This paper introduces a framework for formally establishing a connection between a portion of an algebraic language and a Graph Neural Network (GNN). The framework leverages Context-Free Grammars (CFG) to organize algebraic operations into generative rules that can be translated into a GNN layer model. As CFGs derived directly from a language tend to contain redundancies in their rules and variables, we present a grammar reduction scheme. By applying this strategy, we define a CFG that conforms to the third-order Weisfeiler-Lehman (3-WL) test using MATLANG. From this 3-WL CFG, we derive a GNN model, named G2N2, which is provably 3-WL compliant. Through various experiments, we demonstrate the superior efficiency of G2N2 compared to other 3-WL GNNs across numerous downstream tasks. Specifically, one experiment highlights the benefits of grammar reduction within our framework.
@article{arxiv.2303.01590,
title = {Technical report: Graph Neural Networks go Grammatical},
author = {Jason Piquenot and Aldo Moscatelli and Maxime Bérar and Pierre Héroux and Romain raveaux and Jean-Yves Ramel and Sébastien Adam},
journal= {arXiv preprint arXiv:2303.01590},
year = {2023}
}