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Adversarial examples reveal the blind spots of deep neural networks (DNNs) and represent a major concern for security-critical applications. The transferability of adversarial examples makes real-world attacks possible in black-box…

Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…

Non-adversarial robustness, also known as natural robustness, is a property of deep learning models that enables them to maintain performance even when faced with distribution shifts caused by natural variations in data. However, achieving…

Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating…

Adversarial training has emerged as an effective approach to train robust neural network models that are resistant to adversarial attacks, even in low-label regimes where labeled data is scarce. In this paper, we introduce a novel…

Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or…

Adversarial training (AT) has proven to be one of the most effective ways to defend Deep Neural Networks (DNNs) against adversarial attacks. However, the phenomenon of robust overfitting, i.e., the robustness will drop sharply at a certain…

Neural networks have a number of shortcomings. Amongst the severest ones is the sensitivity to distribution shifts which allows models to be easily fooled into wrong predictions by small perturbations to inputs that are often imperceivable…

Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…

Artificial neural networks in general and deep learning networks in particular established themselves as popular and powerful machine learning algorithms. While the often tremendous sizes of these networks are beneficial when solving…

In this paper, we introduce a novel approach to study reaction-diffusion systems -- dynamic transition theory approach developed in Ma and Wang 2015. This approach generalizes Turing's classical result (linear stability analysis) on pattern…

The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…

Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by a system of a single reaction-diffusion equation coupled…

One of the bottlenecks in robotic intelligence is the instability of neural network models, which, unlike control models, lack a well-defined convergence domain and stability. This leads to risks when applying intelligence in the physical…

Adversarial perturbations are imperceptible changes to input pixels that can change the prediction of deep learning models. Learned weights of models robust to such perturbations are previously found to be transferable across different…

The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a…

Neural networks have demonstrated state-of-the-art performance in various machine learning fields. However, the introduction of malicious perturbations in input data, known as adversarial examples, has been shown to deceive neural network…

Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of…

We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these…