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Artificial Intelligence (AI) increasingly shows its potential to outperform predicate logic algorithms and human control alike. In automatically deriving a system model, AI algorithms learn relations in data that are not detectable for…

Artificial Intelligence · Computer Science 2022-10-12 Simon Daniel Duque Anton , Daniel Schneider , Hans Dieter Schotten

Techniques for understanding the functioning of complex machine learning models are becoming increasingly popular, not only to improve the validation process, but also to extract new insights about the data via exploratory analysis. Though…

Machine Learning · Statistics 2018-11-02 Jayaraman J. Thiagarajan , Irene Kim , Rushil Anirudh , Peer-Timo Bremer

Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical…

Machine Learning · Computer Science 2021-12-03 Achintya Gopal

Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…

Computer Vision and Pattern Recognition · Computer Science 2020-12-01 Riccardo Barbano , Željko Kereta , Chen Zhang , Andreas Hauptmann , Simon Arridge , Bangti Jin

Epistemic uncertainty is crucial for safety-critical applications and data acquisition tasks. Yet, we find an important phenomenon in deep learning models: an epistemic uncertainty collapse as model complexity increases, challenging the…

Machine Learning · Computer Science 2025-05-27 Andreas Kirsch

Uncertainty defines our age: it shapes climate, finance, technology, and society, yet remains profoundly misunderstood. We oscillate between the illusion of control and the paralysis of fatalism. This paper reframes uncertainty not as…

Physics and Society · Physics 2025-10-21 Didier Sornette

Reliable Large Language Models (LLMs) should abstain when confidence is insufficient. However, prior studies often treat refusal as a generic "I don't know'', failing to distinguish input-level ambiguity (data uncertainty) from capability…

Computation and Language · Computer Science 2026-04-21 Jingyi Ren , Ante Wang , Yunghwei Lai , Xiaolong Wang , Linlu Gong , Weitao Li , Weizhi Ma , Yang Liu

Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show…

Machine Learning · Statistics 2024-07-03 Mohammed Fellaji , Frédéric Pennerath

This paper proposes a paradigm of uncertainty injection for training deep learning model to solve robust optimization problems. The majority of existing studies on deep learning focus on the model learning capability, while assuming the…

Machine Learning · Computer Science 2023-02-28 Wei Cui , Wei Yu

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

Machine Learning · Computer Science 2025-03-05 Dimitris Bertsimas , Benjamin Boucher

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…

Machine Learning · Statistics 2022-11-10 Bat-Sheva Einbinder , Yaniv Romano , Matteo Sesia , Yanfei Zhou

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…

Machine Learning · Computer Science 2026-05-29 Jiaxiang Yi , Miguel A. Bessa

One of the ways to make artificial intelligence more natural is to give it some room for doubt. Two main questions should be resolved in that way. First, how to train a model to estimate uncertainties of its own predictions? And then, what…

Computer Vision and Pattern Recognition · Computer Science 2024-04-17 Alexey Kornaev , Elena Kornaeva , Oleg Ivanov , Ilya Pershin , Danis Alukaev

The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…

Artificial Intelligence · Computer Science 2024-03-08 Yoshua Bengio , Nikolay Malkin

Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video…

Artificial Intelligence · Computer Science 2016-11-03 Brenden M. Lake , Tomer D. Ullman , Joshua B. Tenenbaum , Samuel J. Gershman

Interpretable machine learning tackles the important problem that humans cannot understand the behaviors of complex machine learning models and how these models arrive at a particular decision. Although many approaches have been proposed, a…

Machine Learning · Computer Science 2019-05-21 Mengnan Du , Ninghao Liu , Xia Hu

Although AI has become increasingly smart, its wisdom has not kept pace. In this article, we examine what is known about human wisdom and sketch a vision of its AI counterpart. We analyze human wisdom as a set of strategies for solving…

Integrated Assessment Models (IAMs) are pivotal tools that synthesize knowledge from climate science, economics, and policy to evaluate the interactions between human activities and the climate system. They serve as essential instruments…

General Economics · Economics 2025-11-04 Yongyang Cai

Intelligence relies on an agent's knowledge of what it does not know. This capability can be assessed based on the quality of joint predictions of labels across multiple inputs. In principle, ensemble-based approaches produce effective…

While Large Language Models (LLMs) show remarkable capabilities, their unreliability remains a critical barrier to deployment in high-stakes domains. This survey charts a functional evolution in addressing this challenge: the evolution of…

Artificial Intelligence · Computer Science 2026-04-21 Jiaxin Zhang , Wendi Cui , Zhuohang Li , Lifu Huang , Bradley Malin , Caiming Xiong , Chien-Sheng Wu