Inverting generator of GAN through direction embedding discriminator

Generators in generative adversarial networks map latent distributions into data distributions. GAN inversion is mapping data distribution to latent distribution by inverting the generator of GAN. In this paper, I introduce a direction embedding discriminator GAN in which the discriminator learns the inverse mapping of the generator. In the suggested method, when the latent vector is sampled from an i.i.d. (independent and identically distributed) random variable, the latent vector is considered as angular coordinates of spherical coordinates. Thus, the latent vector can be transformed into a point on the surface of the hypersphere in cartesian coordinates. Discriminator embeds the generated data point into cartesian coordinates. The direction of embedded coordinates represents predicted cartesian coordinates of latent vector, and the log of magnitude represents an adversarial value (real/fake). The generator and discriminator are trained cooperative to decrease the angle between the embedded cartesian coordinates from the discriminator and the cartesian coordinates converted from the latent vector considered as angular coordinates of spherical coordinates. The suggested method can be applied during GAN training, does not require additional encoder training, and does not use a reconstruction loss.