The Extraordinary Link Between Deep Neural Networks and the Nature of the Universe

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Deep neural networks are now better than humans at tasks such as face recognition and object recognition.
Despite the huge success of deep neural networks, nobody is quite sure how they achieve their success.
In the language of mathematics, neural networks work by approximating complex mathematical functions with simpler ones.
When it comes to classifying images of cats and dogs, the neural network must implement a function that takes as an input a million grayscale pixels and outputs the probability distribution of what it might represent.
The problem is that there are orders of magnitude more mathematical functions than possible networks to approximate them.
And yet deep neural networks somehow get the right answer.
Now Lin and Tegmark say they’ve worked out why.
So deep neural networks don’t have to approximate any possible mathematical function, only a tiny subset of them.
“For reasons that are still not fully understood, our universe can be accurately described by polynomial Hamiltonians of low order,” say Lin and Tegmark.
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.
There is another property of the universe that neural networks exploit.
This is why the structure of neural networks is important too: the layers in these networks can approximate each step in the causal sequence.
And when phenomena have this hierarchical structure, neural networks make the process of analyzing it significantly easier.
“We have shown that the success of deep and cheap learning depends not only on mathematics but also on physics, which favors certain classes of exceptionally simple probability distributions that deep learning is uniquely suited to model,” conclude Lin and Tegmark.
So not only do Lin and Tegmark’s ideas explain why deep learning machines work so well, they also explain why human brains can make sense of the universe

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