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This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution.…
In this report we show that in a planar exponentially growing network consisting of $N$ nodes, congestion scales as $O(N^2/\log(N))$ independently of how flows may be routed. This is in contrast to the $O(N^{3/2})$ scaling of congestion in…
Generative adversarial networks (GANs) have been a popular deep generative model for real-world applications. Despite many recent efforts on GANs that have been contributed, mode collapse and instability of GANs are still open problems…
Graph neural networks (GNNs) excel on homophilic graphs where connected nodes share labels, but struggle with heterophilic graphs where edges do not imply similarity. Moreover, iterative message passing limits scalability due to…
Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality,…
This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
We introduce a model for a preferentially attached network which has grown from a small world network. Here, the average path length and the clustering coefficient are estimated, and the topological properties of modeled networks are…
The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer…
We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but…
Generative adversarial networks (GANs) are emerging machine learning models for generating synthesized data similar to real data by jointly training a generator and a discriminator. In many applications, data and computational resources are…
Generative Adversarial Networks (GAN) have received wide attention in the machine learning field for their potential to learn high-dimensional, complex real data distribution. Specifically, they do not rely on any assumptions about the…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…