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Deep neural networks (DNNs) are vulnerable to small adversarial perturbations, which are tiny changes to the input data that appear insignificant but cause the model to produce drastically different outputs. Many defense methods require…

Deep neural networks (DNNs) are known to be vulnerable to adversarial examples which contain human-imperceptible perturbations. A series of defending methods, either proactive defence or reactive defence, have been proposed in the recent…

Machine learning systems based on deep neural networks (DNNs) have gained mainstream adoption in many applications. Recently, however, DNNs are shown to be vulnerable to adversarial example attacks with slight perturbations on the inputs.…

Deep neural networks (DNNs) are vulnerable to adversarial examples where inputs with imperceptible perturbations mislead DNNs to incorrect results. Despite the potential risk they bring, adversarial examples are also valuable for providing…

Network security applications, including intrusion detection systems of deep neural networks, are increasing rapidly to make detection task of anomaly activities more accurate and robust. With the rapid increase of using DNN and the volume…

Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…

Few-shot Learning (FSL) methods are being adopted in settings where data is not abundantly available. This is especially seen in medical domains where the annotations are expensive to obtain. Deep Neural Networks have been shown to be…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

We prove deep neural network (DNN for short) expressivity rate bounds for solution sets of a model class of singularly perturbed, elliptic two-point boundary value problems, in Sobolev norms, on the bounded interval $(-1,1)$. We assume that…

Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network…

Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning…

While deep neural networks have proven to be a powerful tool for many recognition and classification tasks, their stability properties are still not well understood. In the past, image classifiers have been shown to be vulnerable to…

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep…

Deep learning models can be fooled by small $l_p$-norm adversarial perturbations and natural perturbations in terms of attributes. Although the robustness against each perturbation has been explored, it remains a challenge to address the…

This paper investigates the mean square exponential stabilization problem for a class of coupled PDE-ODE systems with Markov jump parameters. The considered system consists of multiple coupled hyperbolic PDEs and a finite-dimensional ODE,…

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

As designers of artificial intelligence try to outwit hackers, both sides continue to hone in on AI's inherent vulnerabilities. Designed and trained from certain statistical distributions of data, AI's deep neural networks (DNNs) remain…

Recently, many studies have demonstrated deep neural network (DNN) classifiers can be fooled by the adversarial example, which is crafted via introducing some perturbations into an original sample. Accordingly, some powerful defense…

The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…

Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…