Simplicial Neural Networks
This work addresses the need for neural networks that handle multi-dimensional relational data, such as collaboration networks, but it appears incremental as it generalizes existing graph neural networks.
The authors tackled the problem of extending graph neural networks to richer data structures called simplicial complexes, which encode higher-order interactions, and they developed simplicial neural networks (SNNs) with a new convolution method, achieving results tested on coauthorship complexes for imputing missing data.
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.