1Cademy - Propositions/Theorems of GANs

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Generative adversarial network(GAN)

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Propositions/Theorems of GAN's

Proposition 1: Optimal Discriminator $D$ for given generator $G$ is $D_g^*=\frac {p_{data}(\bold x)} {p_{data}(\bold x) + p_g(\bold x)}$ .
Theorem 1: The global minimum of virtual training criterion $C(G)$ is found if and only if $p_g=p_{data}$ , having value $-\log 4$ .
Proposition 2: $p_g$ converges to $p_{data}$ if:

$G$ and $D$ have enough capacity,
At each step of algorithm 1 the discriminator is allowed to reach its optimum given $G$ ,
$p_g$ is updated to improve the criterion $\mathbb{E}_{\bold x ~ p_{data}}[\log D_G^*(\bold x)] + \mathbb{E}_{\bold x ~ p_g}[\log(1-D_G^*(\bold x)]$ .

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Updated 2021-08-12

Contributors are:

Michael Baz

Who are from:

University of Connecticut

University of Connecticut

References

Generative Adversarial Networks

Tags

Data Science

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