# Calibrating Large Language Models with Sample Consistency

arXiv: https://arxiv.org/abs/2402.13904 · HTML: https://mlsanity.com/paper/2402.13904/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 21 Feb 2024.

## Builds on (most cited first, 30 of 30)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (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)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Text](https://mlsanity.com/paper/1908.06177/) (2019)
- [Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoning](https://mlsanity.com/paper/2107.02794/) (2021)
- [A Close Look into the Calibration of Pre-trained Language Models](https://mlsanity.com/paper/2211.00151/) (2022)
- [Automatic Generation of Socratic Subquestions for Teaching Math Word Problems](https://mlsanity.com/paper/2211.12835/) (2022)
- [Detection of Word Adversarial Examples in Text Classification: Benchmark and Baseline via Robust Density Estimation](https://mlsanity.com/paper/2203.01677/) (2022)
- [SCREWS: A Modular Framework for Reasoning with Revisions](https://mlsanity.com/paper/2309.13075/) (2023)

## Built on by (most cited first, 30 of 73)

- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [The MASK Benchmark: Disentangling Honesty From Accuracy in AI Systems](https://mlsanity.com/paper/2503.03750/) (2025)
- [Rejection Improves Reliability: Training LLMs to Refuse Unknown Questions Using RL from Knowledge Feedback](https://mlsanity.com/paper/2403.18349/) (2024)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [Limitations of Large Language Models in Clinical Problem-Solving Arising from Inflexible Reasoning](https://mlsanity.com/paper/2502.04381/) (2025)
- [DyKnow: Dynamically Verifying Time-Sensitive Factual Knowledge in LLMs](https://mlsanity.com/paper/2404.08700/) (2024)
- [Do Not Design, Learn: A Trainable Scoring Function for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2406.11278/) (2024)
- [A Survey on the Honesty of Large Language Models](https://mlsanity.com/paper/2409.18786/) (2024)
- [HonestLLM: Toward an Honest and Helpful Large Language Model](https://mlsanity.com/paper/2406.00380/) (2024)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [Mirror-Consistency: Harnessing Inconsistency in Majority Voting](https://mlsanity.com/paper/2410.10857/) (2024)
- [Alignment for Efficient Tool Calling of Large Language Models](https://mlsanity.com/paper/2503.06708/) (2025)
- [LLMs Can Teach Themselves to Better Predict the Future](https://mlsanity.com/paper/2502.05253/) (2025)
- [SCOPE: Selective Conformal Optimized Pairwise LLM Judging](https://mlsanity.com/paper/2602.13110/) (2026)
- [QA-Calibration of Language Model Confidence Scores](https://mlsanity.com/paper/2410.06615/) (2024)
- [UAlign: Leveraging Uncertainty Estimations for Factuality Alignment on Large Language Models](https://mlsanity.com/paper/2412.11803/) (2024)
- [Revisiting Self-Consistency from Dynamic Distributional Alignment Perspective on Answer Aggregation](https://mlsanity.com/paper/2502.19830/) (2025)
- [MMBoundary: Advancing MLLM Knowledge Boundary Awareness through Reasoning Step Confidence Calibration](https://mlsanity.com/paper/2505.23224/) (2025)
- [PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains](https://mlsanity.com/paper/2508.21787/) (2025)
- [Calibration Across Layers: Understanding Calibration Evolution in LLMs](https://mlsanity.com/paper/2511.00280/) (2025)
- [Calibrating LLM Judges: Linear Probes for Fast and Reliable Uncertainty Estimation](https://mlsanity.com/paper/2512.22245/) (2025)
- [Optimal Bayesian Stopping for Efficient Inference of Consistent LLM Answers](https://mlsanity.com/paper/2602.05395/) (2026)
- [Navigating Noisy Feedback: Enhancing Reinforcement Learning with Error-Prone Language Models](https://mlsanity.com/paper/2410.17389/) (2024)
- [Conformal Information Pursuit for Interactively Guiding Large Language Models](https://mlsanity.com/paper/2507.03279/) (2025)
- [SIKeD: Self-guided Iterative Knowledge Distillation for mathematical reasoning](https://mlsanity.com/paper/2410.18574/) (2024)
- [B-score: Detecting biases in large language models using response history](https://mlsanity.com/paper/2505.18545/) (2025)
- [Prompt4Trust: A Reinforcement Learning Prompt Augmentation Framework for Clinically-Aligned Confidence Calibration in Multimodal Large Language Models](https://mlsanity.com/paper/2507.09279/) (2025)

## Abstract (arXiv)

Accurately gauging the confidence level of Large Language Models' (LLMs) predictions is pivotal for their reliable application. However, LLMs are often uncalibrated inherently and elude conventional calibration techniques due to their proprietary nature and massive scale. In this work, we explore the potential of deriving confidence from the distribution of multiple randomly sampled model generations, via three measures of consistency. We perform an extensive evaluation across various open and closed-source models on nine reasoning datasets. Results show that consistency-based calibration methods outperform existing post-hoc approaches. Meanwhile, we find that factors such as intermediate explanations, model scaling, and larger sample sizes enhance calibration, while instruction-tuning makes calibration more difficult. Moreover, confidence scores obtained from consistency have the potential to enhance model performance. Finally, we offer practical guidance on choosing suitable consistency metrics for calibration, tailored to the characteristics of various LMs.