That's if you go about it from low-dimensional embedding to feature classification, and predictions based on probabilities for those features. As you mention,

That's if you go about it from low-dimensional embedding to feature classification, and predictions based on probabilities for those features. As you mention, that works if you have metric data, or can juice metrics from abstraction. Modern ML is all about solving for this case; adding manifold hypothesis, as the author noted, may only improve them slightly, or not at all. That isn't what the "manifold hypothesis" is good for. Manifold space is more interesting to think of, not in the deconstruction of metric space, but in the formation of it; i.e. what higher-dimensional, non-metric (intensive), manifold-space, through some complex function (eg physics), results in this lower-dimensional, feature-rich entity; and what is that function (or more interestingly, how does it change the resulting entity-state, given various changes in the manifolds). Which may not be useful for classification, but that's old hat anyway. Personally, I feel that feature dependence for everything NN is brute force. How features come-to-be, even abstractly modeled, is the thing.