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Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for…

Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of…

Our capacity to learn representations from data is related to our ability to design filters that can leverage their coupling with the underlying domain. Graph filters are one such tool for network data and have been used in a myriad of…

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…

Graph convolutional networks (GCNs) have emerged as powerful models for graph learning tasks, exhibiting promising performance in various domains. While their empirical success is evident, there is a growing need to understand their…

Convolutional Neural Networks are very efficient at processing signals defined on a discrete Euclidean space (such as images). However, as they can not be used on signals defined on an arbitrary graph, other models have emerged, aiming to…

Graph convolutional networks have recently gained prominence in collaborative filtering (CF) for recommendations. However, we identify potential bottlenecks in two foundational components. First, the embedding layer leads to a latent space…

Graph learning is currently dominated by graph kernels, which, while powerful, suffer some significant limitations. Convolutional Neural Networks (CNNs) offer a very appealing alternative, but processing graphs with CNNs is not trivial. To…

Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying…

The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…

In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…

Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their…

We study blind deconvolution of signals defined on the nodes of an undirected graph. Although observations are bilinear functions of both unknowns, namely the forward convolutional filter coefficients and the graph signal input, a filter…

Heterophilic Graph Neural Networks (HGNNs) have shown promising results for semi-supervised learning tasks on graphs. Notably, most real-world heterophilic graphs are composed of a mixture of nodes with different neighbor patterns,…

Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…

Graph convolution networks, like message passing graph convolution networks (MPGCNs), have been a powerful tool in representation learning of networked data. However, when data is heterogeneous, most architectures are limited as they employ…