Related papers: A Tensor-Based Formulation of Hetero-functional Gr…

Relational databases are extensively utilized in a variety of modern information system applications, and they always carry valuable data patterns. There are a huge number of data mining or machine learning tasks conducted on relational…

Graph classification is a significant problem in many scientific domains. It addresses tasks such as the classification of proteins and chemical compounds into categories according to their functions, or chemical and structural properties.…

Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…

Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix…

Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been…

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…

Here, we show a method to reconstruct connectivity hypermatrices of a general hypergraph (without any self loop or multiple edge) using tensor. We also study the different spectral properties of these hypermatrices and find that these…

Capturing the composition patterns of relations is a vital task in knowledge graph completion. It also serves as a fundamental step towards multi-hop reasoning over learned knowledge. Previously, several rotation-based translational methods…

There is increasing evidence to suggest functional connectivity networks are non-stationary. This has lead to the development of novel methodologies with which to accurately estimate time-varying functional connectivity networks. Many of…

Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…

!-graphs provide a means of reasoning about infinite families of string diagrams and have proven useful in manipulation of (co)algebraic structures like Hopf algebras, Frobenius algebras, and compositions thereof. However, they have…

Tensor field theory (TFT) focuses on quantum field theory aspects of random tensor models, a quantum-gravity-motivated generalisation of random matrix models. The TFT correlation functions have been shown to be classified by graphs that…

Complex systems that consist of different kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein tensor product to model this type of networks. Several…

We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…

Graph neural networks (GNNs) have achieved remarkable success in node classification. Building on this progress, heterogeneous graph neural networks (HGNNs) integrate relation types and node and edge semantics to leverage heterogeneous…

In graphs, the concept of adjacency is clearly defined: it is a pairwise relationship between vertices. Adjacency in hypergraphs has to integrate hyperedge multi-adicity: the concept of adjacency needs to be defined properly by introducing…

Traditional graph centrality measures effectively quantify node importance but fail to capture the structural uniqueness of multi-scale connectivity patterns -- critical for understanding network resilience and function. This paper…

We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using…

Most previous heterogeneous graph embedding models represent elements in a heterogeneous graph as vector representations in a low-dimensional Euclidean space. However, because heterogeneous graphs inherently possess complex structures, such…

Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by…