It’s a fascinating topic and I’m not aware of any more current research (though it has been a while since I went searching during my machine learning craze a year or so ago). Here are some rambling thoughts…
For ground truth to train on, I suspect you would need a lot of meshes that represent the kind of topology that you consider good and want the machine to learn to emulate. You can then probably make input and output pairs of before and after retopologizing by taking the good mesh and randomly triangulating it, or moving the vertices around, or whatever, to produce the “before” mesh to go with the desired output.
I guess it depends on whether you want to take the approach of improving an existing mesh in place, or trying to cover the surface with a new mesh without specific regard to the vertices that exist in the original.
Getting a lot of good meshes to use is of course problematic and you might need a LOT of examples I think. Maybe you could generate them procedurally, but if you understand the problem that well, then maybe you can come up with a retopology solver without using machine learning.
For representing the mesh and feeding the problem into your network, it would be fun to think you could just feed in the whole mesh (somehow) and say “just learn how to do THIS to it”, but I’m not sure how you would actually do that as you say.
For improving existing topology I was thinking maybe you could pull out little sub-parts of the desired mesh, even as small as one polygon and everything connected to it by a few edges say, then take the points near that spatial location in the “before” mesh as the corresponding input. You can generate a lot more examples from each mesh that way, but a lot of topology decisions like where to put the edge loops kind of need to look at the big picture.
Maybe you want to look at the overall shape and plan the polygon flow, and then fill in the actual polygons as a separate step (I imagine most automatic retopo tools do something like this).
I wonder if there’s a simpler 2D analog that you could start with (optimizing UV maps or something) that would be easier to get started on than the full 3D version.