Weisfeiler and Leman go Hyperbolic: Learning Distance Preserving Node Representations

Michail Chatzianastasis, Giannis Nikolentzos, Michalis Vazirgiannis

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 that 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.