for the optimal function that the discriminator should learn this function turns out to be the ratio between P data of X and P data of X plus P model of X you can do a little bit of algebra on that to rearrange it and you get P data of x over P model of X so we're learning a ratio between the density that the real data is drawn from and the density of the model currently represents estimating that ratio allows us to compute a lot of different divergences like the Jenson Shannon divergence and the KL divergence between the data and