Q:

Training stability of Wasserstein GANs

I am working on a project with Wasserstein GANs and more specifically with an implementation of the improved version of Wasserstein GANs. I have two theoretical questions about wGANs regarding their stability and training process. Firstly, the result of the loss function notoriously is correlated with the quality of the result of the generated samples (that is stated here). Is there some extra bibliography that supports that argument?
Secondly, during my experimental phase, I noticed that training my architecture using wGANs is much faster than using a simple version of GANs. Is that a common behavior? Is there also some literature analysis about that?
Furthermore, one question about the continuous functions that are guaranteed by using Wasserstein loss. I am having some issues understanding this concept in practice, what it means that the normal GANs loss is not continuous function?

A:

You can check Inception Score and Frechet Inception Distance for now.  And also here. The problem is that GANs not having a unified objective functions(there are two networks) there's no agreed way of evaluating and comparing GAN models. INstead people devise metrics that's relating the image distributinos and generator distributions.
wGAN could be faster due to having morestable training procedures as opposed to vanilla GAN(Wasserstein metric, weight clipping and gradient penalty(if  you are using it) ) . I dont know if there's a literature analysis for speed and It may not always the case for WGAN faster than a simple GAN. WGAN cannot find the best Nash equlibirum like GAN.
Think two distributions: p and q. If these distributions overlap, i.e. , their domains overlap, then KL or JS divergence are differentiable. The problem arises when  p and q don't overlap. As in WGAN paper example, say two pdfs on 2D space, V = (0, Z)  , Q = (K , Z) where K is different from 0 and Z is sampled from uniform distribution. If you try to take derivative of KL/JS divergences of these two pdfs well you cannot. This is because these two divergence would be a binary indicator function (equal or not) and we cannot take derivative of these functions. However, if we use Wasserstein loss or Earth-Mover distance, we can take it since we are approximating it as a distance between two points on space.  Short story: Normal GAN loss function is continuous iff the distributions have an overlap, otherwise it is discrete.

Hope this helps

