BScNets: Block Simplicial Complex Neural Networks

Simplicial neural networks (SNNs) have recently emerged as a new direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead predominantly assessing pairwise relations among nodes current practice, allow us describe higher-order interactions and multi-node structures. By building upon connection between convolution operation block Hodge-Laplacian, we propose first SNN for link prediction. Our Block Complex Neural Networks (BScNets) model generalizes existing network (GCN) frameworks by systematically incorporating salient multiple structures different dimensions. We discuss theoretical foundations behind BScNets illustrate its utility prediction eight real-world synthetic datasets. experiments indicate that outperforms state-of-the-art models significant margin while maintaining low computation costs. Finally, show promising alternative tracking spread infectious diseases such COVID-19 measuring effectiveness healthcare risk mitigation strategies.