Weisfeiler and Leman go Hyperbolic: Learning Distance Preserving Node Representations
This addresses a limitation in GNNs for graph learning tasks, though it is incremental as it builds on existing WL and hyperbolic methods.
The paper tackles the problem that standard graph neural networks (GNNs) ignore distances between node representations, which are crucial for learning tasks, by defining a distance function based on the Weisfeiler-Leman (WL) hierarchy and learning representations that preserve these distances using hyperbolic neural networks, achieving competitive performance on node and graph classification datasets.
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.