
Graphs, Convolutions, and Neural Networks
Network data can be conveniently modeled as a graph signal, where data v...
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Stability of Graph Neural Networks to Relative Perturbations
Graph neural networks (GNNs), consisting of a cascade of layers applying...
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Topological Graph Neural Networks
Graph neural networks (GNNs) are a powerful architecture for tackling gr...
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Scalable Graph Neural Network Training: The Case for Sampling
Graph Neural Networks (GNNs) are a new and increasingly popular family o...
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Web Image Context Extraction with Graph Neural Networks and Sentence Embeddings on the DOM tree
Web Image Context Extraction (WICE) consists in obtaining the textual in...
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Stability Properties of Graph Neural Networks
Data stemming from networks exhibit an irregular support, whereby each d...
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Pointspectrum: Equivariance Meets Laplacian Filtering for Graph Representation Learning
Graph Representation Learning (GRL) has become essential for modern grap...
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Discriminability of SingleLayer Graph Neural Networks
Network data can be conveniently modeled as a graph signal, where data values are assigned to the nodes of a graph describing the underlying network topology. Successful learning from network data requires methods that effectively exploit this graph structure. Graph neural networks (GNNs) provide one such method and have exhibited promising performance on a wide range of problems. Understanding why GNNs work is of paramount importance, particularly in applications involving physical networks. We focus on the property of discriminability and establish conditions under which the inclusion of pointwise nonlinearities to a stable graph filter bank leads to an increased discriminative capacity for higheigenvalue content. We define a notion of discriminability tied to the stability of the architecture, show that GNNs are at least as discriminative as linear graph filter banks, and characterize the signals that cannot be discriminated by either.
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