OpenAI Blog

Teaching models to express their uncertainty in words

arXiv AI
Jul 7

The Anatomy of Uncertainty in LLMs

arXiv:2603. 24967v2 Announce Type: replace Abstract: Understanding why a large language model (LLM) is uncertain about the response is important for their reliable deployment.

By Aditya Taparia, Ransalu Senanayake, Kowshik Thopalli, Vivek Narayanaswamy
arXiv Computation and Language
Sep 23

Semantic Self-Distillation for Language Model Uncertainty

Semantic Self-Distillation (SSD) is a method that distills the semantic dispersion of sampled answers from large language models into lightweight student models. These students estimate a prompt-conditioned density before answer generation, providing a prompt-level uncertainty signal via entropy and an answer-level reliability measure through probability density. Experiments on TriviaQA and MMLU show that SSD matches the teacher’s uncertainty estimates while enabling additional tasks such as hallucination prediction, out-of-domain detection, and multiple-choice answer selection.

By Edward Phillips, Sean Wu, Fredrik K. Gustafsson, Boyan Gao, David A. Clifton
arXiv AI
2d ago

Verbalized and Internal Probabilities Are Coupled in Large Language Models

The paper investigates the relationship between a large language model’s internal probability distribution and its verbalized confidence statements. By systematically manipulating training and in‑context data, the authors show that both internal and verbalized probabilities are influenced by distributional and asserted uncertainty in the data. They find that verbalized probabilities align with internal ones beyond what would be expected if they tracked the same sources independently, indicating that verbalized confidence can serve as a probe of the model’s internal distribution.

By Sinead Williamson, Jiaxuan Li, Nick Foti, Russ Webb, Masha Fedzechkina
Hugging Face Trending Papers
Jun 22

The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models

Recent advancements in Large Language Models (LLMs) have enabled sophisticated reasoning and content generation, yet their inherent stochasticity poses significant challenges for ensuring predictive credibility. While traditional uncertainty taxonomy paradigms, such as the dichotomy of aleatoric and epistemic uncertainties, provide conceptual foundations, they often fail to capture the multi-component and multi-stage nature of LLM generation and struggle to evaluate the effectiveness of various Uncertainty Quantification (UQ) methods.

arXiv Machine Learning
1d ago

"very likely" Means "uncertain"? How LLMs Diverge from Humans in Linguistic Uncertainty Quantification

The paper examines how large language models (LLMs) express uncertainty compared to humans, noting that humans use verbal markers like "possible" or "likely" to convey metacognitive awareness. By curating a corpus of human uncertainty markers and benchmarking LLMs against it, the authors find that LLMs encode these markers with numerical levels that differ substantially from human usage. They introduce METHODNAME, an optimization-based algorithm that learns an optimal uncertainty profile over verbal markers directly from LLM outputs, enabling a direct comparison of confidence semantics and revealing systematic disparities in verbal expressions.

By Jinhao Duan, Zicheng Liu, Zijie Liu, Kaidi Xu, Tianlong Chen
arXiv AI
Jul 23

Rethinking Uncertainty Evaluation in Large Language Models

arXiv:2607. 19367v1 Announce Type: new Abstract: Calibration is the primary criterion for evaluating LLM confidence, but it is insufficient: it admits trivially incoherent estimators, depends on the evaluation distribution, and does not test the extent to which the estimation can be interpreted as a consistent, underlying probability function.

By Krish Matta, Atharv Naphade, Andy Zou
arXiv Machine Learning
Jun 11

What Uncertainties Do We Need for Dynamical Systems?

arXiv:2606. 11988v1 Announce Type: new Abstract: The distinction between aleatoric and epistemic uncertainty has received considerable attention in machine learning research, mainly in the context of supervised learning but also in other settings such as generative modeling.

By Yusuf Sale, Christopher B\"ulte, Felix Czaja, Joshua Stiller, Eyke H\"ullermeier
arXiv AI
Aug 28

How Unlikely Is "Unlikely"? Assessing Verbal Probability Perception Across Large Language Models

The study evaluates how large language models (LLMs) interpret verbal probability expressions by mapping words to numbers and testing consistency across 19 models. Results show that LLMs largely mirror human benchmarks—preserving word order, recovering key anchor points, and reflecting the high variance of the term "possible"—but they exhibit a systematic upward bias for negative expressions like "unlikely" and "improbable." Explanation elicitation reduces within‑model variance but increases divergence between models, while a bidirectional roundtrip test reveals that leading models maintain coherent internal representations.

By Christos Petridis, Konstantinos Pelechrinis, Zoran Obradovic