This might make some sense if DNNs were being used to further our understanding of theoretical physics, but afaik they're not. They're being used to classify cat pics. SInce when do you use polynomial Hamiltonians to recognise cats?
These properties mean that neural networks do not need to approximate an infinitude of possible mathematical functions but only a tiny subset of the simplest ones
No finite DNN can approximate sin(x) over the entire real numbers, unless you cheat by having a sin(x) activation function.
"The answer is that the universe is governed by a tiny subset of all possible functions. In other words, when the laws of physics are written down mathematically, they can all be described by functions that have a remarkable set of simple properties."
“For reasons that are still not fully understood, our universe can be accurately described by polynomial Hamiltonians of low order.” These properties mean that neural networks do not need to approximate an infinitude of possible mathematical functions but only a tiny subset of the simplest ones."
Interesting article, and just diving into the paper now, but it looks like this is a big boost to the simulation argument. If the universe is built like a game engine, with stacked sets like Mandelbrots, then the simplicity itself becomes a driver in a fabricated reality.
https://www.technologyreview.com/s/602344/the-extraordinary-link-between-deep-neural-networks-and-the-nature-of-the-universe/
Why does deep and cheap learning work so well?
http://arxiv.org/abs/1608.08225