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Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Attention mechanism has been regarded as an advanced technique to capture long-range feature interactions and to boost the representation capability for convolutional neural networks. However, we found two ignored problems in current…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations…

Anomaly detection on attributed networks aims at finding nodes whose patterns deviate significantly from the majority of reference nodes, which is pervasive in many applications such as network intrusion detection and social spammer…

Deep neural networks need to make robust inference in the presence of occlusion, background clutter, pose and viewpoint variations -- to name a few -- when the task of person re-identification is considered. Attention mechanisms have…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

Graph anomaly detection on attributed networks has become a prevalent research topic due to its broad applications in many influential domains. In real-world scenarios, nodes and edges in attributed networks usually display distinct…

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce…

The utilization of prior knowledge about anomalies is an essential issue for anomaly detections. Recently, the visual attention mechanism has become a promising way to improve the performance of CNNs for some computer vision tasks. In this…

Accurate medical image segmentation is essential for diagnosis and treatment planning of diseases. Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance for automatic medical image segmentation. However, they are…

Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the…

One of the fundamental limitations of Deep Neural Networks (DNN) is its inability to acquire and accumulate new cognitive capabilities. When some new data appears, such as new object classes that are not in the prescribed set of objects…

Inspired by the traditional partial differential equation (PDE) approach for image denoising, we propose a novel neural network architecture, referred as NODE-ImgNet, that combines neural ordinary differential equations (NODEs) with…

Advancements in deep learning techniques have given a boost to the performance of anomaly detection. However, real-world and safety-critical applications demand a level of transparency and reasoning beyond accuracy. The task of anomaly…

Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or…

Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…