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arXiv · 2303.01590

Technical report: Graph Neural Networks go Grammatical

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

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.

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Jason Piquenot, Aldo Moscatelli, Maxime Bérar, Pierre Héroux, Romain raveaux, Jean-Yves Ramel, Sébastien Adam. 2023-03-02. Technical report: Graph Neural Networks go Grammatical. https://arxiv.org/abs/2303.01590

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