Keywords: Geometric Deep Learning, Topological Learning, Laplacian, Simplicial Laplacian, Graph Convolutional Neural Networks, Higher-order relational learning
TL;DR: Simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes.
Abstract: We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not only pairwise relationships but also higher-order interactions between vertices—allowing us to consider richer data, including vector fields and $n$-fold collaboration networks. We define an appropriate notion of convolution that we leverage to construct the desired convolutional neural networks. We test the SNNs on the task of imputing missing data on coauthorship complexes. Code and data are available at https://github.com/stefaniaebli/simplicial_neural_networks.
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