Related papers: Sheaf Hypergraph Networks
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a…
Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions,…
We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph…
Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent…
Many inference tasks on knowledge graphs, including relation prediction, operate on knowledge graph embeddings -- vector representations of the vertices (entities) and edges (relations) that preserve task-relevant structure encoded within…
Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance…
Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in…
Defining cellular sheaves beyond graph structures, such as on simplicial complexes containing higher-dimensional simplices, is an essential and intriguing topic in topological data analysis (TDA) and the development of sheaf neural…
The absence of intrinsic adjacency relations and orientation systems in hypergraphs creates fundamental challenges for constructing sheaf Laplacians of arbitrary degrees. We resolve these limitations through symmetric simplicial sets…
In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They…
We generalize cellular sheaf Laplacians on an ordered finite abstract simplicial complex to the set of simplices of a symmetric simplicial set. We construct a functor from the category of hypergraphs to the category of finite symmetric…
This paper outlines a program in what one might call spectral sheaf theory --- an extension of spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the Hodge Laplacian on a cellular sheaf of vector…
Sheaf diffusion has recently emerged as a promising design pattern for graph representation learning due to its inherent ability to handle heterophilic data and avoid oversmoothing. Meanwhile, cooperative message passing has also been…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Recent work in Topological Deep Learning (TDL) seeks to generalize graph learning's preeminent $message \ passing$ paradigm to more complex relational structures: simplicial complexes, cell complexes, hypergraphs, and combinations thereof.…
In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…
Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better…
Heterogeneous graphs, whose nodes and edges can belong to different types and feature spaces, arise in many real-world domains, including biology, recommendation, social networks, and computer systems. Existing heterogeneous graph neural…