Loss Functions

GAN Hinge Loss

Introduced by Lim et al. in Geometric GAN

The GAN Hinge Loss is a hinge loss based loss function for generative adversarial networks:

$$ L_{D} = -\mathbb{E}_{\left(x, y\right)\sim{p}_{data}}\left[\min\left(0, -1 + D\left(x, y\right)\right)\right] -\mathbb{E}_{z\sim{p_{z}}, y\sim{p_{data}}}\left[\min\left(0, -1 - D\left(G\left(z\right), y\right)\right)\right] $$

$$ L_{G} = -\mathbb{E}_{z\sim{p_{z}}, y\sim{p_{data}}}D\left(G\left(z\right), y\right) $$

Source: Geometric GAN

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