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Training neural networks with verifiable robustness guarantees is challenging. Several existing approaches utilize linear relaxation based neural network output bounds under perturbation, but they can slow down training by a factor of…

Machine Learning · Computer Science 2019-11-28 Huan Zhang , Hongge Chen , Chaowei Xiao , Sven Gowal , Robert Stanforth , Bo Li , Duane Boning , Cho-Jui Hsieh

Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…

Machine Learning · Computer Science 2020-10-27 Jeremiah Zhe Liu , Zi Lin , Shreyas Padhy , Dustin Tran , Tania Bedrax-Weiss , Balaji Lakshminarayanan

Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…

Machine Learning · Computer Science 2022-12-01 Philipp Wagner , Xinyang Wu , Marco F. Huber

Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…

Numerical Analysis · Mathematics 2021-11-30 Christophe Bonneville , Christopher J. Earls

Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of…

Machine Learning · Computer Science 2022-10-07 Jary Pomponi , Simone Scardapane , Aurelio Uncini

Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…

Machine Learning · Computer Science 2025-12-01 Bernhard Klein , Falk Selker , Hendrik Borras , Sophie Steger , Franz Pernkopf , Holger Fröning

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning…

Machine Learning · Statistics 2021-06-01 Sebastian Farquhar , Michael Osborne , Yarin Gal

We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…

Machine Learning · Statistics 2018-06-12 Hao Henry Zhou , Yunyang Xiong , Vikas Singh

Deep Neural Nets (DNNs) learn latent representations induced by their downstream task, objective function, and other parameters. The quality of the learned representations impacts the DNN's generalization ability and the coherence of the…

Machine Learning · Computer Science 2024-02-13 Nir Weingarten , Zohar Yakhini , Moshe Butman , Ran Gilad-Bachrach

The existence of adversarial examples underscores the importance of understanding the robustness of machine learning models. Bayesian neural networks (BNNs), due to their calibrated uncertainty, have been shown to posses favorable…

Machine Learning · Computer Science 2020-12-24 Matthew Yuan , Matthew Wicker , Luca Laurenti

Deployment of deep neural networks (DNNs) in safety- or security-critical systems requires provable guarantees on their correct behaviour. A common requirement is robustness to adversarial perturbations in a neighbourhood around an input.…

Machine Learning · Computer Science 2018-11-21 Wenjie Ruan , Min Wu , Youcheng Sun , Xiaowei Huang , Daniel Kroening , Marta Kwiatkowska

In this work, we propose an effective scheme (called DP-Net) for compressing the deep neural networks (DNNs). It includes a novel dynamic programming (DP) based algorithm to obtain the optimal solution of weight quantization and an…

Machine Learning · Computer Science 2020-03-24 Dingcheng Yang , Wenjian Yu , Ao Zhou , Haoyuan Mu , Gary Yao , Xiaoyi Wang

Bayesian neural networks (BNNs) have become a principal approach to alleviate overconfident predictions in deep learning, but they often suffer from scaling issues due to a large number of distribution parameters. In this paper, we discover…

Machine Learning · Computer Science 2021-12-14 Shiye Lei , Zhuozhuo Tu , Leszek Rutkowski , Feng Zhou , Li Shen , Fengxiang He , Dacheng Tao

Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…

Machine Learning · Computer Science 2015-03-10 Naftali Tishby , Noga Zaslavsky

Deep neural network (DNN) models have achieved state-of-the-art predictive accuracy in a wide range of supervised learning applications. However, accurately quantifying the uncertainty in DNN predictions remains a challenging task. For…

Machine Learning · Computer Science 2022-06-14 Daiwei Zhang , Tianci Liu , Jian Kang

Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…

Artificial Intelligence · Computer Science 2013-02-08 Fabio Gagliardi Cozman

Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…

Machine Learning · Computer Science 2020-01-28 Evgenii Tsymbalov , Sergei Makarychev , Alexander Shapeev , Maxim Panov

We propose Impatient Deep Neural Networks (DNNs) which deal with dynamic time budgets during application. They allow for individual budgets given a priori for each test example and for anytime prediction, i.e., a possible interruption at…

Computer Vision and Pattern Recognition · Computer Science 2016-10-11 Manuel Amthor , Erik Rodner , Joachim Denzler

Bayesian Neural Networks (BNN) have recently emerged in the Deep Learning world for dealing with uncertainty estimation in classification tasks, and are used in many application domains such as astrophysics, autonomous driving...BNN assume…

Machine Learning · Computer Science 2021-02-04 Claire Theobald , Frédéric Pennerath , Brieuc Conan-Guez , Miguel Couceiro , Amedeo Napoli

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

Machine Learning · Statistics 2023-05-25 Insung Kong , Dongyoon Yang , Jongjin Lee , Ilsang Ohn , Gyuseung Baek , Yongdai Kim