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A fundamental challenge in understanding graph neural networks (GNNs) lies in characterizing their optimization dynamics and loss landscape geometry, critical for improving interpretability and robustness. While mode connectivity, a lens…

We derive simple conditions for the stability or instability of the synchronized oscillation of a class of networks of coupled phase-oscillators, which includes many of the systems used in neural modelling.

Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…

This paper derives statistical guarantees for the performance of Graph Neural Networks (GNNs) in link prediction tasks on graphs generated by a graphon. We propose a linear GNN architecture (LG-GNN) that produces consistent estimators for…

Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the…

Graph neural networks (GNNs) have emerged as a series of competent graph learning methods for diverse real-world scenarios, ranging from daily applications like recommendation systems and question answering to cutting-edge technologies such…

One of the most common approaches to the analysis of dynamic networks is through time-window aggregation. The resulting representation is a sequence of static networks, i.e. the snapshot graph. Despite this representation being widely used…

Graph neural networks (GNNs) provide state-of-the-art results in a wide variety of tasks which typically involve predicting features at the vertices of a graph. They are built from layers of graph convolutions which serve as a powerful…

Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to…

Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…

Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…

Graph neural networks (GNNs) have emerged as a powerful tool for effectively mining and learning from graph-structured data, with applications spanning numerous domains. However, most research focuses on static graphs, neglecting the…

Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs.GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating…

This work develops a distributed graph neural network (GNN) methodology for mesh-based modeling applications using a consistent neural message passing layer. As the name implies, the focus is on enabling scalable operations that satisfy…

Neural networks are a promising technique for parameterizing sub-grid-scale physics (e.g. moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption.…

This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…

In this paper, we aim to find the conditions for input-state stability (ISS) and incremental input-state stability ($\delta$ISS) of Gated Graph Neural Networks (GGNNs). We show that this recurrent version of Graph Neural Networks (GNNs) can…