Related papers: Divergence Network: Graphical calculation method o…

Existing graph neural networks may suffer from the "suspended animation problem" when the model architecture goes deep. Meanwhile, for some graph learning scenarios, e.g., nodes with text/image attributes or graphs with long-distance node…

Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…

Node representation learning for directed graphs is critically important to facilitate many graph mining tasks. To capture the directed edges between nodes, existing methods mostly learn two embedding vectors for each node, source vector…

This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…

The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…

We present a method for visualising the response of a deep neural network to a specific input. For image data for instance our method will highlight areas that provide evidence in favor of, and against choosing a certain class. The method…

Graph neural networks can be effectively applied to find solutions for many real-world problems across widely diverse fields. The success of graph neural networks is linked to the message-passing mechanism on the graph, however, the…

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by…

A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…

We theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed by the transverse electric field components of an incident light beam. The divergence is computed in reflection at…

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…