Weisfeiler Leman

The Weisfeiler-Lehman (WL) algorithm is a graph isomorphism test whose iterative color refinement process has become a benchmark for measuring the expressive power of graph neural networks (GNNs). Current research focuses on enhancing GNN expressivity beyond the limitations of the standard WL test by exploring variations like loopy WL, incorporating edge information, and leveraging techniques from transformer networks and hyperbolic geometry. This work is significant because it directly impacts the design of more powerful and efficient GNNs for various applications, including molecular property prediction, knowledge graph reasoning, and point cloud analysis, by providing a theoretical framework for understanding and improving their capabilities.