So basically the map projection problem [1] in higher dimensions?
Violation of topology means that a surface wrongly is mapped to one intersecting itself: Think Klein Bottle.
Like many things in ML, this might be a problem in theory but empirically it isn’t important, or is very low on the stack rank of issues with our models.
It's a problem for the simplest of reasons, information is lost. You cannot reconstruct the original topology.
In terms of the model, it now can't distinguish between what were completely different regions.
From the Klein bottle perspective, a 4D shape gets projected into a 3D shape. On most of the bottle, there is still a 1 to 1 topological mapping from 3D to 4D versions.
But where two surfaces now intersect, there is now no way to distinguish between previously unrelated information. The model won’t be able to anything sensible with that.
TLDR; We don't like folding.