2.2.2. Generative Adversarial Network (GAN)

The GAN ⁴⁴ consists of two networks: the generator network Gθ(Z) maps a latent vector Z∈Z to data space X^∈X and a discriminator network Dω(X) to distinguish whether the samples are coming from the empirical data distribution PDX or generated distribution Pθ(X). Hence, the discriminator network Dω(X) acts like a classifier that assigns probability y=Dω(X)∈[0,1] if X is an actual training sample, and probability 1‐y if X is generated by the model through X^=Gθ(Z) with Z∼QZ. The original GAN ⁴⁴ problem aims to maximize/minimize the binary cross entropy (an adversarial game):

with respect to Discriminator/Generator. Theoretically, when the adversarial process reaches the Nash equilibrium, the mini‐max game attains its global optimum.