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Despite the considerable success of convolutional neural networks in a broad array of domains, recent research has shown these to be vulnerable to small adversarial perturbations, commonly known as adversarial examples. Moreover, such…

Machine Learning · Computer Science 2018-12-06 Yifan Chen , Yevgeniy Vorobeychik

Regularization, whether explicit in terms of a penalty in the loss or implicit in the choice of algorithm, is a cornerstone of modern machine learning. Indeed, controlling the complexity of the model class is particularly important when…

Machine Learning · Statistics 2024-10-22 Matteo Vilucchio , Nikolaos Tsilivis , Bruno Loureiro , Julia Kempe

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

Machine Learning · Computer Science 2020-02-28 Ankit Raj , Yoram Bresler , Bo Li

Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…

Optimization and Control · Mathematics 2025-08-08 Jie Gao , Cesare Molinari , Silvia Villa , Jingwei Liang

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…

Machine Learning · Computer Science 2024-08-23 Jie Wang , Rui Gao , Yao Xie

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we…

Machine Learning · Statistics 2023-06-02 Dongyoon Yang , Insung Kong , Yongdai Kim

Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…

Soft Condensed Matter · Physics 2023-08-10 Himangsu Bhaumik , Daniel Hexner

Adversarial training is widely used to improve the robustness of deep neural networks to adversarial attack. However, adversarial training is prone to overfitting, and the cause is far from clear. This work sheds light on the mechanisms…

Machine Learning · Computer Science 2022-12-12 Lin Li , Michael Spratling

Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The…

Image and Video Processing · Electrical Eng. & Systems 2022-06-22 Margaret Duff , Neill D. F. Campbell , Matthias J. Ehrhardt

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Numerical Analysis · Mathematics 2018-01-31 Martin Benning , Martin Burger

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…

Computer Vision and Pattern Recognition · Computer Science 2021-11-16 Shima Kamyab , Zohreh Azimifar , Rasool Sabzi , Paul Fieguth

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Machine Learning · Statistics 2016-04-15 Gilles Blanchard , Nicole Mücke

State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial…

Machine Learning · Computer Science 2018-11-27 Seyed-Mohsen Moosavi-Dezfooli , Alhussein Fawzi , Jonathan Uesato , Pascal Frossard

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…

Machine Learning · Statistics 2025-02-04 Yasi Zhang , Oscar Leong

This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations.…

Image and Video Processing · Electrical Eng. & Systems 2024-07-10 Alexander Auras , Kanchana Vaishnavi Gandikota , Hannah Droege , Michael Moeller

Deep neural networks are easily fooled by small perturbations known as adversarial attacks. Adversarial Training (AT) is a technique aimed at learning features robust to such attacks and is widely regarded as a very effective defense.…

Machine Learning · Computer Science 2020-09-11 Theodoros Tsiligkaridis , Jay Roberts

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…

Machine Learning · Statistics 2025-10-27 Antônio H. Ribeiro , David Vävinggren , Dave Zachariah , Thomas B. Schön , Francis Bach

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Machine Learning · Computer Science 2010-10-19 Sham M. Kakade , Shai Shalev-Shwartz , Ambuj Tewari

Variational regularization has remained one of the most successful approaches for reconstruction in imaging inverse problems for several decades. With the emergence and astonishing success of deep learning in recent years, a considerable…

Machine Learning · Computer Science 2021-10-26 Subhadip Mukherjee , Carola-Bibiane Schönlieb , Martin Burger

As we seek to deploy machine learning models beyond virtual and controlled domains, it is critical to analyze not only the accuracy or the fact that it works most of the time, but if such a model is truly robust and reliable. This paper…

Machine Learning · Computer Science 2020-07-07 Samuel Henrique Silva , Peyman Najafirad