Related papers: Sheaf Hypergraph Networks
Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Recently various types of topological Laplacians have been studied from the perspective of data analysis. The spectral theory of these Laplacians has significantly extended the scope of algebraic topology and data analysis. Inspired by the…
This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
Graph hypernetworks (GHNs), constructed by combining graph neural networks (GNNs) with hypernetworks (HNs), leverage relational data across various domains such as neural architecture search, molecular property prediction and federated…
Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products…
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via…
A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
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…
Graphs are the most ubiquitous form of structured data representation used in machine learning. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations found in many real-world…
This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a friendly introduction to applied and computational sheaf theory…
Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order…
Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…
Sheaf Neural Networks (SNNs) naturally extend Graph Neural Networks (GNNs) by endowing a cellular sheaf over the graph, equipping nodes and edges with vector spaces and defining linear mappings between them. While the attached geometric…