相关论文: Contraction and Hourglass Persistence for Learning…

Graph neural networks (GNNs) have been broadly studied on dynamic graphs for their representation learning, majority of which focus on graphs with homogeneous structures in the spatial domain. However, many real-world graphs - i.e.,…

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

Graph Convolutional Networks (GCNs) gained traction for graph representation learning, with recent attention on improving performance on heterophilic graphs for various real-world applications. The localized feature aggregation in a typical…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various…

Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…

The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive…

Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the…

In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for…

Dynamic graphs arise in a plethora of practical scenarios such as social networks, communication networks, and financial transaction networks. Given a dynamic graph, it is fundamental and essential to learn a graph representation that is…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

Existing interpretability methods for Large Language Models (LLMs) predominantly capture linear directions or isolated features. This overlooks the high-dimensional, relational, and nonlinear geometry of model representations. We apply…

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…

Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…

Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been…

Graph neural networks (GNNs) have achieved great success in various graph problems. However, most GNNs are Message Passing Neural Networks (MPNNs) based on the homophily assumption, where nodes with the same label are connected in graphs.…