  It has been proposed that random wide neural networks near Gaussian process
are quantum field theories around Gaussian fixed points. In this paper, we
provide a novel map with which a wide class of quantum mechanical systems can
be cast into the form of a neural network with a statistical summation over
network parameters. Our simple idea is to use the universal approximation
theorem of neural networks to generate arbitrary paths in the Feynman's path
integral. The map can be applied to interacting quantum systems / field
theories, even away from the Gaussian limit. Our findings bring machine
learning closer to the quantum world.
