Title: Impact of the latent space on the ability of GANs to fit the distribution. Abstract: The goal of generative models is to model the underlying data distribution of a
sample based dataset. Our intuition is that an accurate model should in principle
also include the sample based dataset as part of its induced probability distribution.
To investigate this, we look at fully trained generative models using the Generative
Adversarial Networks (GAN) framework and analyze the resulting generator
on its ability to memorize the dataset. Further, we show that the size of the initial
latent space is paramount to allow for an accurate reconstruction of the training
data. This gives us a link to compression theory, where Autoencoders (AE) are
used to lower bound the reconstruction capabilities of our generative model. Here,
we observe similar results to the perception-distortion tradeoff (Blau & Michaeli
(2018)). Given a small latent space, the AE produces low quality and the GAN
produces high quality outputs from a perceptual viewpoint. In contrast, the distortion
error is smaller for the AE. By increasing the dimensionality of the latent
space the distortion decreases for both models, but the perceptual quality only
increases for the AE.