# Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models

arXiv: https://arxiv.org/abs/2502.14427 · HTML: https://mlsanity.com/paper/2502.14427/

## Key facts

- Cited by 18 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 20 Feb 2025.

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

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Get To The Point: Summarization with Pointer-Generator Networks](https://mlsanity.com/paper/1704.04368/) (2017)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization](https://mlsanity.com/paper/1911.12237/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Unsupervised Quality Estimation for Neural Machine Translation](https://mlsanity.com/paper/2005.10608/) (2020)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [On the Origin of Hallucinations in Conversational Models: Is it the Datasets or the Models?](https://mlsanity.com/paper/2204.07931/) (2022)
- [A Question-Entailment Approach to Question Answering](https://mlsanity.com/paper/1901.08079/) (2019)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Revisiting Mahalanobis Distance for Transformer-Based Out-of-Domain Detection](https://mlsanity.com/paper/2101.03778/) (2021)

## Built on by (most cited first, 18 of 18)

- [Efficient Hallucination Detection for LLMs Using Uncertainty-Aware Attention Heads](https://mlsanity.com/paper/2505.20045/) (2025)
- [When Models Lie, We Learn: Multilingual Span-Level Hallucination Detection with PsiloQA](https://mlsanity.com/paper/2510.04849/) (2025)
- [Will It Still Be True Tomorrow? Multilingual Evergreen Question Classification to Improve Trustworthy QA](https://mlsanity.com/paper/2505.21115/) (2025)
- [Are LLM Evaluators Really Narcissists? Sanity Checking Self-Preference Evaluations](https://mlsanity.com/paper/2601.22548/) (2026)
- [Geometry-Calibrated Conformal Abstention for Language Models](https://mlsanity.com/paper/2604.27914/) (2026)
- [First Hallucination Tokens Are Different from Conditional Ones](https://mlsanity.com/paper/2507.20836/) (2025)
- [Semantic Self-Distillation for Language Model Uncertainty](https://mlsanity.com/paper/2602.04577/) (2026)
- [The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimation](https://mlsanity.com/paper/2603.24124/) (2026)
- [SIMBA UQ: Similarity-Based Aggregation for Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2510.13836/) (2025)
- [When Should LLMs Be Less Specific? Selective Abstraction for Reliable Long-Form Text Generation](https://mlsanity.com/paper/2602.11908/) (2026)
- [From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2606.27679/) (2026)
- [Token-Level Marginalization for Multi-Label LLM Classifiers](https://mlsanity.com/paper/2511.22312/) (2025)
- [Leveraging LLM Parametric Knowledge for Fact Checking without Retrieval](https://mlsanity.com/paper/2603.05471/) (2026)
- [Efficient Uncertainty Estimation for LLM-based Entity Linking in Tabular Data](https://mlsanity.com/paper/2510.01251/) (2025)
- [Towards Reliable Truth-Aligned Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2604.00445/) (2026)
- [Uncertainty Quantification for Large Language Diffusion Models](https://mlsanity.com/paper/2605.14570/) (2026)
- [SpanUQ: Span-Level Uncertainty Quantification for Large Language Model Generation](https://mlsanity.com/paper/2607.05721/) (2026)
- [Trust Your Guide Only When Certain: Uncertainty-Aware Sparse Alignment at Inference Time](https://mlsanity.com/paper/2609.00624/) (2026)

## Abstract (arXiv)

Uncertainty quantification (UQ) is a prominent approach for eliciting truthful answers from large language models (LLMs). To date, information-based and consistency-based UQ have been the dominant UQ methods for text generation via LLMs. Density-based methods, despite being very effective for UQ in text classification with encoder-based models, have not been very successful with generative LLMs. In this work, we adapt Mahalanobis Distance (MD) - a well-established UQ technique in classification tasks - for text generation and introduce a new supervised UQ method. Our method extracts token embeddings from multiple layers of LLMs, computes MD scores for each token, and uses linear regression trained on these features to provide robust uncertainty scores. Through extensive experiments on eleven datasets, we demonstrate that our approach substantially improves over existing UQ methods, providing accurate and computationally efficient uncertainty scores for both sequence-level selective generation and claim-level fact-checking tasks. Our method also exhibits strong generalization to out-of-domain data, making it suitable for a wide range of LLM-based applications.