Reference Figure 1.

You know that your GAN is trained when D(G(z)) is close to 1

Question

Reference Figure 1.

You know that your GAN is trained when D(G(z)) is close to 1

BlackTom AI · Accepted Answer

The statement to evaluate is: 'You know that your GAN is trained when D(G(z)) is close to 1.'
Option 1: True. This would imply the discriminator classifies generated samples as real with high confidence. However, in the standard GAN training dynamics, when the generator is well trained and the game reaches equilibrium, the discriminator cannot reliably distinguish real from fake, and D(G(z)) tends toward 0.5, not 1. Therefore, this option misrepresents the training signal.
Option 2: False. In a trained GAN under the original minimax formulation, the generator aims to minimize log(1 - D(G(z))) while the discriminator tries to maximize log(D(x)) + log(1 - D(G(z))). At convergence, the discriminator is fooled equally by real and generated data, leading to D(G(z)) ≈ 0.5 for generated samples. Consequently, claiming D(G(z)) close to 1 indicates the discriminator still strongly believes generated data are real, which would imply imperfect or unstable training rather than a proper trained state.
Option 3: If D(G(z)) were close to 0, that would mean the discriminator reliably identifies generated data as fake, which is also not a sign of a trained generator. Persistent D(G(z)) near 0.5 is a hallmark of balance, not extreme certainty in either direction.
Option 4: In practice, depending on the exact GAN variant (e.g., non-saturating loss, Wasserstein GAN, etc.), the interpretation of D(G(z)) can differ, but the classical criterion for a well-trained GAN under the original formulation is not D(G(z)) ≈ 1. It is approximately 0.5 for generated samples, reflecting a generator that fools the discriminator about half the time.

CS-7643-O01, OAN, OSZ Quiz #5: Module 4

Reference Figure 1. You know that your GAN is trained when D(G(z)) is close to 1

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