Related papers: Simplicial 2-Complex Convolutional Neural Nets

We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…

Many neural networks for graphs are based on the graph convolution operator, proposed more than a decade ago. Since then, many alternative definitions have been proposed, that tend to add complexity (and non-linearity) to the model. In this…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…

Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural…

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…

While convolutional neural networks (CNNs) have recently made great strides in supervised classification of data structured on a grid (e.g. images composed of pixel grids), in several interesting datasets, the relations between features can…

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…

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…

Graph Neural Networks have a limitation of solely processing features on graph nodes, neglecting data on high-dimensional structures such as edges and triangles. Simplicial Convolutional Neural Networks (SCNN) represent higher-order…

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…

In the current era of neural networks and big data, higher dimensional data is processed for automation of different application areas. Graphs represent a complex data organization in which dependencies between more than one object or…

Simplicial neural networks (SNN) have recently emerged as the newest direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead of pre-dominantly assessing…

We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes. It performs convolutions based on the multi-hop simplicial adjacencies via common faces and cofaces independently…

Graph convolutional learning has led to many exciting discoveries in diverse areas. However, in some applications, traditional graphs are insufficient to capture the structure and intricacies of the data. In such scenarios, multigraphs…

Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they…

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…

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…