Technical report: Graph Neural Networks go Grammatical
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 mod...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2303.01590 |