GANs: generator and discriminator

The generator ${\mathcal{G}}_{\theta }$ takes noise $z$ drawn from a simple input distribution (Gaussian or uniform) — think of $z$ as a latent representation of an image — and turns it into fake samples. Its output distribution is written ${\mathcal{G}}_{\theta }(\mathcal{K})$.

The discriminator $D$ receives real samples from the data distribution $\mathbb{X}$ (label $y=1$) and fake samples (label $y=0$) and is trained to tell them apart. When training the generator, its fake samples are presented with label $y=1$ so that the generator learns to fool $D$.

Both networks are fine-tuned in alternation from the discriminator's feedback.