Simplicial Attention

Simplicial attention networks (SANs) represent a novel approach to neural network design that leverages the higher-order structural information present in simplicial complexes—generalizations of graphs encompassing nodes, edges, triangles, and higher-dimensional simplices. Current research focuses on developing SAN architectures, often incorporating self-attention mechanisms and Hodge-Laplacian operators, to effectively process data defined on these complexes. These models aim to improve upon traditional graph neural networks by capturing complex, multi-level interactions within data, leading to enhanced performance in various applications such as graph classification, trajectory prediction, and missing data imputation. The resulting improvements in data representation and analysis hold significant potential across diverse scientific fields and practical applications.