Aren't manifolds generally task-dependent? I've been debating whether the data lies on a manifold, or whether the data attributes that are task-relevant (and o

Aren't manifolds generally task-dependent? I've been debating whether the data lies on a manifold, or whether the data attributes that are task-relevant (and of our interest) lie on a manifold? I suspect it is the latter, but I've seen Platonic Representation Hypothesis that seems to hint it is the former.