I couldn't find any mention about a trained NN, this is strictly about the initial state. Yang does reference a few papers that supposedly leverage the GP correspondence to gain some insight about how to better initialize a NN, for example this: https://arxiv.org/abs/1803.01719
In addition to the paper mentioned by @fgabriel, this paper
 explains it in more detail as well, and the equations you are looking for are 14, 15, and 16.
I have only barely glanced at the paper mind-you, so I couldn't say the details but still.