Exactly! Now consider that deep networks that classify images are tasked with getting reliable statistics in very high dimensional spaces. Conv nets are being forced to map from high dimensional spaces down to a very low dimensional categorical decision. This is why weird classification errors you see in "adversarial examples" keep popping up. The learned classification boundaries are very spiky, and it's easy for the world to fall in between the spikes. More data can't solve it (at least not practically) because there are way too many gaps between the spikes.

A more tractable approach is to learn to use dynamics for perception rather than ("just") statistics. The dynamical physics of a ball rolling is much simpler (lower dimensional, more tractable) than a statistical view of millions of differently illuminated pixels hitting a camera.

(A colleague of mine has a blog post on this issue of "statistics and dynamics" at http://blog.piekniewski.info/2016/11/01/statistics-and-dynam...)