[D] StyleGAN2 Path Length Regularization Implementation Clarification

I am trying to implement stylegan2 and there are so many things here that are not explained either well, or at all in the paper.

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1. How exactly is path length regularization implemented? In [this](https://github.com/rosinality/stylegan2-pytorch/blob/bef283a1c24087da704d16c30abc8e36e63efa0e/train.py#L87) PT code we can see that the $|J\^T\_w.y|$ is computed as follows:

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def g_path_regularize(fake_img, latents, mean_path_length, decay=0.01):
noise = torch.randn_like(fake_img) / math.sqrt(
fake_img.shape[2] * fake_img.shape[3]
)
grad, = autograd.grad(
outputs=(fake_img * noise).sum(), inputs=latents, create_graph=True
)
path_lengths = torch.sqrt(grad.pow(2).sum(2).mean(1))

path_mean = mean_path_length + decay …

implementation machinelearning path regularization stylegan2