (2025)
- [Strategic Scaling of Test-Time Compute: A Bandit Learning Approach](https://mlsanity.com/paper/2506.12721/) (2025)

## Built on by (most cited first, 2 of 2)

- [Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning](https://mlsanity.com/paper/2604.01170/) (2026)
- [From Discovery to Decision: Finite-Budget Recoverability in LLM Voting](https://mlsanity.com/paper/2610.01014/) (2026)

## Abstract (arXiv)

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.