I think "manifolds" in AI are not the same as actual smooth manifolds. For starters I would not expect them to have locally the same dimension across the whole dataset.
What I meant is that I can imagine cases where some part of the dataset may look like R2 and then colapse to have a spike that looks like R1, so it is not a standard manifold where all of it has the same dimension.
Appart from that, these "manifolds" have noise, so that is another difference with the standard manifolds.
