Related papers: Dimensional reduction of dynamical systems on grap…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…
Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
Dynamic networks, also called network streams, are an important data representation that applies to many real-world domains. Many sets of network data such as e-mail networks, social networks, or internet traffic networks are best…
A key limitation in using various modern methods of machine learning in developing feedback control policies is the lack of appropriate methodologies to analyze their long-term dynamics, in terms of making any sort of guarantees (even…
Complex networks with expanding dimensions are studied, where the networks may be directed and weighted, and network nodes are varying in discrete time in the sense that some new nodes may be added and some old nodes may be removed from…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical…
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
This manuscript investigates the one-pass stochastic gradient descent (SGD) dynamics of a two-layer neural network trained on Gaussian data and labels generated by a similar, though not necessarily identical, target function. We rigorously…
Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…