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What is: Relativistic GAN?

SourceThe relativistic discriminator: a key element missing from standard GAN
Year2000
Data SourceCC BY-SA - https://paperswithcode.com

A Relativistic GAN is a type of generative adversarial network. It has a relativistic discriminator which estimates the probability that the given real data is more realistic than a randomly sampled fake data. The idea is to endow GANs with the property that the probability of real data being real (D(x_r)D\left(x\_{r}\right)) should decrease as the probability of fake data being real (D(x_f)D\left(x\_{f}\right)) increases.

With a standard GAN, we can achieve this as follows. The standard GAN discriminator can be defined, in term of the non-transformed layer C(x)C\left(x\right), as D(x)=sigmoid(C(x))D\left(x\right) = \text{sigmoid}\left(C\left(x\right)\right). A simple way to make discriminator relativistic - having the output of DD depend on both real and fake data - is to sample from real/fake data pairs x~=(x_r,x_f)\tilde{x} = \left(x\_{r}, x\_{f}\right) and define it as D(x~)=sigmoid(C(x_r)C(x_f))D\left(\tilde{x}\right) = \text{sigmoid}\left(C\left(x\_{r}\right) − C\left(x\_{f}\right)\right). The modification can be interpreted as: the discriminator estimates the probability that the given real data is more realistic than a randomly sampled fake data.

More generally a Relativistic GAN can be interpreted as having a discriminator of the form a(C(x_r)C(x_f))a\left(C\left(x\_{r}\right)−C\left(x\_{f}\right)\right), where aa is the activation function, to be relativistic.