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Deep Neural Networks (DNNs) have recently led to significant improvements in many fields. However, DNNs are vulnerable to adversarial examples which are samples with imperceptible perturbations while dramatically misleading the DNNs.…

Adversarial attacks significantly threaten the robustness of deep neural networks (DNNs). Despite the multiple defensive methods employed, they are nevertheless vulnerable to poison attacks, where attackers meddle with the initial training…

Imitation learning presents an effective approach to alleviate the resource-intensive and time-consuming nature of policy learning from scratch in the solution space. Even though the resulting policy can mimic expert demonstrations…

Deep Neural Networks (DNNs) have been shown to be vulnerable to adversarial examples. While numerous successful adversarial attacks have been proposed, defenses against these attacks remain relatively understudied. Existing defense…

A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…

Deep neural networks (DNNs) are known to be vulnerable to adversarial images, while their robustness in text classification is rarely studied. Several lines of text attack methods have been proposed in the literature, including…

The objective of this paper is to enhance the optimization process for neural networks by developing a dynamic learning rate algorithm that effectively integrates exponential decay and advanced anti-overfitting strategies. Our primary…

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…

Deep neural networks (DNNs) are incredibly vulnerable to crafted, imperceptible adversarial perturbations. While adversarial training (AT) has proven to be an effective defense approach, the AT mechanism for robustness improvement is not…

Adversarial examples (AEs) pose severe threats to the applications of deep neural networks (DNNs) to safety-critical domains, e.g., autonomous driving. While there has been a vast body of AE defense solutions, to the best of our knowledge,…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

The impact of designing for security of AI is critical for humanity in the AI era. With humans increasingly becoming dependent upon AI, there is a need for neural networks that work reliably, inspite of Adversarial attacks. The vision for…

In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…

Deep neural networks (DNNs) have proven to be quite effective in a vast array of machine learning tasks, with recent examples in cyber security and autonomous vehicles. Despite the superior performance of DNNs in these applications, it has…

In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

Stable Diffusion (SD) often produces degraded outputs when the training dataset contains adversarial noise. Adversarial purification offers a promising solution by removing adversarial noise from contaminated data. However, existing…

Point-to-point and periodic motions are ubiquitous in the world of robotics. To master these motions, Autonomous Dynamic System (DS) based algorithms are fundamental in the domain of Learning from Demonstration (LfD). However, these…

Despite being effective in many application areas, Deep Neural Networks (DNNs) are vulnerable to being attacked. In object recognition, the attack takes the form of a small perturbation added to an image, that causes the DNN to misclassify,…

In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of…

Neural networks are known to be vulnerable to adversarial attacks -- slight but carefully constructed perturbations of the inputs which can drastically impair the network's performance. Many defense methods have been proposed for improving…