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Mini-batch training of Graph Neural Networks (GNNs) is fundamentally different from training on i.i.d. data: sampling a subgraph alters the topology and introduces boundary effects, leading prior work to develop structure-aware samplers…

Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A…

Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the…

Comprehending the interplay between spatial and temporal characteristics of neural dynamics can contribute to our understanding of information processing in the human brain. Graph neural networks (GNNs) provide a new possibility to…

Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions…

In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with…

Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…

In the presence of system-environment coupling, classical complex systems undergo stochastic dynamics, where rich phenomena can emerge at large spatio-temporal scales. To investigate these phenomena, numerical approaches for simulating…

First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…

Accurate traffic forecasting, the foundation of intelligent transportation systems (ITS), has never been more significant than nowadays due to the prosperity of smart cities and urban computing. Recently, Graph Neural Network truly…

Graph Neural Networks (GNNs) often struggle with noisy edges. We propose Latent Space Constrained Graph Neural Networks (LSC-GNN) to incorporate external "clean" links and guide embeddings of a noisy target graph. We train two encoders--one…

Spatially embedded networks (SENs) represent a special type of complex graph, whose topologies are constrained by the networks' embedded spatial environments. The graph representation of such networks is thereby influenced by the embedded…

Graph neural networks (GNNs) have achieved great success on various tasks and fields that require relational modeling. GNNs aggregate node features using the graph structure as inductive biases resulting in flexible and powerful models.…

Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a…

We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…

We study the effect of high-order statistics of data on the learning dynamics of neural networks (NNs) by using a moment-controllable non-Gaussian data model. Considering the expressivity of two-layer neural networks, we first construct the…

In this work, we study non-asymptotic bounds on correlation between two time realizations of stable linear systems with isotropic Gaussian noise. Consequently, via sampling from a sub-trajectory and using \emph{Talagrands'} inequality, we…

Understanding spatio-temporal patterns in polar ice layers is essential for tracking changes in ice sheet balance and assessing ice dynamics. While convolutional neural networks are widely used in learning ice layer patterns from raw…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

Graph Neural Networks (GNNs) have become a standard approach for learning from graph-structured data. However, their reliance on parametric classifiers (most often linear softmax layers) limits interpretability and sometimes hinders…