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?

  • $\begingroup$ Hi and welcome to AI! $\log 2$ is not the negative of $-\log 4$. Can you clarify this? $\endgroup$ – nbro Mar 27 at 17:08
  • 1
    $\begingroup$ 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) $\endgroup$ – Oisin Peppard Mar 27 at 17:19

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