"...multiple hidden layers..."
"...multiple hidden layers where mathematical computations occur..."
The technology concepts of Google Deep Dream more or less makes those "hidden" layers more or less visible. It's not off the shelf, but the concept of bringing those hidden layers to the surface is quite obvious.
Deep Dream is visual, but the same concept could be applied to any application.
We went over this obvious connection a couple years ago, when Deep Dream was in the press. There's really no excuse for "hidden" layers today, and certainly not for any safety critical systems.