# Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs

arXiv: https://arxiv.org/abs/2305.11860 · HTML: https://mlsanity.com/paper/2305.11860/

## Key facts

- Cited by 115 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 31 of its 54 references that are in the map.
- First posted on arXiv 19 May 2023.

## 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 31)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [BERT Loses Patience: Fast and Robust Inference with Early Exit](https://mlsanity.com/paper/2006.04152/) (2020)
- [DynaBERT: Dynamic BERT with Adaptive Width and Depth](https://mlsanity.com/paper/2004.04037/) (2020)
- [FastBERT: a Self-distilling BERT with Adaptive Inference Time](https://mlsanity.com/paper/2004.02178/) (2020)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Rationale-Augmented Ensembles in Language Models](https://mlsanity.com/paper/2207.00747/) (2022)
- [Top-KAST: Top-K Always Sparse Training](https://mlsanity.com/paper/2106.03517/) (2021)
- [Consistent Accelerated Inference via Confident Adaptive Transformers](https://mlsanity.com/paper/2104.08803/) (2021)
- [Towards Teachable Reasoning Systems: Using a Dynamic Memory of User Feedback for Continual System Improvement](https://mlsanity.com/paper/2204.13074/) (2022)
- [Sampling Bias in Deep Active Classification: An Empirical Study](https://mlsanity.com/paper/1909.09389/) (2019)
- [Early Exit or Not: Resource-Efficient Blind Quality Enhancement for Compressed Images](https://mlsanity.com/paper/2006.16581/) (2020)
- [Adaptive Computation with Elastic Input Sequence](https://mlsanity.com/paper/2301.13195/) (2023)
- [RomeBERT: Robust Training of Multi-Exit BERT](https://mlsanity.com/paper/2101.09755/) (2021)
- [An Adaptive Sampling Scheme to Efficiently Train Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1709.02764/) (2017)

## Built on by (most cited first, 30 of 115)

- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [AutoMix: Automatically Mixing Language Models](https://mlsanity.com/paper/2310.12963/) (2023)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [Have LLMs Advanced Enough? A Challenging Problem Solving Benchmark For Large Language Models](https://mlsanity.com/paper/2305.15074/) (2023)
- [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)
- [Sampling-Efficient Test-Time Scaling: Self-Estimating the Best-of-N Sampling in Early Decoding](https://mlsanity.com/paper/2503.01422/) (2025)
- [Efficiently Scaling LLM Reasoning with Certaindex](https://mlsanity.com/paper/2412.20993/) (2024)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [MAgICoRe: Multi-Agent, Iterative, Coarse-to-Fine Refinement for Reasoning](https://mlsanity.com/paper/2409.12147/) (2024)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [AlphaVerus: Bootstrapping Formally Verified Code Generation through Self-Improving Translation and Treefinement](https://mlsanity.com/paper/2412.06176/) (2024)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization](https://mlsanity.com/paper/2501.17974/) (2025)
- [Does Your Reasoning Model Implicitly Know When to Stop Thinking?](https://mlsanity.com/paper/2602.08354/) (2026)
- [TSRBench: A Comprehensive Multi-task Multi-modal Time Series Reasoning Benchmark for Generalist Models](https://mlsanity.com/paper/2601.18744/) (2026)
- [Path-Consistency with Prefix Enhancement for Efficient Inference in LLMs](https://mlsanity.com/paper/2409.01281/) (2024)
- [Semantic Consistency for Assuring Reliability of Large Language Models](https://mlsanity.com/paper/2308.09138/) (2023)
- [Lost at the Beginning of Reasoning](https://mlsanity.com/paper/2506.22058/) (2025)
- [Parallel-Probe: Towards Efficient Parallel Thinking via 2D Probing](https://mlsanity.com/paper/2602.03845/) (2026)
- [Improving Consistency in Large Language Models through Chain of Guidance](https://mlsanity.com/paper/2502.15924/) (2025)
- [Learning to Focus: Causal Attention Distillation via Gradient-Guided Token Pruning](https://mlsanity.com/paper/2506.07851/) (2025)
- [Adaptive-Solver Framework for Dynamic Strategy Selection in Large Language Model Reasoning](https://mlsanity.com/paper/2310.01446/) (2023)
- [Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMs](https://mlsanity.com/paper/2510.17472/) (2025)

## Abstract (arXiv)

A popular approach for improving the correctness of output from large language models (LLMs) is Self-Consistency - poll the LLM multiple times and output the most frequent solution. Existing Self-Consistency techniques always generate a constant number of samples per question, where a better approach will be to non-uniformly distribute the available budget based on the amount of agreement in the samples generated so far. In response, we introduce Adaptive-Consistency, a cost-efficient, model-agnostic technique that dynamically adjusts the number of samples per question using a lightweight stopping criterion. Our experiments over 17 reasoning and code generation datasets and three LLMs demonstrate that Adaptive-Consistency reduces sample budget by up to 7.9 times with an average accuracy drop of less than 0.1%. Our code and data are available at https://www.sample-step-by-step.info