$3$ Problem $3$: Mode Collapse $(40$ points$)$

GANs are notoriously difficult to train. One of the famous training issues is the

mode collapse. When mode collapse happen, the generator ignores the variety

of the training data and produces the same output in most of the time.

a$.(5$ points$)$ Explain the mode collapse problem happens in GANs in $2-3$

sentences.

b$.(10$ points$)$ UnRolled GAN $[4]$ alleviates the mode collapse problem of

GAN training by forecasting the future K steps of which networks? Explain

your choice in $1-2$ sentences.

A$.$ Generator

B$.$ Discriminator

c$.(10$ points$)$ MAD$-$GAN $[5]$ uses several generators to alleviate the mode

collapse problem. Given a fake data, the discriminator needs to recognize the

generator that produces it$.$ Why this helps to alleviate the mode collapse prob$-$

lem?

d$.(15$ points$)$ Wasserstein GAN $6,7$ is designed to train the generator by

minimizing the Wasserstein distance $($AKA earth mover's distance$)$ between the

real data distribution and generated data distribution. WGAN helps stable the

training of GAN and alleviate the mode collapse issue. Explain why Wasserstein

distance is better than KL$/$JS divergence when there is no overlap between

$2$ distributions? How was this notion used to develop the Wasserstein GAN

Discriminator $D$ and Generator $G$ losses compared to standard GAN.