I am not well versed in topological deep learning; but can topological concepts be learned by a graph neural network -- like can there a be topological layer(s) that learns the topology of the graphs, like how it's easy to visualize how a CNN architecture can see different hierarchical patterns at deep depths, seemingly learning the greater complexities of a image representation and understanding?
The paper seems to be using homology as the topological feature here. I've done some work in Topological Data Analysis before and it feels like the hidden issue is that computing homology is generally very inefficient(Since it usually amounts to reducing an nxn matrix).<p>It definitely feels like graphs/topology should be helpful tools to work with data(Since graph-like structures are good representations of the real world), but we need to solve this efficiency issue before this can be possible.<p>Also to address the confusion on how category theory comes into it, category theory studies abstract structures where you have objects and relationships between these objects. A lot of algebraic topology(Which is the sort of topology relevant here) is built in the language of category theory(Either by neccesity or by convention).