Now we will examine the loss function of GAN. Before going ahead, let's recap the notations:

• A noise that is fed as an input to the generator is represented by
• The uniform or normal distribution from which the noise is sampled is represented by
• An input image is represented by
• Real data distribution or distribution of our training set is represented by
• Fake data distribution or distribution of the generator is represented by

When we write , it implies that image is sampled from the real distribution, . Similarly, denotes that image is sampled from the generator distribution, , and implies that the generator input, , is sampled from the uniform distribution, .

We've learned that both the generator and discriminator are neural networks and both of them update their parameters through backpropagation. We now need to find the optimal generator parameter, , and the discriminator parameter, .