# Optimal Self-Consistency for Efficient Reasoning with Large Language Models

arXiv: https://arxiv.org/abs/2511.12309 · HTML: https://mlsanity.com/paper/2511.12309/

## Key facts

- Cited by 9 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 35 of its 41 references that are in the map.
- First posted on arXiv 15 Nov 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, 30 of 35)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [SelfCheck: Using LLMs to Zero-Shot Check Their Own Step-by-Step Reasoning](https://mlsanity.com/paper/2308.00436/) (2023)
- [Observational Scaling Laws and the Predictability of Language Model Performance](https://mlsanity.com/paper/2405.10938/) (2024)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning](https://mlsanity.com/paper/2408.13457/) (2024)
- [Self-Consistency Preference Optimization](https://mlsanity.com/paper/2411.04109/) (2024)
- [Why Has Predicting Downstream Capabilities of Frontier AI Models with Scale Remained Elusive?](https://mlsanity.com/paper/2406.04391/) (2024)
- [Optimizing Temperature for Language Models with Multi-Sample Inference](https://mlsanity.com/paper/2502.05234/) (2025)
- [Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods](https://mlsanity.com/paper/2408.14511/) (2024)
- [Ranked Voting based Self-Consistency of Large Language Models](https://mlsanity.com/paper/2505.10772/) (2025)
- [Mirror-Consistency: Harnessing Inconsistency in Majority Voting](https://mlsanity.com/paper/2410.10857/) (2024)
- [Consistency in Language Models: Current Landscape, Challenges, and Future Directions](https://mlsanity.com/paper/2505.00268/) (2025)
- [Evaluating System 1 vs. 2 Reasoning Approaches for Zero-Shot Time Series Forecasting: A Benchmark and Insights](https://mlsanity.com/paper/2503.01895/) (2025)
- [Sample Complexity and Representation Ability of Test-time Scaling Paradigms](https://mlsanity.com/paper/2506.05295/) (2025)
- [Revisiting Self-Consistency from Dynamic Distributional Alignment Perspective on Answer Aggregation](https://mlsanity.com/paper/2502.19830/) (2025)

## Built on by (most cited first, 9 of 9)

- [Optimal Bayesian Stopping for Efficient Inference of Consistent LLM Answers](https://mlsanity.com/paper/2602.05395/) (2026)
- [Internalizing LLM Reasoning via Discovery and Replay of Latent Actions](https://mlsanity.com/paper/2602.04925/) (2026)
- [Beyond Consensus: Trace-Level Synthesis in Mixture of Agents](https://mlsanity.com/paper/2605.29116/) (2026)
- [Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoning](https://mlsanity.com/paper/2605.26849/) (2026)
- [Quantum-Inspired Trace-Augmented Evidence Selection for Reasoning over Structured Hypothesis Spaces](https://mlsanity.com/paper/2606.06941/) (2026)
- [Strategic Self-Consistency](https://mlsanity.com/paper/2609.30352/) (2026)
- [Provable Test-Time Scaling for Beam Search in LLM Reasoning](https://mlsanity.com/paper/2609.38672/) (2026)
- [From Discovery to Decision: Finite-Budget Recoverability in LLM Voting](https://mlsanity.com/paper/2610.01014/) (2026)
- [Compare to Correct: Pairwise-Guided Logit Adjustment for LLM Test-Time Scaling](https://mlsanity.com/paper/2610.18583/) (2026)

## Abstract (arXiv)

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 understanding 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, supports batching, and can fit any budget of samples, ensuring it can be easily applied to any self-consistency application.