# ConSol: Sequential Probability Ratio Testing to Find Consistent LLM Reasoning Paths Efficiently

arXiv: https://arxiv.org/abs/2503.17587 · HTML: https://mlsanity.com/paper/2503.17587/

## 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 5 of its 15 references that are in the map.
- First posted on arXiv 22 Mar 2025.

## 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, 5 of 5)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)

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

- [ATLAS: Agentic Test-time Learning-to-Allocate Scaling](https://mlsanity.com/paper/2606.01667/) (2026)
- [LA-MARRVEL: A Knowledge-Grounded, Language-Aware LLM Framework for Clinically Robust Rare Disease Gene Prioritization](https://mlsanity.com/paper/2511.02263/) (2025)

## Abstract (arXiv)

Recent advancements in large language models (LLMs) integrating explicit reasoning, such as OpenAI's o3-mini, DeepSeek-R1, and QWQ-32B, enable smaller models to solve complex tasks by generating intermediate reasoning steps prior to providing answers. However, this approach significantly increases computational costs, both monetarily and environmentally. The widely-used self-consistency method further exacerbates these costs by aggregating multiple reasoning paths to improve accuracy, often requiring between 40 to 64 samples per task. Although aggregation effectively reduces variance and bias, additional sampling can lead to diminishing returns when early samples yield consistent results. To address inefficiencies, we propose leveraging Sequential Probability Ratio Testing (SPRT) to dynamically terminate sampling once sufficient consistency is achieved. We calibrate SPRT parameters specifically for LLM applications, accounting for sensitivity to detect the mode of the distribution. Our experiments demonstrate that incorporating SPRT significantly enhances token efficiency, achieving comparable accuracy to self-consistency methods but at a substantially reduced computational cost. To promote transparency and facilitate reproducibility, we have made the source code and datasets used in our experiments publicly available at our GitHub repository: https://github.com/LiuzLab/consol, or available as a PyPI package: pip install consol. We hope that this resource will support further research and encourage the development of new methods building upon our work.