Efficient representation learning for higher-order data with simplicial complexes

Graph-based machine learning is experiencing explosive growth, driven by impressive recent developments and wide applicability. Typical approaches for graph representation learning predominantly focus on pairwise interactions, while neglecting the patterns of higher-order interactions common to complex systems. This paper explores many-body interaction models, centering on simplicial complexes. From a theoretical point of view, we offer a pair of insights illustrating why higher-order models are necessary, why non-graph-based models generally cannot generalize well, while graph-based models may be able to do so. We conduct experiments on synthetic data, co-citation networks, co-authorship networks and gene-disease associations and show that simplicial complexes with certain relaxations can more efficiently capture underlying higher-order structures than non-graph structure, regular graph, hypergraph, and traditional simplicial complexbased learning frameworks.