Related papers: Graph neural networks and MSO
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
We introduce a new logic for describing properties of graphs, which we call low rank MSO. This is the fragment of monadic second-order logic in which set quantification is restricted to vertex sets of bounded cutrank. We prove the following…
Most graph neural networks (GNNs) utilize approximations of the general graph convolution derived in the graph Fourier domain. While GNNs are typically applied in the multi-input multi-output (MIMO) case, the approximations are performed in…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these…
Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power…
In this paper we explore whether or not deep neural architectures can learn to classify Boolean satisfiability (SAT). We devote considerable time to discussing the theoretical properties of SAT. Then, we define a graph representation for…
Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture…
The expressive power of message-passing graph neural networks (MPNNs) is reasonably well understood, primarily through combinatorial techniques from graph isomorphism testing. However, MPNNs' generalization abilities -- making meaningful…
Expansion property of a graph refers to its strong connectivity as well as sparseness. It has been reported that deep neural networks can be pruned to a high degree of sparsity while maintaining their performance. Such pruning is essential…
Graph neural networks (GNNs) have gained prominence in recommendation systems in recent years. By representing the user-item matrix as a bipartite and undirected graph, GNNs have demonstrated their potential to capture short- and…
Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…
We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers ``simple'' problems such as graph classification or regressing real-valued graph properties. For such tasks, the…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…