Earlier quoted context omitted.
I will read the post later, but I can tell you right now that I'm a physicist and when I was first introduced to deep learning my first thought, especially in the context of visual recognition, was "this smells of renormalization group".
Do you happen to know any good introductory texts to the renormalization group?
Some others I have sitting beside me at my desk right now are http://www.amazon.com/Theory-Critical-Phenomena-Introduction..., http://www.amazon.com/Renormalization-Introduction-Operator-... and http://www.amazon.com/Renormalization-Methods-Guide-For-Begi...
The most modern treatment is probably http://www.amazon.com/Scaling-Renormalization-Statistical-Ph...
(For God's sake, stay away from anything written by Zinn-Justin, Itzykson, or Zuber unless you know what you're doing)