The discriminator wants to be able to distinguish between real and generated images. It wants to output 1 for real image and 0 for generated images. The discriminator loss function has the following formula, again simplified because of the way GAN training and labeling works:

This loss function has two terms to it:

• Binomial cross entropy applied to the discriminator model results in some real data x​
• Binomial cross entropy applied to the discriminator model result for generated data, G(z)

As earlier, we take the negative of these and want to maximize this loss function when training our GAN. When this loss is maximized, it means the discriminator is capable of distinguishing between real and generated outputs. Note that this loss is maximized when the discriminator outputs 1 for real images and 0 for generated images.