discriminator

The discriminator is the "judge" of a GAN: shown an image, it decides whether it is a real training image or a fake from the generator. It is an ordinary image classifier, but its true purpose is not classification for its own sake — it is to manufacture a learning signal for the generator. Every time it detects a fake, the gradient of "what made this look fake" is passed back to the generator as instructions for improvement. A good discriminator is what makes a good generator possible.

Precisely, the discriminator is a function D mapping an image x to a value in [0,1], the estimated probability that x is real; it is trained as a binary classifier to maximize E over real x of log D(x), plus E over z of log(1 − D(G(z))) — that is, push D(real) toward 1 and D(fake) toward 0. Architecturally (per DCGAN) it is a strided-convolution CNN with LeakyReLU and normalization, downsampling to a single logit. For a fixed generator the optimal discriminator is D*(x) = p_data(x) / (p_data(x) + p_g(x)) — it reports the relative density of real versus generated at each point, which is precisely the information the generator needs to move p_g toward p_data.

The two networks must stay roughly balanced. If the discriminator becomes too strong it pushes D(fake) toward 0, where the saturating generator loss has no gradient and learning stalls; if too weak it gives uninformative signals. Techniques to keep it well-behaved include the non-saturating generator loss, one-sided label smoothing, spectral normalization (bounding the discriminator's Lipschitz constant), and gradient penalties. In Wasserstein GAN the discriminator is replaced by a critic that outputs an unbounded real-valued score (not a probability), estimating the Earth-Mover distance, and is constrained to be 1-Lipschitz.