# WGAN-GP Loss formalization

I have to write the formalization of the loss function of my network, built following the WGAN-GP model. The discriminator takes 3 consecutive images as input (such as 3 consecutive frames of a video) and must evaluate if the intermediate image is a possible image between the first and the third.

I thought something like this, but is it correct to identify x1, x2 and x3 coming from Pr even if they are 3 consecutive images? Only the first is chosen randomly, the others are simply the next two.

EDIT:

EDIT 2:

I replaced Pr with p_r(x1, x3) and p_r(x1, x2, x3) to reinforce the fact that x2 and x3 are taken after x1, so they depend on the choice of x1. Is it more correct this way?

• Can you confirm that the generator for $\tilde{x}$ is being conditioned on $x_1, x_3$? Also that $\hat{x}$ is a random mix of real $x_2$ and a generated $\tilde{x}$? – Neil Slater Nov 4 '20 at 13:26
• @NeilSlater yes, I confirm. I added a change to the original post under EDIT regarding the second thing – Gibser Nov 4 '20 at 13:28
• Please, put your main specific question in the title. – nbro Nov 5 '20 at 15:02