# Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models

arXiv: https://arxiv.org/abs/2305.19187 · HTML: https://mlsanity.com/paper/2305.19187/

## Key facts

- Cited by 293 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 68 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 38)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [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)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [Selective Question Answering under Domain Shift](https://mlsanity.com/paper/2006.09462/) (2020)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [Addressing Failure Prediction by Learning Model Confidence](https://mlsanity.com/paper/1910.04851/) (2019)

## Built on by (most cited first, 30 of 293)

- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Exploring the Potential of Large Language Models (LLMs) in Learning on Graphs](https://mlsanity.com/paper/2307.03393/) (2023)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Benchmarking LLMs via Uncertainty Quantification](https://mlsanity.com/paper/2401.12794/) (2024)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Know Your Limits: A Survey of Abstention in Large Language Models](https://mlsanity.com/paper/2407.18418/) (2024)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Survey on Large Language Model-Enhanced Reinforcement Learning: Concept, Taxonomy, and Methods](https://mlsanity.com/paper/2404.00282/) (2024)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Trust or Escalate: LLM Judges with Provable Guarantees for Human Agreement](https://mlsanity.com/paper/2407.18370/) (2024)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [SAFE: Multitask Failure Detection for Vision-Language-Action Models](https://mlsanity.com/paper/2506.09937/) (2025)
- [Learning to Route LLMs with Confidence Tokens](https://mlsanity.com/paper/2410.13284/) (2024)
- [Uncertainty in Natural Language Generation: From Theory to Applications](https://mlsanity.com/paper/2307.15703/) (2023)
- [Mitigating LLM Hallucinations via Conformal Abstention](https://mlsanity.com/paper/2405.01563/) (2024)
- [GAM-Agent: Game-Theoretic and Uncertainty-Aware Collaboration for Complex Visual Reasoning](https://mlsanity.com/paper/2505.23399/) (2025)
- [Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation](https://mlsanity.com/paper/2410.13640/) (2024)
- [Uncertainty-Based Abstention in LLMs Improves Safety and Reduces Hallucinations](https://mlsanity.com/paper/2404.10960/) (2024)
- [Conformal Alignment: Knowing When to Trust Foundation Models with Guarantees](https://mlsanity.com/paper/2405.10301/) (2024)
- [Internal Consistency and Self-Feedback in Large Language Models: A Survey](https://mlsanity.com/paper/2407.14507/) (2024)
- [Steer LLM Latents for Hallucination Detection](https://mlsanity.com/paper/2503.01917/) (2025)
- [A Survey of Large Language Model Agents for Question Answering](https://mlsanity.com/paper/2503.19213/) (2025)
- [MARS: Meaning-Aware Response Scoring for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2402.11756/) (2024)
- [Multicalibration for Confidence Scoring in LLMs](https://mlsanity.com/paper/2404.04689/) (2024)
- [Characterizing Truthfulness in Large Language Model Generations with Local Intrinsic Dimension](https://mlsanity.com/paper/2402.18048/) (2024)
- [UProp: Investigating the Uncertainty Propagation of LLMs in Multi-Step Agentic Decision-Making](https://mlsanity.com/paper/2506.17419/) (2025)

## Abstract (arXiv)

Large language models (LLMs) specializing in natural language generation (NLG) have recently started exhibiting promising capabilities across a variety of domains. However, gauging the trustworthiness of responses generated by LLMs remains an open challenge, with limited research on uncertainty quantification (UQ) for NLG. Furthermore, existing literature typically assumes white-box access to language models, which is becoming unrealistic either due to the closed-source nature of the latest LLMs or computational constraints. In this work, we investigate UQ in NLG for *black-box* LLMs. We first differentiate *uncertainty* vs *confidence*: the former refers to the ``dispersion'' of the potential predictions for a fixed input, and the latter refers to the confidence on a particular prediction/generation. We then propose and compare several confidence/uncertainty measures, applying them to *selective NLG* where unreliable results could either be ignored or yielded for further assessment. Experiments were carried out with several popular LLMs on question-answering datasets (for evaluation purposes). Results reveal that a simple measure for the semantic dispersion can be a reliable predictor of the quality of LLM responses, providing valuable insights for practitioners on uncertainty management when adopting LLMs. The code to replicate our experiments is available at https://github.com/zlin7/UQ-NLG.