# Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness

arXiv: https://arxiv.org/abs/2308.16175 · HTML: https://mlsanity.com/paper/2308.16175/

## Key facts

- Cited by 122 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 41 references that are in the map.
- First posted on arXiv 30 Aug 2023.

## Builds on (most cited first, 30 of 33)

- [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)
- [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)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [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)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [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)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [InstructZero: Efficient Instruction Optimization for Black-Box Large Language Models](https://mlsanity.com/paper/2306.03082/) (2023)
- [How Many Demonstrations Do You Need for In-context Learning?](https://mlsanity.com/paper/2303.08119/) (2023)

## Built on by (most cited first, 30 of 122)

- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Non-Determinism of "Deterministic" LLM Settings](https://mlsanity.com/paper/2408.04667/) (2024)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [SAFE: Multitask Failure Detection for Vision-Language-Action Models](https://mlsanity.com/paper/2506.09937/) (2025)
- [Towards Conversational Diagnostic AI](https://mlsanity.com/paper/2401.05654/) (2024)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice](https://mlsanity.com/paper/2410.15326/) (2024)
- [Internal Consistency and Self-Feedback in Large Language Models: A Survey](https://mlsanity.com/paper/2407.14507/) (2024)
- [MARS: Meaning-Aware Response Scoring for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2402.11756/) (2024)
- [Knowledge Boundary of Large Language Models: A Survey](https://mlsanity.com/paper/2412.12472/) (2024)
- [Uncertainty quantification in fine-tuned LLMs using LoRA ensembles](https://mlsanity.com/paper/2402.12264/) (2024)
- [Calibrating Long-form Generations from Large Language Models](https://mlsanity.com/paper/2402.06544/) (2024)
- [Content Moderation by LLM: From Accuracy to Legitimacy](https://mlsanity.com/paper/2409.03219/) (2024)
- [Improving Uncertainty Quantification in Large Language Models via Semantic Embeddings](https://mlsanity.com/paper/2410.22685/) (2024)
- [Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistency](https://mlsanity.com/paper/2502.04964/) (2025)
- [Cycles of Thought: Measuring LLM Confidence through Stable Explanations](https://mlsanity.com/paper/2406.03441/) (2024)
- [Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Models](https://mlsanity.com/paper/2408.02085/) (2024)
- [Understanding the Uncertainty of LLM Explanations: A Perspective Based on Reasoning Topology](https://mlsanity.com/paper/2502.17026/) (2025)
- [Do Not Design, Learn: A Trainable Scoring Function for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2406.11278/) (2024)
- [LLM Uncertainty Quantification through Directional Entailment Graph and Claim Level Response Augmentation](https://mlsanity.com/paper/2407.00994/) (2024)
- [ExpSeek: Self-Triggered Experience Seeking for Web Agents](https://mlsanity.com/paper/2601.08605/) (2026)
- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Estimating the Hallucination Rate of Generative AI](https://mlsanity.com/paper/2406.07457/) (2024)
- [Fairness and Bias in Multimodal AI: A Survey](https://mlsanity.com/paper/2406.19097/) (2024)
- [Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure](https://mlsanity.com/paper/2412.15176/) (2024)
- [Uncertainty Quantification of Large Language Models through Multi-Dimensional Responses](https://mlsanity.com/paper/2502.16820/) (2025)

## Abstract (arXiv)

We introduce BSDetector, a method for detecting bad and speculative answers from a pretrained Large Language Model by estimating a numeric confidence score for any output it generated. Our uncertainty quantification technique works for any LLM accessible only via a black-box API, whose training data remains unknown. By expending a bit of extra computation, users of any LLM API can now get the same response as they would ordinarily, as well as a confidence estimate that cautions when not to trust this response. Experiments on both closed and open-form Question-Answer benchmarks reveal that BSDetector more accurately identifies incorrect LLM responses than alternative uncertainty estimation procedures (for both GPT-3 and ChatGPT). By sampling multiple responses from the LLM and considering the one with the highest confidence score, we can additionally obtain more accurate responses from the same LLM, without any extra training steps. In applications involving automated evaluation with LLMs, accounting for our confidence scores leads to more reliable evaluation in both human-in-the-loop and fully-automated settings (across both GPT 3.5 and 4).