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Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate…

Artificial Intelligence · Computer Science 2026-02-02 Hao Yi , Yulan Hu , Xin Li , Sheng Ouyang , Lizhong Ding , Yong Liu

Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a…

Machine Learning · Computer Science 2018-11-06 Hui-Ling Zhen , Xi Lin , Alan Z. Tang , Zhenhua Li , Qingfu Zhang , Sam Kwong

Deep Neural Networks (DNNs), despite their tremendous success in recent years, could still cast doubts on their predictions due to the intrinsic uncertainty associated with their learning process. Ensemble techniques and post-hoc…

Machine Learning · Computer Science 2022-03-03 Chunwei Ma , Ziyun Huang , Jiayi Xian , Mingchen Gao , Jinhui Xu

Precise probabilistic forecasts are fundamental for energy risk management, and there is a wide range of both statistical and machine learning models for this purpose. Inherent to these probabilistic models is some form of uncertainty…

Machine Learning · Computer Science 2025-10-10 Andreas Lebedev , Abhinav Das , Sven Pappert , Stephan Schlüter

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

Machine Learning · Computer Science 2023-05-24 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to…

Machine Learning · Statistics 2023-06-27 Takuo Matsubara , Niek Tax , Richard Mudd , Ido Guy

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…

The neural network (NN)-based direct uncertainty quantification (UQ) methods have achieved the state of the art performance since the first inauguration, known as the lower-upper-bound estimation (LUBE) method. However, currently-available…

Machine Learning · Statistics 2024-07-16 H M Dipu Kabir , Abbas Khosravi , Abdollah Kavousi-Fard , Saeid Nahavandi , Dipti Srinivasan

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

Continual learning (CL) refers to the ability to continuously learn and accumulate new knowledge while retaining useful information from past experiences. Although numerous CL methods have been proposed in recent years, it is not…

Machine Learning · Statistics 2025-03-27 Hanwen Xing , Christopher Yau

With the advancement of deep learning technology, neural networks have demonstrated their excellent ability to provide accurate predictions in many tasks. However, a lack of consideration for neural network calibration will not gain trust…

Machine Learning · Computer Science 2022-11-30 Lei Hsiung , Yung-Chen Tang , Pin-Yu Chen , Tsung-Yi Ho

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

Laplace approximations are classic, computationally lightweight means for constructing Bayesian neural networks (BNNs). As in other approximate BNNs, one cannot necessarily expect the induced predictive uncertainty to be calibrated. Here we…

Machine Learning · Computer Science 2021-06-08 Agustinus Kristiadi , Matthias Hein , Philipp Hennig

Model calibration, which is concerned with how frequently the model predicts correctly, not only plays a vital part in statistical model design, but also has substantial practical applications, such as optimal decision-making in the real…

Machine Learning · Statistics 2023-01-18 Erdong Guo , David Draper , Maria De Iorio

While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…

Machine Learning · Computer Science 2020-04-08 Fredrik K. Gustafsson , Martin Danelljan , Thomas B. Schön

Large Language Models (LLMs) have been widely employed in programming language analysis to enhance human productivity. Yet, their reliability can be compromised by various code distribution shifts, leading to inconsistent outputs. While…

Software Engineering · Computer Science 2024-02-12 Yufei Li , Simin Chen , Yanghong Guo , Wei Yang , Yue Dong , Cong Liu

Machine unlearning seeks to remove the influence of specified data from a trained model. While the unlearning accuracy provides a widely used metric for assessing unlearning performance, it falls short in assessing the reliability of…

Machine Learning · Computer Science 2026-05-13 Yingdan Shi , Sijia Liu , Kaize Ding , Ren Wang

Uncertainty quantification of machine learning and deep learning methods plays an important role in enhancing trust to the obtained result. In recent years, a numerous number of uncertainty quantification methods have been introduced. Monte…

Machine Learning · Computer Science 2023-02-07 Afshar Shamsi , Hamzeh Asgharnezhad , AmirReza Tajally , Saeid Nahavandi , Henry Leung

Deep neural networks, despite their high accuracy, often exhibit poor confidence calibration, limiting their reliability in high-stakes applications. Current ad-hoc confidence calibration methods attempt to fix this during training but face…

Machine Learning · Computer Science 2026-04-15 Sandra Gómez-Gálvez , Tobias Olenyi , Gillian Dobbie , Katerina Taškova

The calibration of predictive distributions has been widely studied in deep learning, but the same cannot be said about the more specific epistemic uncertainty as produced by Deep Ensembles, Bayesian Deep Networks, or Evidential Deep…

Machine Learning · Computer Science 2024-07-18 Mohammed Fellaji , Frédéric Pennerath , Brieuc Conan-Guez , Miguel Couceiro
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