Title: Dist2Cycle: A Simplicial Neural Network for Homology Localization
Abstract: Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This construction is central towards detection of higher dimensional topological features of data, such as non-contractible k-cycles encoded through homology, features to which graphs remain oblivious. We propose Dist2Cycle, a graph convolutional (GCN) model for learning functions parametrized by the k-homological features of simplicial complexes, specifically, the distance of each k-simplex of a complex from its nearest "optimal" k-th homology generator. Paper to appear in AAAI2022.