The content delves into the GWL framework to understand how design choices impact geometric GNN expressivity. It discusses depth, invariant vs. equivariant message passing, and body order of scalarization. Synthetic experiments are provided to supplement theoretical insights.
The study shows that popular G-equivariant GNNs may require more iterations than prescribed by GWL for certain tasks. Additionally, it reveals limitations of G-invariant models in capturing global geometry and identifying rotational symmetries with higher-order tensors.
Practical implications include the need for higher-order tensors in G-equivariant models and potential issues with oversquashing in deep networks. Theoretical results connect discrimination capabilities with universal approximation in geometric GNNs.
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