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Deep Neural Networks (DNNs) are a revolutionary force in the ongoing information revolution, and yet their intrinsic properties remain a mystery. In particular, it is widely known that DNNs are highly sensitive to noise, whether adversarial…
Successful deep learning models often involve training neural network architectures that contain more parameters than the number of training samples. Such overparametrized models have been extensively studied in recent years, and the…
The emergence of Deep Neural Networks (DNNs) has revolutionized various domains by enabling the resolution of complex tasks spanning image recognition, natural language processing, and scientific problem-solving. However, this progress has…
The robustness of deep neural networks (DNNs) against adversarial example attacks has raised wide attention. For smoothed classifiers, we propose the worst-case adversarial loss over input distributions as a robustness certificate. Compared…
Deep neural networks are vulnerable to so-called adversarial examples: inputs which are intentionally constructed to cause the model to make incorrect predictions or classifications. Adversarial examples are often visually indistinguishable…
This paper studies the approximation capacity of neural networks with an arbitrary activation function and with norm constraint on the weights. Upper and lower bounds on the approximation error of these networks are computed for smooth…
Deep neural networks (DNNs) are vulnerable to adversarial examples, in which DNNs are misled to false outputs due to inputs containing imperceptible perturbations. Adversarial training, a reliable and effective method of defense, may…
In this paper, the robustness and accuracy of the deep neural network (DNN) was enhanced by introducing the $L_{2,\infty}$ normalization of the weight matrices of the DNN with Relu as the activation function. It is proved that the…
In this paper, we uniquely study the adversarial robustness of deep neural networks (NN) for classification tasks against that of optimal classifiers. We look at the smallest magnitude of possible additive perturbations that can change a…
Deep neural networks (DNNs) are powerful nonlinear architectures that are known to be robust to random perturbations of the input. However, these models are vulnerable to adversarial perturbations--small input changes crafted explicitly to…
Deep neural network (DNN) models are wellknown to easily misclassify prediction results by using input images with small perturbations, called adversarial examples. In this paper, we propose a novel adversarial detector, which consists of a…
Understanding and certifying the generalization performance of machine learning algorithms -- i.e. obtaining theoretical estimates of the test error from the training error -- is a central theme of statistical learning theory. Among the…
Adversarial training (AT) is a canonical method for enhancing the robustness of deep neural networks (DNNs). However, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time AT can be detrimental…
Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when…
Adversarial attacks have received increasing attention and it has been widely recognized that classical DNNs have weak adversarial robustness. The most commonly used adversarial defense method, adversarial training, improves the adversarial…
In the last a few decades, deep neural networks have achieved remarkable success in machine learning, computer vision, and pattern recognition. Recent studies however show that neural networks (both shallow and deep) may be easily fooled by…
While deep learning has resulted in major breakthroughs in many application domains, the frameworks commonly used in deep learning remain fragile to artificially-crafted and imperceptible changes in the data. In response to this fragility,…
Deep Neural Networks (DNNs) needs to be both efficient and robust for practical uses. Quantization and structure simplification are promising ways to adapt DNNs to mobile devices, and adversarial training is the most popular method to make…
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…
Deep neural networks (DNNs) have been widely applied to various applications, including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to…