핵심 개념
Generative adversarial networks (GANs) can be optimized to make the generator distribution close to the target distribution by satisfying metrizable conditions on the discriminator, including direction optimality, separability, and injectivity.
초록
The paper addresses the question of whether GAN optimization actually makes the generator distribution close to the target distribution. It derives metrizable conditions, sufficient conditions for the discriminator to serve as the distance between the distributions, by connecting the GAN formulation with the concept of sliced optimal transport.
The key insights are:
The authors introduce the Functional Mean Divergence (FM) and Functional Mean Divergence* (FM*) to analyze the metrizability of the discriminator.
They show that direction optimality, separability, and injectivity of the discriminator's feature mapping are sufficient conditions for the discriminator to be a metrizable distance.
Based on these theoretical results, the authors propose the Slicing Adversarial Network (SAN), which modifies the GAN training scheme to enforce direction optimality on the discriminator.
Experiments on synthetic and image datasets support the theoretical results and demonstrate the effectiveness of SAN compared to standard GANs.
SAN can be easily applied to existing GANs by simple modifications to the discriminator architecture and training objective.
통계
The target probability distribution is modeled as a mixture of 8 isotropic Gaussians in a 2D space.
The generator uses a 10-dimensional latent space.