Simplicial 2-Complex Convolutional Neural NetworksDownload PDF

Oct 10, 2020 (edited Dec 02, 2020)NeurIPS 2020 Workshop TDA and Beyond Blind SubmissionReaders: Everyone
  • 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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