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Consistency-based methods have emerged as an effective approach to uncertainty quantification (UQ) in large language models. These methods typically rely on several generations obtained via multinomial sampling, measuring their agreement…

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…

Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving…

Probability · Mathematics 2020-09-04 Jeremiah Birrell , Markos A. Katsoulakis , Luc Rey-Bellet

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…

Large language models (LLMs) have revolutionized the field of natural language processing with their impressive reasoning and question-answering capabilities. However, these models are sometimes prone to generating credible-sounding but…

Computation and Language · Computer Science 2026-04-21 Ranganath Krishnan , Piyush Khanna , Omesh Tickoo

Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial…

Machine Learning · Statistics 2024-10-29 Alberto Portela , Julio R. Banga , Marcos Matabuena

With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and…

Computation and Language · Computer Science 2024-11-04 Xin Qiu , Risto Miikkulainen

The rise of large language models (LLMs) and their tight integration into our daily life make it essential to dedicate efforts towards their trustworthiness. Uncertainty quantification for LLMs can establish more human trust into their…

Computation and Language · Computer Science 2026-05-06 Daniel Yang , Yao-Hung Hubert Tsai , Makoto Yamada

Large Language Models (LLMs) are prone to hallucination, particularly in long-form generations. A promising direction to mitigate hallucination is to teach LLMs to express uncertainty explicitly when they lack sufficient knowledge. However,…

Computation and Language · Computer Science 2025-10-10 Ruihan Yang , Caiqi Zhang , Zhisong Zhang , Xinting Huang , Dong Yu , Nigel Collier , Deqing Yang

Large Reasoning Models (LRMs) have recently demonstrated significant improvements in complex reasoning. While quantifying generation uncertainty in LRMs is crucial, traditional methods are often insufficient because they do not provide…

Artificial Intelligence · Computer Science 2026-04-16 Yangyi Li , Chenxu Zhao , Mengdi Huai

Deep Neural Networks (DNNs) have demonstrated remarkable performance across various domains, including computer vision and natural language processing. However, they often struggle to accurately quantify the uncertainty of their…

Machine Learning · Computer Science 2025-11-14 Adrien Lafage , Olivier Laurent , Firas Gabetni , Gianni Franchi

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…

Machine Learning · Computer Science 2019-06-04 Minsuk Shin , Young Lee , Jun S. Liu

The generation of texts using Large Language Models (LLMs) is inherently uncertain, with sources of uncertainty being not only the generation of texts, but also the prompt used and the downstream interpretation. Within this work, we provide…

Machine Learning · Computer Science 2026-03-30 Steffen Herbold , Florian Lemmerich

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally…

Machine Learning · Computer Science 2026-03-09 Azza Jenane , Nassim Walha , Lukas Kuhn , Florian Buettner

Hallucinations, defined as instances where Large Language Models (LLMs) generate false or misleading content, pose a significant challenge that impacts the safety and trust of downstream applications. We introduce UQLM, a Python package for…

Computation and Language · Computer Science 2026-03-05 Dylan Bouchard , Mohit Singh Chauhan , David Skarbrevik , Ho-Kyeong Ra , Viren Bajaj , Zeya Ahmad

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification…

Machine Learning · Computer Science 2025-06-09 Sima Noorani , Shayan Kiyani , George Pappas , Hamed Hassani

Prompt optimization algorithms for Large Language Models (LLMs) excel in multi-step reasoning but still lack effective uncertainty estimation. This paper introduces a benchmark dataset to evaluate uncertainty metrics, focusing on Answer,…

Machine Learning · Computer Science 2024-12-30 Pei-Fu Guo , Yun-Da Tsai , Shou-De Lin

Machine learning (ML) is often viewed as a powerful data analysis tool that is easy to learn because of its black-box nature. Yet this very nature also makes it difficult to quantify confidence in predictions extracted from ML models, and…

Machine Learning · Computer Science 2025-09-30 Paul Patrone , Anthony Kearsley

Uncertainty quantification (UQ) in Large Language Models (LLMs) is essential for their safe and reliable deployment, particularly in critical applications where incorrect outputs can have serious consequences. Current UQ methods typically…

Computation and Language · Computer Science 2025-04-10 Nicola Cecere , Andrea Bacciu , Ignacio Fernández Tobías , Amin Mantrach

Reliable uncertainty quantification (UQ) is essential for developing machine-learned interatomic potentials (MLIPs) in predictive atomistic simulations. Conformal prediction (CP) is a statistical framework that constructs prediction…

Chemical Physics · Physics 2025-10-02 Cheuk Hin Ho , Christoph Ortner , Yangshuai Wang