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Redundancy in deep neural network (DNN) models has always been one of their most intriguing and important properties. DNNs have been shown to overparameterize, or extract a lot of redundant features. In this work, we explore the impact of…

Learning deep representations to solve complex machine learning tasks has become the prominent trend in the past few years. Indeed, Deep Neural Networks are now the golden standard in domains as various as computer vision, natural language…

Deep Neural Networks (DNNs) have emerged as a powerful mechanism and are being increasingly deployed in real-world safety-critical domains. Despite the widespread success, their complex architecture makes proving any formal guarantees about…

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In…

Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a…

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training…

This paper provides theoretical insights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, responding to an open question in the…

Deep neural networks have significantly alleviated the burden of feature engineering, but comparable efforts are now required to determine effective architectures for these networks. Furthermore, as network sizes have become excessively…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Feature selection has drawn much attention over the last decades in machine learning because it can reduce data dimensionality while maintaining the original physical meaning of features, which enables better interpretability than feature…

The paper examines the potential of deep learning to support decisions in financial risk management. We develop a deep learning model for predicting whether individual spread traders secure profits from future trades. This task embodies…

Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…

One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…

We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of…

Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering…

In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…

The success of deep learning algorithms generally depends on large-scale data, while humans appear to have inherent ability of knowledge transfer, by recognizing and applying relevant knowledge from previous learning experiences when…

Deep neural networks (DNN) have shown remarkable success in the classification of physiological signals. In this study we propose a method for examining to what extent does a DNN's performance rely on rediscovering existing features of the…

A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…