Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. We propose a general, combinatorial , and unifying construction for performing neural network-type computations on cell complexes. Furthermore, we introduce inter-cellular message passing schemes, message passing schemes on cell complexes that take the topology of the underlying space into account . In particular, our method generalizes many of the most popular types of graph neural networks .
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a combinatorial formalism that allows the inclusion of complicated relationships of restrictive structures such as graphs and meshes. In this paper, we proposeCell Complexes Neural Networks (CXNs), a general, combinatorial and unifying construction for performing neural network-type computations on cell complexes. We introduce an inter-cellular message passing scheme on cell complexes that takes the topology of the underlying space into account and generalizes message passing scheme to graphs. Finally, we introduce a unified cell complex encoder-decoder framework that enables learning representation of cells for a given complex inside the Euclidean spaces. In particular, we show how our cell complex autoencoder construction can give, in the special casecell2vec, a generalization for node2vec .
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Cell Complexes Neural Networks (CXNs)
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and generalizes message passing scheme to graphs. Finally, we introduce a unified cell complex encoder-decoder framework that enables learning representation of cells for a given complex inside the Euclidean spaces.
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our method generalizes many of the most popular types of graph neural networks
we show how our cell complex autoencoder construction can give, in the special case
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cell2vec
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, a generalization for node2vec