Cell Complex Neural Networks
This work addresses the need for more flexible neural network models in domains like graphs and meshes, though it appears incremental as it builds on existing graph-based methods.
The paper tackles the problem of performing neural network computations on cell complexes, which generalize graphs and other structures, by proposing Cell Complex Neural Networks (CXNs) with an inter-cellular message passing scheme and an encoder-decoder framework, resulting in a generalization of node2vec called cell2vec.
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 propose \textbf{Cell 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 case \textbf{cell2vec}, a generalization for node2vec.