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The robustness of deep neural networks (DNNs) is crucial to the hosting system's reliability and security. Formal verification has been demonstrated to be effective in providing provable robustness guarantees. To improve its scalability,…

Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are also a few results in the literature which prove that DNNs…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…

This survey provides an in-depth and explanatory review of the approximation properties of deep neural networks, with a focus on feed-forward and residual architectures. The primary objective is to examine how effectively neural networks…

This work presents an in-depth analysis of the majority of the deep neural networks (DNNs) proposed in the state of the art for image recognition. For each DNN multiple performance indices are observed, such as recognition accuracy, model…

Deep Neural Networks (DNN) have improved the quality of several non-safety related products in the past years. However, before DNNs should be deployed to safety-critical applications, their robustness needs to be systematically analyzed. A…

Deep learning (DL) techniques are on the rise in the software engineering research community. More and more approaches have been developed on top of DL models, also due to the unprecedented amount of software-related data that can be used…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

Deep neural networks (DNNs) have shown their success as high-dimensional function approximators in many applications; however, training DNNs can be challenging in general. DNN training is commonly phrased as a stochastic optimization…

Surgical training in medical school residency programs has followed the apprenticeship model. The learning and assessment process is inherently subjective and time-consuming. Thus, there is a need for objective methods to assess surgical…

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…

This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…

Recent research has seen many behavioral comparisons between humans and deep neural networks (DNNs) in the domain of image classification. Often, comparison studies focus on the end-result of the learning process by measuring and comparing…

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…

Combining computational technologies and humanities is an ongoing effort aimed at making resources such as texts, images, audio, video, and other artifacts digitally available, searchable, and analyzable. In recent years, deep neural…

In recent years, deep neural networks (DNNs) have known an important rise in popularity. However, although they are state-of-the-art in many machine learning challenges, they still suffer from several limitations. For example, DNNs require…

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim…

Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches,…

A recent paper by Davies et al (2021) describes how deep learning (DL) technology was used to find plausible hypotheses that have led to two original mathematical results: one in knot theory, one in representation theory. I argue here that…