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Visual recognition is currently one of the most important and active research areas in computer vision, pattern recognition, and even the general field of artificial intelligence. It has great fundamental importance and strong industrial…

By replacing standard non-linearities with polynomial activations, Polynomial Neural Networks (PNNs) are pivotal for applications such as privacy-preserving inference via Homomorphic Encryption (HE). However, training PNNs effectively…

During the last decade, deep neural networks (DNN) have demonstrated impressive performances solving a wide range of problems in various domains such as medicine, finance, law, etc. Despite their great performances, they have long been…

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

Deep Neural Networks (DNN) have shown great promise in many classification applications, yet are widely known to have poorly calibrated predictions when they are over-parametrized. Improving DNN calibration without comprising on model…

Deep neural networks (DNNs) have become powerful tools for modeling complex data structures through sequentially integrating simple functions in each hidden layer. In survival analysis, recent advances of DNNs primarily focus on enhancing…

Deep Neural Networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) data sets. Understanding which features in the data determine the output of these nested,…

We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…

Overparametrized Deep Neural Networks (DNNs) have demonstrated remarkable success in a wide variety of domains too high-dimensional for classical shallow networks subject to the curse of dimensionality. However, open questions about…

Recently, artificial neural networks (ANNs) in conjunction with stochastic gradient descent optimization methods have been employed to approximately compute solutions of possibly rather high-dimensional partial differential equations…

Deep convolutional neural networks (DCNNs) have recently demonstrated high-quality results in single-image super-resolution (SR). DCNNs often suffer from over-parametrization and large amounts of redundancy, which results in inefficient…

A wide range of practically important problems is nowadays efficiently solved using artificial neural networks. This gave momentum to intensive development of their optical implementations, among which, the so-called diffractive neural…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

Expressivity is one of the most significant issues in assessing neural networks. In this paper, we provide a quantitative analysis of the expressivity for the deep neural network (DNN) from its dynamic model, where the Hilbert space is…

Deep neural networks (DNNs) are poorly calibrated when trained in conventional ways. To improve confidence calibration of DNNs, we propose a novel training method, distance-based learning from errors (DBLE). DBLE bases its confidence…

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…

We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo points for training deep neural network (DNN) surrogates of Data-to-Observable (DtO) maps in engineering design. Our analysis reveals higher-order…

Deep neural networks (DNNs) are powerful learning machines that have enabled breakthroughs in several domains. In this work, we introduce a new retrospective loss to improve the training of deep neural network models by utilizing the prior…