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Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

Graph adversarial attacks are usually produced from the two perspectives of topology/structure and node feature, both of them represent the paramount characteristics learned by today's deep learning models. Although some defense…

State-of-the-art deep neural networks (DNNs) have been proved to have excellent performance on unsupervised domain adaption (UDA). However, recent work shows that DNNs perform poorly when being attacked by adversarial samples, where these…

Deep learning models can reveal sensitive information about individual training examples, and while differential privacy (DP) provides guarantees restricting such leakage, it also alters optimization dynamics in poorly understood ways. We…

Adversarial robustness corresponds to the susceptibility of deep neural networks to imperceptible perturbations made at test time. In the context of image tasks, many algorithms have been proposed to make neural networks robust to…

We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…

Deep neural networks have achieved state-of-the-art performance in a variety of fields. Recent works observe that a class of widely used neural networks can be viewed as the Euler method of numerical discretization. From the numerical…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

Although Deep Neural Networks (DNNs), such as the convolutional neural networks (CNN) and Vision Transformers (ViTs), have been successfully applied in the field of computer vision, they are demonstrated to be vulnerable to well-sought…

Deep equilibrium models (DEQs) refrain from the traditional layer-stacking paradigm and turn to find the fixed point of a single layer. DEQs have achieved promising performance on different applications with featured memory efficiency. At…

Deep Neural Networks (DNNs) are vulnerable to adversarial attacks. Existing methods are devoted to developing various robust training strategies or regularizations to update the weights of the neural network. But beyond the weights, the…

Deep neural networks (DNNs) have achieved remarkable success in various tasks (e.g., image classification, speech recognition, and natural language processing (NLP)). However, researchers have demonstrated that DNN-based models are…

Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

A conventional approach to train neural ordinary differential equations (ODEs) is to fix an ODE solver and then learn the neural network's weights to optimize a target loss function. However, such an approach is tailored for a specific…

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical…

Improving the resistance of deep neural networks against adversarial attacks is important for deploying models to realistic applications. However, most defense methods are designed to defend against intensity perturbations and ignore…

Deep neural networks (DNNs) have achieved remarkable success in computer vision tasks such as image classification, segmentation, and object detection. However, they are vulnerable to adversarial attacks, which can cause incorrect…

In recent years, Deep Neural Networks (DNNs) have had a dramatic impact on a variety of problems that were long considered very difficult, e. g., image classification and automatic language translation to name just a few. The accuracy of…

Adversarial examples can cause catastrophic mistakes in Deep Neural Network (DNNs) based vision systems e.g., for classification, segmentation and object detection. The vulnerability of DNNs against such attacks can prove a major roadblock…