Related papers: Weisfeiler and Lehman Go Topological: Message Pass…
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…
This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial…
Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many complex systems. An effective way to incorporate them is to…
Today, it is more important than ever before for users to have trust in the models they use. As Machine Learning models fall under increased regulatory scrutiny and begin to see more applications in high-stakes situations, it becomes…
In recent studies, neural message passing has proved to be an effective way to design graph neural networks (GNNs), which have achieved state-of-the-art performance in many graph-based tasks. However, current neural-message passing…
We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell{}$MPNN, that can count cycles up to length $r + 2$. Most notably, we show that…
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…
The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a very useful combinatorial tool in graph isomorphism testing. We address the applicability of $k$-WL to recognition of graph properties. Let $G$ be an input graph with $n$…
Message passing neural networks (MPNNs) operate on graphs by exchanging information between neigbouring nodes. MPNNs have been successfully applied to various node-, edge-, and graph-level tasks in areas like molecular science, computer…
Learning representations of sets of nodes in a graph is crucial for applications ranging from node-role discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in graph…
Numerous subgraph-enhanced graph neural networks (GNNs) have emerged recently, provably boosting the expressive power of standard (message-passing) GNNs. However, there is a limited understanding of how these approaches relate to each other…
Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler--Leman algorithm ($1\text{-}\mathsf{WL}$). Here, the $1\text{-}\mathsf{WL}$ is a well-studied heuristic for…
Graph representation learning methods have mostly been limited to the modelling of node-wise interactions. Recently, there has been an increased interest in understanding how higher-order structures can be utilised to further enhance the…
As a classical approach on graph learning, the propagation-aggregation methodology is widely exploited by many of Graph Neural Networks (GNNs), wherein the representation of a node is updated by aggregating representations from itself and…
Graph Neural Networks (GNNs) have become a prominent approach to machine learning with graphs and have been increasingly applied in a multitude of domains. Nevertheless, since most existing GNN models are based on flat message-passing…
Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral graph neural networks, reflecting two largely separate research traditions in machine learning and signal processing. This paper…
Graph neural networks (GNNs) are widely used in graph learning and most architectures propagate information by passing messages between vertices. In this work, we shift our attention to GNNs that perform message passing on edges and…
Identifying similar network structures is key to capture graph isomorphisms and learn representations that exploit structural information encoded in graph data. This work shows that ego-networks can produce a structural encoding scheme for…
Graph Neural Networks based on the message-passing (MP) mechanism are a dominant approach for handling graph-structured data. However, they are inherently limited to modeling only pairwise interactions, making it difficult to explicitly…
The expressive power of graph neural network formalisms is commonly measured by their ability to distinguish graphs. For many formalisms, the k-dimensional Weisfeiler-Leman (k-WL) graph isomorphism test is used as a yardstick. In this paper…