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The goal of graph summarization is to represent large graphs in a structured and compact way. A graph summary based on equivalence classes preserves pre-defined features of a graph's vertex within a $k$-hop neighborhood such as the vertex…

Graph neural networks (GNNs) are a class of effective deep learning models for node classification tasks; yet their predictive capability may be severely compromised under adversarially designed unnoticeable perturbations to the graph…

This paper studies the expressive power of graph neural networks falling within the message-passing framework (GNNmp). Two results are presented. First, GNNmp are shown to be Turing universal under sufficient conditions on their depth,…

We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be…

Pruning at Initialisation methods discover sparse, trainable subnetworks before training, but their theoretical mechanisms remain elusive. Existing analyses are often limited to finite-width statistics, lacking a rigorous characterisation…

Deep learning methods are achieving ever-increasing performance on many artificial intelligence tasks. A major limitation of deep models is that they are not amenable to interpretability. This limitation can be circumvented by developing…

Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented…

Graph Neural Networks (GNNs) rely on graph convolutions to exploit meaningful patterns in networked data. Based on matrix multiplications, convolutions incur in high computational costs leading to scalability limitations in practice. To…

State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond…

Graph Neural Networks (GNNs), a generalization of deep neural networks on graph data have been widely used in various domains, ranging from drug discovery to recommender systems. However, GNNs on such applications are limited when there are…

Graph neural networks (GNNs) are widely used for learning node embeddings in graphs, typically adopting a message-passing scheme. This approach, however, leads to the neighbor explosion problem, with exponentially growing computational and…

As real-world graphs expand in size, larger GNN models with billions of parameters are deployed. High parameter count in such models makes training and inference on graphs expensive and challenging. To reduce the computational and memory…

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…

Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains…

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data…

We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally…

Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…

Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite…

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…