Related papers: Beyond Weisfeiler-Lehman: A Quantitative Framework…

Graph Neural Networks (GNNs) have emerged as a powerful category of learning architecture for handling graph-structured data. However, existing GNNs typically ignore crucial structural characteristics in node-induced subgraphs, which thus…

Combinatorial complexes have unified set-based (e.g., graphs, hypergraphs) and part-whole (e.g., simplicial, cellular complexes) structures into a common topological framework. Existing topological neural networks and Weisfeiler-Lehman…

In recent years, a wide variety of graph neural network (GNN) architectures have emerged, each with its own strengths, weaknesses, and complexities. Various techniques, including rewiring, lifting, and node annotation with centrality…

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…

This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and…

Subgraph GNNs enhance message-passing GNNs expressivity by representing graphs as sets of subgraphs, demonstrating impressive performance across various tasks. However, their scalability is hindered by the need to process large numbers of…

Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman…

The invariance to permutations of the adjacency matrix, i.e., graph isomorphism, is an overarching requirement for Graph Neural Networks (GNNs). Conventionally, this prerequisite can be satisfied by the invariant operations over node…

Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open…

Graph Neural Networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the…

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…

Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator…

Diffusion models have gained popularity in graph generation tasks; however, the extent of their expressivity concerning the graph distributions they can learn is not fully understood. Unlike models in other domains, popular backbones for…

Graph Neural Networks (GNNs) have recently been used for node and graph classification tasks with great success, but GNNs model dependencies among the attributes of nearby neighboring nodes rather than dependencies among observed node…

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely…

Graph Neural Networks (GNNs) excel in handling graph-structured data but often underperform in link prediction tasks compared to classical methods, mainly due to the limitations of the commonly used message-passing principle. Notably, their…

We investigate the vulnerability of Graph Neural Networks (GNNs) to bit-flip attacks (BFAs) by introducing an analytical framework to study the influence of architectural features, graph properties, and their interaction. The expressivity…

We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving…

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…

While lifting map has significantly enhanced the expressivity of graph neural networks, extending this paradigm to hypergraphs remains fragmented. To address this, we introduce the categorical Weisfeiler-Lehman framework, which formalizes…