WGAN-GP Loss
WGAN-GP Loss
**Wasserstein Gradient Penalty Loss**, or **WGAN-GP Loss**, is a loss used for generative adversarial networks that augments the Wasserstein loss with a gradient norm penalty for random samples $\mathbf{\hat{x}} \sim \mathbb{P}\_{\hat{\mathbf{x}}}$ to achieve Lipschitz continuity:

$$ L = \mathbb{E}\_{\mathbf{\hat{x}} \sim \mathbb{P}\_{g}}\left[D\left(\tilde{\mathbf{x}}\right)\right] - \mathbb{E}\_{\mathbf{x} \sim \mathbb{P}\_{r}}\left[D\left(\mathbf{x}\right)\right] + \lambda\mathbb{E}\_{\mathbf{\hat{x}} \sim \mathbb{P}\_{\hat{\mathbf{x}}}}\left[\left(||\nabla\_{\tilde{\mathbf{x}}}D\left(\mathbf{\tilde{x}}\right)||\_{2}-1\right)^{2}\right]$$

It was introduced as part of the [WGAN-GP](https://paperswithcode.com/method/wgan-gp) overall model.
Improved Training of Wasserstein GANs
https://paperswithcode.com/paper/improved-training-of-wasserstein-gans
Improved Training of Wasserstein GANs