<p>In Goodfellow's paper, he says:</p>

<blockquote>
  <p>Hence, by inspecting Eq. 4 at <span class="math-container">$D^*_G (\mathbf{x}) = \frac{1}{2}$</span>, we find <span class="math-container">$C(G) = \log \frac{1}{2}+ \log \frac{1}{2} = − \log 4$</span>. To see that this is the best possible value of <span class="math-container">$C(G)$</span></p>
</blockquote>

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

<p>What am I missing?</p>

CC BY-SA 4.0
2020-03-27T17:08:11.597Z
Hi and welcome to AI! $\log 2$ is not the negative of $-\log 4$. Can you clarify this?
nbro
CC BY-SA 4.0
2020-03-27T17:19:42.787Z
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
<objective-functions><generative-adversarial-networks><papers><pytorch>
Why does GAN loss converge to log(2) and not -log(2)?
Oisin Peppard
# Why does GAN loss converge to log(2) and not -log(2)?

(Asked by: username_0 on 2020-03-27)

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?

**Tags:** objective-functions, generative-adversarial-networks, papers, pytorch

> **Comments:**
> **username_1**: Hi and welcome to AI! $\log 2$ is not the negative of $-\log 4$. Can you clarify this?  
> **username_0**: 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)  

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## 0 answers

