Simplicial Neural Networks

TL;DR

This paper introduces simplicial neural networks (SNNs), extending graph neural networks to handle higher-order topological data like vector fields and collaboration networks, with applications in data imputation.

Contribution

The paper proposes a new class of neural networks based on simplicial complexes, enabling analysis of multi-dimensional relationships beyond pairwise interactions.

Findings

Effective data imputation on coauthorship complexes

Generalizes GNNs to higher-dimensional topological spaces

Demonstrates the ability to handle richer data types

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.