Body: <p>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.
  <a href="https://i.sstatic.net/jJ7EX.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/jJ7EX.png" alt="enter image description here" /></a></p>
  <p>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.</p>
  <p><strong>EDIT</strong>:</p>
  <p><a href="https://i.sstatic.net/XVihd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XVihd.png" alt="enter image description here" /></a></p>
  <p><strong>EDIT 2</strong>:</p>
  <p>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?
  <a href="https://i.sstatic.net/W6jTV.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/W6jTV.png" alt="enter image description here" /></a></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-11-04T13:26:02.497Z
Comments.Text: 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 $\tilde{x}$?
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-11-04T13:28:21.260Z
Comments.Text: @NeilSlater yes, I confirm. I added a change to the original post under EDIT regarding the second thing
Comments.UserDisplayName: Gibser
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-11-05T15:02:44.107Z
Comments.Text: Please, put your main **specific** question in the title.
Comments.UserDisplayName: nbro
Tags: <deep-learning><generative-adversarial-networks><loss><wasserstein-metric><wasserstein-gan>
Title: WGAN-GP Loss formalization
UserDisplayName: Gibser
ThreadText: # WGAN-GP Loss formalization
  
  (Asked by: username_0 on 2020-11-04)
  
  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.
  [![enter image description here](https://i.sstatic.net/jJ7EX.png)](https://i.sstatic.net/jJ7EX.png)
  
  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**:
  
  [![enter image description here](https://i.sstatic.net/XVihd.png)](https://i.sstatic.net/XVihd.png)
  
  **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?
  [![enter image description here](https://i.sstatic.net/W6jTV.png)](https://i.sstatic.net/W6jTV.png)
  
  **Tags:** deep-learning, generative-adversarial-networks, loss, wasserstein-metric, wasserstein-gan
  
  > **Comments:**
  > **username_1**: 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 $\tilde{x}$?  
  > **username_0**: @username_1 yes, I confirm. I added a change to the original post under EDIT regarding the second thing  
  > **username_2**: Please, put your main **specific** question in the title.  
  
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  ## 0 answers
  
  