Hypergraph Neural Networks with Logic Clauses

João Pedro Gandarela de Souza, Gerson Zaverucha, Artur S. d'Avila Garcez

Abstract: The analysis of structure in complex datasets has become essential to solving difficult Machine Learning problems. Relational aspects of data, capturing relationships between objects, play a crucial role in understanding the underlying data structure. While traditional graph algorithms have been widely used for binary relations, recent evidence suggests that hypergraphs can provide a more effective approach for modeling complex, non-binary relations. Hypergraph Neural Networks (HGNN) have been shown to offer a small improvement in performance when compared to Graph Neural Networks (GNN). In this paper, a new approach is proposed for inserting relational domain knowledge into HGNNs using a logic clause expressing non-binary relations. We evaluate the performance of this new hypergraph model, called Bottom-clause HGNN (BHGNN), in comparison with well-known approaches. Results show that BHGNN can achieve statistically significant improvement of performance, based on the Wilcoxon signed-ranks test, in comparison with HGNN and GNNs.