相关论文: Some Might Say All You Need Is Sum

We study the expressive power of graph neural networks (GNNs) with mean as the aggregation function, with the following results. In the non-uniform setting, such GNNs have exactly the same expressive power as ratio modal logic, which has…

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…

Although there has been significant interest in applying machine learning techniques to structured data, the expressivity (i.e., a description of what can be learned) of such techniques is still poorly understood. In this paper, we study…

Graph neural networks (GNNs) are frequently used for knowledge graph completion. Their black-box nature has motivated work that uses sound logical rules to explain predictions and characterise their expressivity. However, despite the…

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 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 networks (GNNs) have achieved great success in many graph learning tasks. The main aspect powering existing GNNs is the multi-layer network architecture to learn the nonlinear graph representations for the specific learning…

We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained…

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…

Expressivity and generalization are two critical aspects of graph neural networks (GNNs). While significant progress has been made in studying the expressivity of GNNs, much less is known about their generalization capabilities,…

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,…

Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of premetrics that capture different degrees…

We study the generalization capabilities of Message Passing Neural Networks (MPNNs), a prevalent class of Graph Neural Networks (GNN). We derive generalization bounds specifically for MPNNs with normalized sum aggregation and mean…

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) show strong expressive power on graph data mining, by aggregating information from neighbors and using the integrated representation in the downstream tasks. The same aggregation methods and parameters for each…

The counting power of Message Passing Neural Networks (MPNN) has been the subject of many recent papers, showing that they can express logic that involves counting up to a threshold or more generally satisfy a linear arithmetic constraint.…

In this paper, we fully answer the above question through a key algebraic condition on graph functions, called \textit{permutation compatibility}, that relates permutations of weights and features of the graph to functional constraints. We…

Graph neural networks (GNNs) have been widely used in graph-related contexts. It is known that the separation power of GNNs is equivalent to that of the Weisfeiler-Lehman (WL) test; hence, GNNs are imperfect at identifying all…

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…

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…