[youoy]

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.

[ottaborra]

Something to chew on for me. But what is a manifold then if not a topological space that is locally the same as R^(some dimension) ?

[youoy]

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.