Check out the recent paper "Building Machines That Learn and Think Like People":
https://arxiv.org/abs/1604.00289
Humans can see one or a few examples of a novel object, such as a cat, and create a fully 3D mental model of it. So we know what it will look like in different orientations and lighting conditions.
I.e. we can recognise static 2D photos of cats, 2D movies of cats, 3D movies of cats, and real cats in the real world.
The invariants are probably relatively simple - a set of head geometries and head feature shapes/distribution, with some secondary colour and texture confirmation.
What's interesting is that we can recognise modifiers to the invariants - e.g. a shaved cat is still recognisably a cat, but parsed as "cat without fur."
We can also recognise invariants when they're pared down to essentials in cartoons and sketches.
https://www.youtube.com/watch?v=R9qdyXCVNVk
A lot of learning is really just data compression - finding a minimal set of low-resource invariant specifics from a wide range of noisy high-resource inputs.
While in general I felt something similar that it has to be not just reams of data but also some sort of model (meta data) that when combined can produce innumerable combinations more easily.