Related papers: Combinatorial Complexes: Bridging the Gap Between …
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This…
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…
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…
Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…
Concept Bottleneck Models (CBMs) provide explicit interpretations for deep neural networks through concepts and allow intervention with concepts to adjust final predictions. Existing CBMs assume concepts are conditionally independent given…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
We introduce higher dimensional hypergraphs, which is a generalization of Baez-Dolans's opetopic sets and Hermida-Makkai-Power's multigraphs. This is based on a simple combinatorial structure called shells and the formal composites of…
Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works…
Hypergraph neural networks (HGNNs) effectively model complex high-order relationships in domains like protein interactions and social networks by connecting multiple vertices through hyperedges, enhancing modeling capabilities, and reducing…
Many problems in machine learning can be cast as learning functions from sets to graphs, or more generally to hypergraphs; in short, Set2Graph functions. Examples include clustering, learning vertex and edge features on graphs, and learning…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
In this work, we propose a novel segmental hypergraph representation to model overlapping entity mentions that are prevalent in many practical datasets. We show that our model built on top of such a new representation is able to capture…