The Judge Grows Certain

A GAN is training on photographs of faces. Its discriminator ends, as binary classifiers do, in a single sigmoid unit:

$D = \sigma(z) = \frac{1}{1 + e^{-z}}, \qquad \sigma'(z) = \sigma(z)\bigl(1 - \sigma(z)\bigr)$

where $z$ is the raw score the last layer produces and $D$ is the probability the discriminator assigns to "this one is real".

The generator never looks at a real face. Everything it learns arrives as a gradient that leaves the discriminator's verdict and travels backwards into the generator's weights — and on the way out it must pass through that final sigmoid, so the signal from each sample is multiplied by $\sigma'(z)$ evaluated at that sample.

The team records the discriminator's average verdict on a batch of generated faces at two points in the run:

They are delighted with the second row: the judge now catches almost every fake.

Using $\sigma'$ at each batch's mean verdict as a stand-in for the whole batch, how has the size of the signal reaching the generator changed between the two checkpoints?