A Gentle Introduction to Graph Neural Networks (2021)

It seems GNNs operate on a fixed topology. What if I want to approximate some transformation of the topology of the graph? For example learning how to layout a graph, or converting program abstract syntax trees to data flow graphs.

The whole point of GNNs is that they generalize to arbitrary topologies by explicitly conditioning the idea of "neighbours" on the graph specifying the topology. Graph layout has been tried here https://github.com/limbo018/DREAMPlace to great fanfare although there is recent drama about it https://www.semanticscholar.org/paper/The-False-Dawn%3A-Reev... . Graph transformations are a thing as well https://arxiv.org/abs/2012.01470 but it's a tricky problem because you implicitly need to solve the graph matching problem

Graph layout is extremely interesting for infographics, since a handmade graph will almost always beat what tools such as graphviz can come up with (and I'm not even mentioning algorithms that go beyond Sugiyama's for which there is only a paper).

Any progress on this front ?

Maybe homology can help, it is a sort of calculus for discrete structures where you count how many N dimensional hole there are over time. Dunno about NN but that is what they can do with fMRI.