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We study mechanisms to characterize how the asymptotic convergence of backpropagation in deep architectures, in general, is related to the network structure, and how it may be influenced by other design choices including activation type,…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
We study networks constructed from gene expression data obtained from many types of cancers. The networks are constructed by connecting vertices that belong to each others' list of K-nearest-neighbors, with K being an a priori selected…
Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of…
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices…
Networks are representations of complex underlying social processes. However, the same given network may be more suitable to model one behavior of individuals than another. In many cases, aggregate population models may be more effective…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system (e.g. the implied level of systemic risk) requires detailed information about the structure of the underlying network.…
We consider the problem of identifying the topology of a weighted, undirected network $\mathcal G$ from observing snapshots of multiple independent consensus dynamics. Specifically, we observe the opinion profiles of a group of agents for a…
Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…
Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…
We present $\varepsilon$-retrain, an exploration strategy encouraging a behavioral preference while optimizing policies with monotonic improvement guarantees. To this end, we introduce an iterative procedure for collecting retrain areas --…
Network pruning is an effective method to reduce the computational expense of over-parameterized neural networks for deployment on low-resource systems. Recent state-of-the-art techniques for retraining pruned networks such as weight…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…