Related papers: On the Convergence of Network Systems
For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…
The concept of community detection has long been used as a key device for handling the mesoscale structures in networks. Suitably conducted community detection reveals various embedded informative substructures of network topology. However,…
Nonextensivity is foreseeable in network ensembles, as heterogeneous interactions generally exist in complex networked systems that need to be described by network ensembles. But this nonextensivity has not been literatured proved yet. In…
Network structures, consisting of nodes and edges, have applications in almost all subjects. A set of nodes is called a community if the nodes have strong interrelations. Industries (including cell phone carriers and online social media…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
We connect the mixing behaviour of random walks over a graph to the power of the local-consistency algorithm for the solution of the corresponding constraint satisfaction problem (CSP). We extend this connection to arbitrary CSPs and their…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms…
The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…