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This paper explores the connection between learning trajectories of Deep Neural Networks (DNNs) and their generalization capabilities when optimized using (stochastic) gradient descent algorithms. Instead of concentrating solely on the…

Convolutional Neural Networks (CNNs) show impressive performance in the standard classification setting where training and testing data are drawn i.i.d. from a given domain. However, CNNs do not readily generalize to new domains with…

Reducing network complexity has been a major research focus in recent years with the advent of mobile technology. Convolutional Neural Networks that perform various vision tasks without memory overhaul is the need of the hour. This paper…

Recent progress in empirical and certified robustness promises to deliver reliable and deployable Deep Neural Networks (DNNs). Despite that success, most existing evaluations of DNN robustness have been done on images sampled from the same…

A key factor for ensuring safety in Autonomous Vehicles (AVs) is to avoid any abnormal behaviors under undesirable and unpredicted circumstances. As AVs increasingly rely on Deep Neural Networks (DNNs) to perform safety-critical tasks,…

We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear…

Bayesian Neural Networks (BNNs) provide principled uncertainty quantification but suffer from substantial computational and memory overhead compared to deterministic networks. While quantization techniques have successfully reduced resource…

Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, little consideration has been given to uncertainty quantification over the output image. Here…

Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs,…

Theoretical understanding of deep learning is one of the most important tasks facing the statistics and machine learning communities. While deep neural networks (DNNs) originated as engineering methods and models of biological networks in…

Quantifying the complexity of feed-forward neural networks (FFNNs) remains challenging due to their nonlinear, hierarchical structure and numerous parameters. We apply generalized degrees of freedom (GDF) to measure model complexity in…

Emerging deep-learning (DL)-based techniques have significant potential to revolutionize biomedical imaging. However, one outstanding challenge is the lack of reliability assessment in the DL predictions, whose errors are commonly revealed…

In recent years, convolutional neural networks (CNNs) are used in a large number of tasks in computer vision. One of them is object detection for autonomous driving. Although CNNs are used widely in many areas, what happens inside the…

This paper aims to analyze the generalization power of deep neural networks (DNNs) from the perspective of interactions. Unlike previous analysis of a DNN's generalization power in a highdimensional feature space, we find that the…

Face recognition algorithms based on deep convolutional neural networks (DCNNs) have made progress on the task of recognizing faces in unconstrained viewing conditions. These networks operate with compact feature-based face representations…

Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of…

Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…

In this work, we investigate the value of uncertainty modeling in 3D super-resolution with convolutional neural networks (CNNs). Deep learning has shown success in a plethora of medical image transformation problems, such as…

Improving the generalization ability of Deep Neural Networks (DNNs) is critical for their practical uses, which has been a longstanding challenge. Some theoretical studies have uncovered that DNNs have preferences for some frequency…

Sometimes it is not enough for a DNN to produce an outcome. For example, in applications such as healthcare, users need to understand the rationale of the decisions. Therefore, it is imperative to develop algorithms to learn models with…