Simplifying Simplex Convolutional Networks

Topological deep learning (TDL) has recently emerged as a family of neural networks for data on topological domains (e.g., graphs and cellular complexes). In the context of graph data, TDL provides a recipe for leveraging high-order information, e.g., from cliques, to boost the expressiveness of graph neural networks. This additional power comes at a computational cost, stemming from message passing between higher-order structures. In this paper, we alleviate the computing toll of TDL by proposing SimpleXCN, a linear convolutional model for simplicial complexes. SimpleXCN derives naturally from removing non-linearities of base TDL architectures. Despite its simplicity, SimpleXCN remains competitive with established topological neural networks in node classification tasks. Our experiments show a reduction of approximately 25% in time and 10 times in the number of parameters, and consequently a significant reduction in memory usage of up to 50% compared to other SNNs.