Optimal Self-Consistency for Efficient Reasoning with Large Language Models

Austin Feng, Marius Alonso, Ambroise Odonnat, Vasilii Feofanov, Ievgen Redko
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:29981-30005, 2026.

Abstract

Self-consistency (SC) is a widely-used test-time inference technique for improving performance in chain-of-thought reasoning. It consists of generating multiple responses, or "samples," from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, self-consistency is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC’s scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses $4.8\times$ fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, we note that Blend-ASC is hyperparameter-free and can fit any budget of samples, ensuring it can be easily applied to any self-consistency application.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-feng26a, title = {Optimal Self-Consistency for Efficient Reasoning with Large Language Models}, author = {Feng, Austin and Alonso, Marius and Odonnat, Ambroise and Feofanov, Vasilii and Redko, Ievgen}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {29981--30005}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/feng26a/feng26a.pdf}, url = {https://proceedings.mlr.press/v306/feng26a.html}, abstract = {Self-consistency (SC) is a widely-used test-time inference technique for improving performance in chain-of-thought reasoning. It consists of generating multiple responses, or "samples," from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, self-consistency is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC’s scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses $4.8\times$ fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, we note that Blend-ASC is hyperparameter-free and can fit any budget of samples, ensuring it can be easily applied to any self-consistency application.} }
Endnote
%0 Conference Paper %T Optimal Self-Consistency for Efficient Reasoning with Large Language Models %A Austin Feng %A Marius Alonso %A Ambroise Odonnat %A Vasilii Feofanov %A Ievgen Redko %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-feng26a %I PMLR %P 29981--30005 %U https://proceedings.mlr.press/v306/feng26a.html %V 306 %X Self-consistency (SC) is a widely-used test-time inference technique for improving performance in chain-of-thought reasoning. It consists of generating multiple responses, or "samples," from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, self-consistency is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical treatment of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC’s scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses $4.8\times$ fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, we note that Blend-ASC is hyperparameter-free and can fit any budget of samples, ensuring it can be easily applied to any self-consistency application.
APA
Feng, A., Alonso, M., Odonnat, A., Feofanov, V. & Redko, I.. (2026). Optimal Self-Consistency for Efficient Reasoning with Large Language Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:29981-30005 Available from https://proceedings.mlr.press/v306/feng26a.html.

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