# Why does GAN loss converge to log(2) and not -log(2)?

In Goodfellow's paper, he says:

Hence, by inspecting Eq. 4 at $$D^*_G (\mathbf{x}) = \frac{1}{2}$$, we find $$C(G) = \log \frac{1}{2}+ \log \frac{1}{2} = − \log 4$$. To see that this is the best possible value of $$C(G)$$

i.e. $$D$$ and $$G$$ loss should converge to $$\log \frac{1}{2}$$. This makes perfect sense. When I train a GAN in PyTorch with BCEloss, the loss for $$D$$ and $$G$$ converge to $$\log(2)$$, the negative of what Goodfellow states and what I'd expect.

What am I missing?

• Hi and welcome to AI! $\log 2$ is not the negative of $-\log 4$. Can you clarify this? – nbro Mar 27 at 17:08
• Sorry, individual loss for D and G are log(½) = -log(2). When added together the total loss is -2log(2) = -log(4), whereas I am getting log(2) + log(2) = log(4) – Oisin Peppard Mar 27 at 17:19