Six Pairs Before the Judge

A conditional GAN generates handwritten digits on demand. Its discriminator never sees an example on its own — it always receives a pair: the example together with the label it is supposed to go with. It outputs $D$, its estimate that the pair is a genuine one, meaning a real photograph shown with its own correct label.

The training targets follow from that. A pair gets target $1$ only if the image is real and the label matches it. Everything else gets target $0$ — a generated image, and also a real photograph shown with the wrong label.

The discriminator is a plain binary classifier, so each pair costs

$\ell = -\ln D \quad \text{when the target is } 1, \qquad \ell = -\ln(1 - D) \quad \text{when the target is } 0$

and the batch loss is the average of $\ell$ over the pairs in the batch.

What is the discriminator's average loss over this batch of 6 pairs?

Use natural logarithms and round the answer to 2 decimal places.