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Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial…

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional…

Convolutional Neural Networks (CNNs) are generally prone to noise interruptions, i.e., small image noise can cause drastic changes in the output. To suppress the noise effect to the final predication, we enhance CNNs by replacing…

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…

Handling haphazard streaming data, such as data from edge devices, presents a challenging problem. Over time, the incoming data becomes inconsistent, with missing, faulty, or new inputs reappearing. Therefore, it requires models that are…

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…

This paper embodies the Fox's ${\mathcal H}$-transform theory into a unifying modeling and analysis of HetNets. The proposed framework has the potential, due to the Fox's ${\mathcal H}$-functions versatility, of significantly simplifying…

The multivariate contaminated normal (MCN) distribution represents a simple heavy-tailed generalization of the multivariate normal (MN) distribution to model elliptical contoured scatters in the presence of mild outliers, referred to as…

Previous studies have shown the great potential of capsule networks for the spatial contextual feature extraction from {hyperspectral images (HSIs)}. However, the sampling locations of the convolutional kernels of capsules are fixed and…

Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…

Deep learning neural network technique (DNN) is one of the most efficient and general approach of multivariate data analysis of the collider experiments. The important step of the analysis is the optimization of the input space for…

Convolutional neural networks (CNNs) have demonstrated strong performance in visual recognition tasks, but their inherent reliance on regular grid structures limits their capacity to model complex topological relationships and non-local…

Graph neural networks (GNNs) have become the state of the art for various graph-related tasks and are particularly prominent in heterogeneous graphs (HetGs). However, several issues plague this paradigm: first, the difficulty in fully…

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…

Graph Neural Networks (GNNs) is an architecture for structural data, and has been adopted in a mass of tasks and achieved fabulous results, such as link prediction, node classification, graph classification and so on. Generally, for a…

Keyword Spotting (KWS) provides the start signal of ASR problem, and thus it is essential to ensure a high recall rate. However, its real-time property requires low computation complexity. This contradiction inspires people to find a…

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…

We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model…

Automated knowledge graph (KG) construction is essential for navigating the rapidly expanding body of scientific literature. However, existing approaches struggle to recognize long multi-word entities, often fail to generalize across…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…