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 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.

References in corpus (5)

• Geometric deep learning: going beyond Euclidean data
• On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
• Missing Data Imputation with Adversarially-trained Graph Convolutional Networks
• Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
• DeepSphere: a graph-based spherical CNN

Cited by in corpus (7)

• Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond
• Dirac signal processing of higher-order topological signals
• Signal Processing on Cell Complexes
• Cell Attention Networks
• Hodgelets: Localized Spectral Representations of Flows on Simplicial Complexes
• Simplicial Complex Representation Learning
• Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes