Related papers: On Structural Expressive Power of Graph Transforme…

Graph neural network (GNN)'s success in graph classification is closely related to the Weisfeiler-Lehman (1-WL) algorithm. By iteratively aggregating neighboring node features to a center node, both 1-WL and GNN obtain a node representation…

The isomorphism problem is a fundamental problem in network analysis, which involves capturing both low-order and high-order structural information. In terms of extracting low-order structural information, graph isomorphism algorithms…

In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection…

Graph Neural Networks (GNNs) have emerged as the de facto standard for representation learning on graphs, owing to their ability to effectively integrate graph topology and node attributes. However, the inherent suboptimal nature of node…

The ability of a graph neural network (GNN) to leverage both the graph topology and graph labels is fundamental to building discriminative node and graph embeddings. Building on previous work, we theoretically show that edGNN, our model for…

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…

In this paper we present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for…

Despite significant advances in Graph Neural Networks (GNNs), their limited expressivity remains a fundamental challenge. Research on GNN expressivity has produced many expressive architectures, leading to architecture hierarchies with…

Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to…

Recent studies suggest that large language models (LLMs) possess the capability to solve graph reasoning tasks. Notably, even when graph structures are embedded within textual descriptions, LLMs can still effectively answer related…

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level…

Graph neural networks (GNNs) are widely applied in graph data modeling. However, existing GNNs are often trained in a task-driven manner that fails to fully capture the intrinsic nature of the graph structure, resulting in sub-optimal node…

We propose a novel expressivity framework for Graph Neural Networks (GNNs) grounded in Boolean function theory, enabling a fine-grained analysis of their ability to capture complex subpopulation structures. We introduce the notion of…

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…

Subgraph GNNs are a recent class of expressive Graph Neural Networks (GNNs) which model graphs as collections of subgraphs. So far, the design space of possible Subgraph GNN architectures as well as their basic theoretical properties are…

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of…

Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral…

The problem of graph isomorphism is an important but challenging problem in the field of graph analysis, for example: analyzing the similarity of two chemical molecules, or studying the expressive ability of graph neural networks. WL test…

Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying…

We present a fully non neural learning framework based on Graph Laplacian Wavelet Transforms (GLWT). Unlike traditional architectures that rely on convolutional, recurrent, or attention based neural networks, our model operates purely in…