Why Does Path Length Regularisation Work

Path length regularisation is a new trick for training GAN (i.e. Generative Adversarial Networks) proposed by NVIDIA in their StyleGAN2 paper. In appendix C of the paper, authors of which provide its readers with somewhat obscure explanations of the effects of the trick, leaving novices like me greatly baffled. In this article, I will decompose the whole theory into more detailed proofs of several lemmas respectively, targeting at a deeper comprehension of this prominent piece of art.