Machine Learning; Graph Neural Networks; Weisfeiler-Leman (WL) Test; Hierarchical Graph Pooling; Theory and Expressivity in GNNs
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Abstract:
Considerable efforts have been dedicated to exploring methods that enhance the expressiveness of graph neural networks. Current endeavors primarily focus on modifying the message-passing process to overcome limitations imposed by the Weisfeiler-Leman test, often at the expense of increasing computational cost. In practical applications, message-passing layers are interleaved with pooling layers for graph-level tasks, enabling the learning of increasingly abstract and coarser representations of input graphs. In this work, we formally prove two directions that allow pooling methods to increase the expressive power of a graph neural network while keeping the message-passing method unchanged. We systemically assign eight frequently used pooling operators to our theoretical conditions for increasing expressivity and introduce a novel pooling method XP, short for eXpressive Pooling, as an additional simple method that satisfies our theoretical conditions. Experiments conducted on the Brec dataset confirm that those pooling methods that satisfy our conditions empirically increase the expressivity of graph neural networks.
