Related papers: Hypernetwork Theory: The Structural Kernel
Hypergraphs, with their capacity to depict high-order relationships, have emerged as a significant extension of traditional graphs. Although Graph Neural Networks (GNNs) have remarkable performance in graph representation learning, their…
Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…
We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
Link prediction, as a frontier task in complex network topology analysis, aims to infer the existence of latent links between node pairs based on observed nodes and structural information. We propose an ensemble link prediction model that…
This article describes the application of recently introduced complex networks concepts and methods to the characterization and analysis of cortical bone structure. Three-dimensional reconstructions of the system of channels underlying bone…
Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure -- a binary classification task that uses a deep fully-connected neural network to classify…
Textual documents are commonly connected in a hierarchical graph structure where a central document links to others with an exponentially growing connectivity. Though Hyperbolic Graph Neural Networks (HGNNs) excel at capturing such graph…
The relational model is the most commonly used data model for storing large datasets, perhaps due to the simplicity of the tabular format which had revolutionized database management systems. However, many real world objects are recursive…
Semantic networks, such as the knowledge graph, can represent the knowledge leveraging the graph structure. Although the knowledge graph shows promising values in natural language processing, it suffers from incompleteness. This paper…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
Large pre-trained models, or foundation models, have shown impressive performance when adapted to a variety of downstream tasks, often out-performing specialized models. Hypernetworks, neural networks that generate some or all of the…
While Large Language Models (LLMs) demonstrate remarkable proficiency in semantic understanding, they often struggle to ensure structural consistency and reasoning reliability in complex decision-making tasks that demand rigorous logic.…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
Recent works on relational triple extraction have shown the superiority of jointly extracting entities and relations over the pipelined extraction manner. However, most existing joint models fail to balance the modeling of entity features…