# Fine-Grained Uncertainty Decomposition in Large Language Models: A Spectral Approach

arXiv: https://arxiv.org/abs/2509.22272 · HTML: https://mlsanity.com/paper/2509.22272/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [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)
- [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)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [AmbigQA: Answering Ambiguous Open-domain Questions](https://mlsanity.com/paper/2004.10645/) (2020)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [ChatGPT: A Meta-Analysis after 2.5 Months](https://mlsanity.com/paper/2302.13795/) (2023)
- [The Widespread Adoption of Large Language Model-Assisted Writing Across Society](https://mlsanity.com/paper/2502.09747/) (2025)
- [Probabilistic Contrastive Learning Recovers the Correct Aleatoric Uncertainty of Ambiguous Inputs](https://mlsanity.com/paper/2302.02865/) (2023)
- [Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition](https://mlsanity.com/paper/2210.12256/) (2022)
- [A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Models](https://mlsanity.com/paper/2310.05833/) (2023)

## Built on by (most cited first, 10 of 10)

- [The Illusion of Certainty: Uncertainty Quantification for LLMs Fails under Ambiguity](https://mlsanity.com/paper/2511.04418/) (2025)
- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [When Confidence Takes the Wrong Path: Diagnosing Retrieval-State Lock-In in RAG](https://mlsanity.com/paper/2606.22728/) (2026)
- [The Role of Ambiguity in Error Prediction via Uncertainty Quantification](https://mlsanity.com/paper/2606.02093/) (2026)
- [A Risk Decomposition Framework for Pre-Hoc Fine-Tuning Prediction](https://mlsanity.com/paper/2606.17649/) (2026)
- [Eigenvalue Calibration for Semantic Embeddings of Large Language Models](https://mlsanity.com/paper/2607.08377/) (2026)
- [Limits of Reliability and Scaling in Language Models](https://mlsanity.com/paper/2607.14112/) (2026)
- [From Tokens to Semantics: Leveraging Complementary Signals for Hallucination Detection in Black-Box LLMs](https://mlsanity.com/paper/2609.02679/) (2026)
- [From Answers to Interpretations: Rethinking Ambiguity-Induced Aleatoric Uncertainty Estimation in LLMs](https://mlsanity.com/paper/2609.04543/) (2026)
- [What Is a Clarification? Estimating Model-Dependent Input Ambiguity](https://mlsanity.com/paper/2610.20052/) (2026)

## Abstract (arXiv)

As Large Language Models (LLMs) are increasingly integrated in diverse applications, obtaining reliable measures of their predictive uncertainty has become critically important. A precise distinction between aleatoric uncertainty, arising from inherent ambiguities within input data, and epistemic uncertainty, originating exclusively from model limitations, is essential to effectively address each uncertainty source. In this paper, we introduce Spectral Uncertainty, a novel approach to quantifying and decomposing uncertainties in LLMs. Leveraging the Von Neumann entropy from quantum information theory, Spectral Uncertainty provides a rigorous theoretical foundation for separating total uncertainty into distinct aleatoric and epistemic components. Unlike existing baseline methods, our approach incorporates a fine-grained representation of semantic similarity, enabling nuanced differentiation among various semantic interpretations in model responses. Empirical evaluations demonstrate that Spectral Uncertainty outperforms state-of-the-art methods in estimating both aleatoric and total uncertainty across diverse models and benchmark datasets.