Keywords: persistent homology, laplacian, simplicial complex, convolution, neural net, machine learning
TL;DR: We develop a convolutional neural network layer on simplicial 2-complexes.
Abstract: Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in general do not account for higher order relations between their hyperedges. Simplicial complexes offer a middle ground, with a rich theory to draw on. We develop a convolutional neural network layer on simplicial 2-complexes.
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