We can consider the failure cases of the WL algorithm to motivate provably more powerful graph neural networks. However, message passing approaches generally fail to identify closed triangles in a graph, which can be considered to be a critical limitation. This paper suggests that we use the relational pooling approach, which considers augmenting message passing graph neural networks with unique node ID features.

University of Michigan - Ann Arbor

It is important to research on how we can make graph neural networks more powerful than WL algorithm because there are some research that indicates that models such as message-passing graph neural networks are no more powerful than the WL algorithm.

Graph Neural Networks and WL algorithm

Relational pooling approach benefits

Even though the relational pooling approach can produce graph neural networks models that are more powerful than the WL algorithm, there are limitations to the relational pooling approach. The two key limitations are that the full algorithm is computationally intractable and there is no way to characterize how much powerful this approach can make graph neural networks in comparison to the WL algorithm.

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