Robert, please consider some of this as the difference between math and
engineering. Math desires rigor. Engineering desires working solutions. When
an engineering solution is being described, you shouldn't expect the same level
of rigor as in a mathematical proof. Often all we can say is
Amazon uses deep neural nets in many, many areas. There is some overlap with
the kind of nets used in AlphaGo. I passed a link to the paper on to one of
our researchers and he found it very interesting. DNN works very well when
there is a lot of labelled data to learn from. It can be useful
