# Cycles of Thought: Measuring LLM Confidence through Stable Explanations

arXiv: https://arxiv.org/abs/2406.03441 · HTML: https://mlsanity.com/paper/2406.03441/

## Key facts

- Cited by 29 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 33 of its 52 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## 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 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [What Large Language Models Know and What People Think They Know](https://mlsanity.com/paper/2401.13835/) (2024)
- [Chain-of-Thought Hub: A Continuous Effort to Measure Large Language Models' Reasoning Performance](https://mlsanity.com/paper/2305.17306/) (2023)
- [Batch Calibration: Rethinking Calibration for In-Context Learning and Prompt Engineering](https://mlsanity.com/paper/2309.17249/) (2023)
- [Towards Better Chain-of-Thought Prompting Strategies: A Survey](https://mlsanity.com/paper/2310.04959/) (2023)
- [Uncertainty in Natural Language Generation: From Theory to Applications](https://mlsanity.com/paper/2307.15703/) (2023)
- [Look Before You Leap: An Exploratory Study of Uncertainty Measurement for Large Language Models](https://mlsanity.com/paper/2307.10236/) (2023)
- [Think Twice Before Trusting: Self-Detection for Large Language Models through Comprehensive Answer Reflection](https://mlsanity.com/paper/2403.09972/) (2024)
- [Llamas Know What GPTs Don't Show: Surrogate Models for Confidence Estimation](https://mlsanity.com/paper/2311.08877/) (2023)

## Built on by (most cited first, 29 of 29)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [VGRP-Bench: Visual Grid Reasoning Puzzle Benchmark for Large Vision-Language Models](https://mlsanity.com/paper/2503.23064/) (2025)
- [MetaFaith: Faithful Natural Language Uncertainty Expression in LLMs](https://mlsanity.com/paper/2505.24858/) (2025)
- [Understanding the Impact of Confidence in Retrieval Augmented Generation: A Case Study in the Medical Domain](https://mlsanity.com/paper/2412.20309/) (2024)
- [A Survey of Calibration Process for Black-Box LLMs](https://mlsanity.com/paper/2412.12767/) (2024)
- [Self-Training Large Language Models with Confident Reasoning](https://mlsanity.com/paper/2505.17454/) (2025)
- [Black-box Optimization of LLM Outputs by Asking for Directions](https://mlsanity.com/paper/2510.16794/) (2025)
- [How Confident are Video Models? Empowering Video Models to Express their Uncertainty](https://mlsanity.com/paper/2510.02571/) (2025)
- [Uncertainty Quantification for Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2510.11483/) (2025)
- [Comparing Uncertainty Measurement and Mitigation Methods for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2504.18346/) (2025)
- [Identify, Isolate, and Purge: Mitigating Hallucinations in LVLMs via Self-Evolving Distillation](https://mlsanity.com/paper/2507.04680/) (2025)
- [Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs](https://mlsanity.com/paper/2606.32032/) (2026)
- [Rehabilitation Exercise Quality Assessment and Feedback Generation Using Large Language Models with Prompt Engineering](https://mlsanity.com/paper/2505.18412/) (2025)
- [Towards Harmonized Uncertainty Estimation for Large Language Models](https://mlsanity.com/paper/2505.19073/) (2025)
- [Confidence Estimation for Text-to-SQL in Large Language Models](https://mlsanity.com/paper/2508.14056/) (2025)
- [Can Multiple Responses from an LLM Reveal the Sources of Its Uncertainty?](https://mlsanity.com/paper/2509.04464/) (2025)
- [FalseCrashReducer: Mitigating False Positive Crashes in OSS-Fuzz-Gen Using Agentic AI](https://mlsanity.com/paper/2510.02185/) (2025)
- [Can LLMs Use Linguistic Uncertainty Markers to Reliably Reflect Intrinsic Confidence?](https://mlsanity.com/paper/2605.28778/) (2026)
- [The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2606.22792/) (2026)
- [Judging with Personality and Confidence: A Study on Personality-Conditioned LLM Relevance Assessment](https://mlsanity.com/paper/2601.01862/) (2026)
- [D-Models and E-Models: Diversity-Stability Trade-offs in the Sampling Behavior of Large Language Models](https://mlsanity.com/paper/2601.17865/) (2026)
- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)
- [Evaluating Prompt Engineering Techniques for Accuracy and Confidence Elicitation in Medical LLMs](https://mlsanity.com/paper/2506.00072/) (2025)
- [Dual-Process Scaffold Reasoning for Enhancing LLM Code Debugging](https://mlsanity.com/paper/2511.08052/) (2025)
- [Fact-Checking with Large Language Models via Probabilistic Certainty and Consistency](https://mlsanity.com/paper/2601.02574/) (2026)
- [Task Abstention for Large Language Models in Code Generation](https://mlsanity.com/paper/2605.17029/) (2026)
- [Right Answer, Wrong Reason: Accuracy, Consistency, and Consensus Are Misleading Indicators of LLM Faithfulness in Clinical Decision Support](https://mlsanity.com/paper/2609.32817/) (2026)
- [Zero-Shot Visualization: Exploring Text Corpora with User-Prompted Axes](https://mlsanity.com/paper/2610.06889/) (2026)

## Abstract (arXiv)

In many high-risk machine learning applications it is essential for a model to indicate when it is uncertain about a prediction. While large language models (LLMs) can reach and even surpass human-level accuracy on a variety of benchmarks, their overconfidence in incorrect responses is still a well-documented failure mode. Traditional methods for ML uncertainty quantification can be difficult to directly adapt to LLMs due to the computational cost of implementation and closed-source nature of many models. A variety of black-box methods have recently been proposed, but these often rely on heuristics such as self-verbalized confidence. We instead propose a framework for measuring an LLM's uncertainty with respect to the distribution of generated explanations for an answer. While utilizing explanations is not a new idea in and of itself, by interpreting each possible model+explanation pair as a test-time classifier we can calculate a posterior answer distribution over the most likely of these classifiers. We demonstrate how a specific instance of this framework using explanation entailment as our classifier likelihood improves confidence score metrics (in particular AURC and AUROC) over baselines across five different datasets. We believe these results indicate that our framework is both a well-principled and effective way of quantifying uncertainty in LLMs.