Generative adversial network (GAN) is a type of generative model that maps a
high-dimensional noise to samples in target distribution. However, the
dimension of noise required in GAN is not well understood. Previous approaches
view GAN as a mapping from a continuous distribution to another continous
distribution. In this paper, we propose to view GAN as a discrete sampler
instead. From this perspective, we build a connection between the minimum noise
required and the bits to losslessly compress the images. Furthermore, to
understand the behaviour of GAN when noise dimension is limited, we propose
divergence-entropy trade-off. This trade-off depicts the best divergence we can
achieve when noise is limited. And as rate distortion trade-off, it can be
numerically solved when source distribution is known. Finally, we verifies our
theory with experiments on image generation.

全球学术知名期刊报道了一项关于生成对抗网络（GAN）的研究，该研究提出了将 GAN 视为离散采样器的新观点，并建立了噪声维度与无损压缩图像所需比特数之间的关系。此外，还提出了一种新的分歧 - 熵权衡方法，用于揭示在噪声受限的情况下 GAN 的行为特征，并通过图像生成实验证实了理论推断。