This repository has code for my PhD Dissertation titled Simplicial Methods in Graph Machine Learning In this thesis, we propose different neural network architectures that use Simplicial Sets. Simplicial Sets are combinatorial objects that generalize directed graphs from binary relations to higher relations. These architectures, therefore, may fall under the purview of Graph Neural Networks (GNNs), but with graphs lifted. In particular, these architectures may be ported into pipelines of off-the-shelf implementations of GNNs.
Past experience tells us that graph neural networks "need" to be undirected. Theory tells us something otherwise1. Current research in this respect tells us that the natural asymmetry in directed graphs, once quantified and made crucial part of the message passing, really does help with the performance of GNNs. By extension, higher relations based on directed graphs perform better than their undirected counterparts. Think of these directed higher relations as ``oriented communities''.
1: Sometimes, we rely on empirical evidence too much and dismiss theory. Sometimes, we shouldn't.