# Uncertainty Quantification of Large Language Models through Multi-Dimensional Responses

arXiv: https://arxiv.org/abs/2502.16820 · HTML: https://mlsanity.com/paper/2502.16820/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 22 of 22)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Selective Question Answering under Domain Shift](https://mlsanity.com/paper/2006.09462/) (2020)
- [LLM Lies: Hallucinations are not Bugs, but Features as Adversarial Examples](https://mlsanity.com/paper/2310.01469/) (2023)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Decomposition Dilemmas: Does Claim Decomposition Boost or Burden Fact-Checking Performance?](https://mlsanity.com/paper/2411.02400/) (2024)
- [Uncertainty-Aware Machine Translation Evaluation](https://mlsanity.com/paper/2109.06352/) (2021)
- [FACT-GPT: Fact-Checking Augmentation via Claim Matching with LLMs](https://mlsanity.com/paper/2402.05904/) (2024)
- [LLM Uncertainty Quantification through Directional Entailment Graph and Claim Level Response Augmentation](https://mlsanity.com/paper/2407.00994/) (2024)
- [From Aleatoric to Epistemic: Exploring Uncertainty Quantification Techniques in Artificial Intelligence](https://mlsanity.com/paper/2501.03282/) (2025)

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

- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Joint Evaluation of Answer and Reasoning Consistency for Hallucination Detection in Large Reasoning Models](https://mlsanity.com/paper/2506.04832/) (2025)
- [Generative AI in Transportation Planning: A Survey](https://mlsanity.com/paper/2503.07158/) (2025)
- [Every Response Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition](https://mlsanity.com/paper/2604.08708/) (2026)
- [Are LLM Uncertainty and Correctness Encoded by the Same Features? A Functional Dissociation via Sparse Autoencoders](https://mlsanity.com/paper/2604.19974/) (2026)
- [Walking Through Uncertainty: An Empirical Study of Uncertainty Estimation for Audio-Aware Large Language Models](https://mlsanity.com/paper/2604.25591/) (2026)
- [Improving Semantic Uncertainty Quantification in LVLMs with Semantic Gaussian Processes](https://mlsanity.com/paper/2512.14177/) (2025)
- [SymLight: Exploring Interpretable and Deployable Symbolic Policies for Traffic Signal Control](https://mlsanity.com/paper/2511.05790/) (2025)
- [ALARM: Automated MLLM-Based Anomaly Detection in Complex-EnviRonment Monitoring with Uncertainty Quantification](https://mlsanity.com/paper/2512.03101/) (2025)
- [Anatomy of a Lie: A Multi-Stage Diagnostic Framework for Tracing Hallucinations in Vision-Language Models](https://mlsanity.com/paper/2603.15557/) (2026)
- [Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution](https://mlsanity.com/paper/2605.19228/) (2026)
- [Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty](https://mlsanity.com/paper/2606.17312/) (2026)
- [A Systematic Evaluation of Black-Box Uncertainty Estimation Methods for Large Language Models](https://mlsanity.com/paper/2606.19868/) (2026)
- [The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2606.22792/) (2026)
- [Beyond statistical significance: Quantifying uncertainty and statistical variability in multilingual and multitask NLP evaluation](https://mlsanity.com/paper/2509.22612/) (2025)
- [Embedding Trust: Semantic Isotropy Predicts Nonfactuality in Long-Form Text Generation](https://mlsanity.com/paper/2510.21891/) (2025)
- [Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering](https://mlsanity.com/paper/2605.19220/) (2026)
- [Leveraging Visual Signals for Robust Token-Level Uncertainty in Vision-Language Generation](https://mlsanity.com/paper/2605.27136/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks due to large training datasets and powerful transformer architecture. However, the reliability of responses from LLMs remains a question. Uncertainty quantification (UQ) of LLMs is crucial for ensuring their reliability, especially in areas such as healthcare, finance, and decision-making. Existing UQ methods primarily focus on semantic similarity, overlooking the deeper knowledge dimensions embedded in responses. We introduce a multi-dimensional UQ framework that integrates semantic and knowledge-aware similarity analysis. By generating multiple responses and leveraging auxiliary LLMs to extract implicit knowledge, we construct separate similarity matrices and apply tensor decomposition to derive a comprehensive uncertainty representation. This approach disentangles overlapping information from both semantic and knowledge dimensions, capturing both semantic variations and factual consistency, leading to more accurate UQ. Our empirical evaluations demonstrate that our method outperforms existing techniques in identifying uncertain responses, offering a more robust framework for enhancing LLM reliability in high-stakes applications.