Simplicial Neural Networks

Explore simplicial neural networks (SNNs), a groundbreaking extension of graph neural networks, in this 52-minute conference talk. Delve into the world of topological spaces called simplicial complexes, which encode higher-order interactions beyond pairwise relationships. Learn how SNNs can process richer data structures, including vector fields and n-fold collaboration networks. Discover the novel concept of simplicial convolution and its application in constructing advanced convolutional neural networks. Examine the practical application of SNNs in imputing missing data on coauthorship complexes. Gain insights into Laplacians for simplicial complexes, the architecture of SNNs, and their accuracy in predicting missing citations. Conclude with an overview of other topological neural networks and potential future directions in this exciting field of applied algebraic topology.

Intro
Convolutional Neural Networks (CNN)
Data on non-regular grids
Beyond pairwise interactions Simplicial complexes can model fold interaction
Why neural networks on simplicial complexes?
Laplacians for Simplicial Complexes
Simplicial Convolutional Layer
Architecture of Simplicial Neural Networks (SNNS)
Others Topological Neural Networks
Accuracy in predicting missing citations with SNNS