"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

Can you explain why that's a misconception? Or at least point me to a source that explains it?

I've started working with neural networks lately and I don't know too much yet, but the idea that they recreate the generative process behind a system, at least implicitly, seems almost obvious. If I train a neural network on a simple linear function, the weights on the network will probably change to reflect the coefficients of that function. Does this not generalize?

Well, consider a neural net for distinguishing dogs from cats. This neural network might develop features that look like "dog-like eyes" and "cat-like eyes," which are pattern-matched across the image. Images with more activation on the first feature are claimed to be dogs and images with more activation on the second feature are claimed to be cats, along with input from many other features. This is fairly typical-sounding.

Now imagine how bonkers a neural net would have to be in order to reproduce the generative process behind the image... (read more)