# SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models

arXiv: https://arxiv.org/abs/2403.02509 · HTML: https://mlsanity.com/paper/2403.02509/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 4 Mar 2024.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [How Language Model Hallucinations Can Snowball](https://mlsanity.com/paper/2305.13534/) (2023)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [How Robust is GPT-3.5 to Predecessors? A Comprehensive Study on Language Understanding Tasks](https://mlsanity.com/paper/2303.00293/) (2023)
- [Exploiting Epistemic Uncertainty of Anatomy Segmentation for Anomaly Detection in Retinal OCT](https://mlsanity.com/paper/1905.12806/) (2019)
- [Exploiting epistemic uncertainty of the deep learning models to generate adversarial samples](https://mlsanity.com/paper/2102.04150/) (2021)

## Built on by (most cited first, 30 of 56)

- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation](https://mlsanity.com/paper/2410.13640/) (2024)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [DYNAMICQA: Tracing Internal Knowledge Conflicts in Language Models](https://mlsanity.com/paper/2407.17023/) (2024)
- [Understanding Model Calibration -- A gentle introduction and visual exploration of calibration and the expected calibration error (ECE)](https://mlsanity.com/paper/2501.19047/) (2025)
- [Uncertainty-Aware Hybrid Inference with On-Device Small and Remote Large Language Models](https://mlsanity.com/paper/2412.12687/) (2024)
- [Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure](https://mlsanity.com/paper/2412.15176/) (2024)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [MUR: Momentum Uncertainty guided Reasoning for Large Language Models](https://mlsanity.com/paper/2507.14958/) (2025)
- [Enhancing Hallucination Detection through Noise Injection](https://mlsanity.com/paper/2502.03799/) (2025)
- [Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification](https://mlsanity.com/paper/2604.17112/) (2026)
- [Textual Bayes: Quantifying Prompt Uncertainty in LLM-Based Systems](https://mlsanity.com/paper/2506.10060/) (2025)
- [Semantic Uncertainty Quantification of Hallucinations in LLMs: A Quantum Tensor Network Based Method](https://mlsanity.com/paper/2601.20026/) (2026)
- [Functional-level Uncertainty Quantification for Calibrated Fine-tuning on LLMs](https://mlsanity.com/paper/2410.06431/) (2024)
- [Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models](https://mlsanity.com/paper/2506.09684/) (2025)
- [The Consistency Hypothesis in Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2506.21849/) (2025)
- [Communication-Efficient Hybrid Language Model via Uncertainty-Aware Opportunistic and Compressed Transmission](https://mlsanity.com/paper/2505.11788/) (2025)
- [CoRE: Enhancing Metacognition with Label-free Self-evaluation in LRMs](https://mlsanity.com/paper/2507.06087/) (2025)
- [D2HScore: Reasoning-Aware Hallucination Detection via Semantic Breadth and Depth Analysis in LLMs](https://mlsanity.com/paper/2509.11569/) (2025)
- [HEDGE: Hallucination Estimation via Dense Geometric Entropy for VQA with Vision-Language Models](https://mlsanity.com/paper/2511.12693/) (2025)
- [Recurrent Confidence Chain: Temporal-Aware Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2601.13368/) (2026)
- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [Understanding The Effect Of Temperature On Alignment With Human Opinions](https://mlsanity.com/paper/2411.10080/) (2024)
- [Comparing Uncertainty Measurement and Mitigation Methods for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2504.18346/) (2025)
- [Uncertainty Profiles for LLMs: Uncertainty Source Decomposition and Adaptive Model-Metric Selection](https://mlsanity.com/paper/2505.07309/) (2025)
- [Semantic Self-Distillation for Language Model Uncertainty](https://mlsanity.com/paper/2602.04577/) (2026)
- [Beyond Consensus: Trace-Level Synthesis in Mixture of Agents](https://mlsanity.com/paper/2605.29116/) (2026)
- [Improving Semantic Uncertainty Quantification in LVLMs with Semantic Gaussian Processes](https://mlsanity.com/paper/2512.14177/) (2025)
- [Variability Need Not Imply Error: The Case of Adequate but Semantically Distinct Responses](https://mlsanity.com/paper/2412.15683/) (2024)
- [Toward Efficient Uncertainty in LLMs through Evidential Knowledge Distillation](https://mlsanity.com/paper/2507.18366/) (2025)

## Abstract (arXiv)

In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the critical need for uncertainty quantification (UQ) in LLMs. While previous works have mainly focused on addressing aleatoric uncertainty, the full spectrum of uncertainties, including epistemic, remains inadequately explored. Motivated by this gap, we introduce a novel UQ method, sampling with perturbation for UQ (SPUQ), designed to tackle both aleatoric and epistemic uncertainties. The method entails generating a set of perturbations for LLM inputs, sampling outputs for each perturbation, and incorporating an aggregation module that generalizes the sampling uncertainty approach for text generation tasks. Through extensive experiments on various datasets, we investigated different perturbation and aggregation techniques. Our findings show a substantial improvement in model uncertainty calibration, with a reduction in Expected Calibration Error (ECE) by 50% on average. Our findings suggest that our proposed UQ method offers promising steps toward enhancing the reliability and trustworthiness of LLMs.