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Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth.…

Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent…

Recent studies have shown that deep neural networks are vulnerable to adversarial examples, but most of the methods proposed to defense adversarial examples cannot solve this problem fundamentally. In this paper, we theoretically prove that…

We propose a new defense mechanism against adversarial attacks inspired by an optical co-processor, providing robustness without compromising natural accuracy in both white-box and black-box settings. This hardware co-processor performs a…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…

Research on improving the robustness of neural networks to adversarial noise - imperceptible malicious perturbations of the data - has received significant attention. The currently uncontested state-of-the-art defense to obtain robust deep…

Deep equilibrium models (DEQs) refrain from the traditional layer-stacking paradigm and turn to find the fixed point of a single layer. DEQs have achieved promising performance on different applications with featured memory efficiency. At…

Adversarial training is an effective methodology for training deep neural networks that are robust against adversarial, norm-bounded perturbations. However, the computational cost of adversarial training grows prohibitively as the size of…

Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial…

The instability of Generative Adversarial Network (GAN) training has frequently been attributed to gradient descent. Consequently, recent methods have aimed to tailor the models and training procedures to stabilise the discrete updates. In…

We introduce OS-net (Orbitally Stable neural NETworks), a new family of neural network architectures specifically designed for periodic dynamical data. OS-net is a special case of Neural Ordinary Differential Equations (NODEs) and takes…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

In recent years, neural networks have demonstrated outstanding effectiveness in a large amount of applications.However, recent works have shown that neural networks are susceptible to adversarial examples, indicating possible flaws…

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

Neural Ordinary Differential Equations (Neural ODEs) are the continuous analog of Residual Neural Networks (ResNets). We investigate whether the discrete dynamics defined by a ResNet are close to the continuous one of a Neural ODE. We first…

Adversarial attack methods have demonstrated the fragility of deep neural networks. Their imperceptible perturbations are frequently able fool classifiers into potentially dangerous misclassifications. We propose a novel way to interpret…

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…