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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…

State of the art computer vision models have been shown to be vulnerable to small adversarial perturbations of the input. In other words, most images in the data distribution are both correctly classified by the model and are very close to…

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…

As a defense strategy against adversarial attacks, adversarial detection aims to identify and filter out adversarial data from the data flow based on discrepancies in distribution and noise patterns between natural and adversarial data.…

Adversarial training is the industry standard for producing models that are robust to small adversarial perturbations. However, machine learning practitioners need models that are robust to other kinds of changes that occur naturally, such…

Neural networks are known to be susceptible to adversarial samples: small variations of natural examples crafted to deliberately mislead the models. While they can be easily generated using gradient-based techniques in digital and physical…

Adversarial examples have attracted significant attention in machine learning, but the reasons for their existence and pervasiveness remain unclear. We demonstrate that adversarial examples can be directly attributed to the presence of…

Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing…

Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…

The reliability of a learning model is key to the successful deployment of machine learning in various industries. Creating a robust model, particularly one unaffected by adversarial attacks, requires a comprehensive understanding of the…

Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate…

Almost all adversarial attacks are formulated to add an imperceptible perturbation to an image in order to fool a model. Here, we consider the opposite which is adversarial examples that can fool a human but not a model. A large enough and…

In Virtual Reality (VR), adversarial attack remains a significant security threat. Most deep learning-based methods for physical and digital adversarial attacks focus on enhancing attack performance by crafting adversarial examples that…

Adversarial attacks have verified the existence of the vulnerability of neural networks. By adding small perturbations to a benign example, adversarial attacks successfully generate adversarial examples that lead misclassification of deep…

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

Deep Neural Networks (DNNs) have shown remarkable performance in a diverse range of machine learning applications. However, it is widely known that DNNs are vulnerable to simple adversarial perturbations, which causes the model to…

Deep neural networks are susceptible to adversarial examples while suffering from incorrect predictions via imperceptible perturbations. Transfer-based attacks create adversarial examples for surrogate models and transfer these examples to…

The existence of adversarial examples in which an imperceptible change in the input can fool well trained neural networks was experimentally discovered by Szegedy et al in 2013, who called them "Intriguing properties of neural networks".…

Machine learning models, including state-of-the-art deep neural networks, are vulnerable to small perturbations that cause unexpected classification errors. This unexpected lack of robustness raises fundamental questions about their…

Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…