相关论文: Expressive Power of Invariant and Equivariant Grap…
The study of Graph Neural Networks has received considerable interest in the past few years. By extending deep learning to graph-structured data, GNNs can solve a diverse set of tasks in fields including social science, chemistry, and…
Incorporating spectral information to enhance Graph Neural Networks (GNNs) has shown promising results but raises a fundamental challenge due to the inherent ambiguity of eigenvectors. Various architectures have been proposed to address…
Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this…
Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power.…
Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming…
Graph neural networks (GNNs) are effective machine learning models for various graph learning problems. Despite their empirical successes, the theoretical limitations of GNNs have been revealed recently. Consequently, many GNN models have…
Graph Neural Network (GNN) aggregates the neighborhood of each node into the node embedding and shows its powerful capability for graph representation learning. However, most existing GNN variants aggregate the neighborhood information in a…
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…
Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix…
Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…
Graph neural networks (GNNs) are a widely used class of machine learning models for graph-structured data, based on local aggregation over neighbors. GNNs have close connections to logic. In particular, their expressive power is linked to…
Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…
Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add…
Many problems in computer vision and machine learning can be cast as learning on hypergraphs that represent higher-order relations. Recent approaches for hypergraph learning extend graph neural networks based on message passing, which is…
Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…
We perform the first adversarial robustness study into Graph Neural Networks (GNNs) that are provably more powerful than traditional Message Passing Neural Networks (MPNNs). In particular, we use adversarial robustness as a tool to uncover…
Graph neural networks (GNNs) have limited expressive power, failing to represent many graph classes correctly. While more expressive graph representation learning (GRL) alternatives can distinguish some of these classes, they are…
While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the…
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,…
The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in…