Simplicial Neural Networks
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 multidimensional extensions of graphs that encode not only pairwise relationships but also higherorder 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.03633
 Bibcode:
 2020arXiv201003633E
 Keywords:

 Computer Science  Machine Learning;
 Mathematics  Algebraic Topology;
 Statistics  Machine Learning