Lecture: Loss-Sensitive GAN on Lipschitz Densities


  • GAN is unregularized model. (cannot match prior)
  • requires infinity capacity

JSD problem

  • unable to generalize
  • vanishing gradient (a perfect discriminator, Arjovsky et al. 2017)

=> regularized GAN


Bounded -> derivative is less than kappa -> lipschitz densities

under some integral

non-vanish gradient

non-vanishing gradient proval

non-parametric analysis (using LP to prove, despite the mode flation)


GAN not ~

model complexity

  • bouned domain
  • model size

bounded domain (value is bounded, not infty)

模型多项式复杂度 -> 有泛化性 指数复杂度 -> 无泛化性

conditional LS-GAN

focus on classification problem: $L: X\times Y \to \mathbb{R}$, Y is label