Weisfeiler and Leman go Hyperbolic: Learning Distance Preserving Node Representations

Abstract

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 between these models and the Weisfeiler-Leman (WL) test of isomorphism, an algorithm that can successfully test isomorphism for a broad class of graphs. Recently, much research has focused on measuring the expressive power of GNNs. For instance, it has been shown that standard MPNNs are at most as powerful as WL in terms of distinguishing non-isomorphic graphs. However, these studies have largely ignored the distances between the representations of nodes/graphs which are of paramount importance for learning tasks. In this paper, we define a distance function between nodes which is based on the hierarchy produced by the WL algorithm, and propose a model that learns representations which preserve those distances between nodes. Since the emerging hierarchy corresponds to a tree, to learn these representations, we capitalize on recent advances in the field of hyperbolic neural networks. We empirically evaluate the proposed model on standard node and graph classification datasets where it achieves competitive performance with state-of-the-art models.

arXiv commentAccepted at AISTATS 2023

References in corpus (12)

• Neural Message Passing for Quantum Chemistry
• Molecular Graph Convolutions: Moving Beyond Fingerprints
• Hierarchical Graph Representation Learning with Differentiable Pooling
• TUDataset: A collection of benchmark datasets for learning with graphs
• Hyperbolic Graph Convolutional Neural Networks
• Representation Tradeoffs for Hyperbolic Embeddings
• Robust Spatial Filtering with Graph Convolutional Neural Networks
• Lipschitz regularity of deep neural networks: analysis and efficient estimation
• A Survey on The Expressive Power of Graph Neural Networks
• Wasserstein Weisfeiler-Lehman Graph Kernels
• Weisfeiler and Leman go Machine Learning: The Story so far
• Discriminative structural graph classification