Paper ID: 2303.01590

Technical report: Graph Neural Networks go Grammatical

Jason Piquenot, Aldo Moscatelli, Maxime Bérar, Pierre Héroux, Romain raveaux, Jean-Yves Ramel, Sébastien Adam

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 G$^2$N$^2$, which is provably 3-WL compliant. Through various experiments, we demonstrate the superior efficiency of G$^2$N$^2$ compared to other 3-WL GNNs across numerous downstream tasks. Specifically, one experiment highlights the benefits of grammar reduction within our framework.

Submitted: Mar 2, 2023