Do GANs use class labels in the training process?
The author suspected GANs doesn't require labels. This is correct. The discriminator is trained to classify real and fake images. Since we know which images are real and which are generated by the generator, we do not need labels to train the discriminator. The generator is trained to fool the discriminator, which also doesn't require labels.
This is one of the most attractive benefits of GANs [1]. Usually, we refer to methods that do not require labels as unsupervised learning. That said, if we had labels, maybe we could train a GAN that uses the labels to improve performance. This idea underlies the follow-up work by [2] who introduced the conditional GAN.
If this is the case, then how do researchers propose to use the discriminator network for classification tasks?
There seems to be a misunderstanding here. The purpose of the discriminator is NOT to act as a classifier on real data. The purpose of the discriminator is to "tell the generator how to improve its fakes". This is done by using the discriminator as a loss function, which we can backpropagate gradients through if it is a neural network. After training, we usually discard the discriminator.
The generator network would also be difficult to use, seeing as we don't know what setting of the input vector 'Z' will result in the required generated image.
It seems the underlying reason for posting the question lies here. The input vector 'Z' is chosen such that it follows some distribution, typically a normal distribution. But then what happens if we take 'Z', a random vector with normally distributed entries, and computes 'G(Z)'? We get a new vector which follows a very complicated distribution that depends on G. The entire idea of GANs is to change G such that this new complicated distribution is close to the distribution of our data. This idea is formalized with f-Divergences in [3].
[1] https://arxiv.org/abs/1406.2661
[2] https://arxiv.org/abs/1411.1784
[3] https://arxiv.org/abs/1606.00709