Structural Preservation and the Logical Expressiveness of Graph Neural Networks
A new paper explores the logical expressiveness of graph neural networks (GNNs) by examining their structural preservation properties. Researchers established correspondences between specific fragments of graded modal logic and classes of GNN classifiers preserved under embeddings, injective homomorphisms, and homomorphisms. The findings characterize the expressiveness of broad GNN classes independent of specific architectural choices, while also demonstrating that these classes can be realized with equivalent GNN architectures. AI
IMPACT Establishes theoretical links between GNN architectures and logical formalisms, potentially guiding future model design.