We consider the problem of optimizing the discriminator in generative
adversarial networks (GANs) subject to higher-order gradient regularization. We
show analytically, via the least-squares (LSGAN) and Wasserstein (WGAN) GAN
variants, that the discriminator optimization problem is one of interpolation
in $n$-dimensions. The optimal discriminator, derived using variational
Calculus, turns out to be the solution to a partial differential equation
involving the iterated Laplacian or the polyharmonic operator. The solution is
implementable in closed-form via polyharmonic radial basis function (RBF)
interpolation. In view of the polyharmonic connection, we refer to the
corresponding GANs as Poly-LSGAN and Poly-WGAN. Through experimental validation
on multivariate Gaussians, we show that implementing the optimal RBF
discriminator in closed-form, with penalty orders $m \approx\lceil \frac{n}{2}
\rceil $, results in superior performance, compared to training GAN with
arbitrarily chosen discriminator architectures. We employ the Poly-WGAN
discriminator to model the latent space distribution of the data with
encoder-decoder-based GAN flavors such as Wasserstein autoencoders.

该论文提出了一种使用多项式调和径向基函数来优化生成对抗网络中鉴别器的方法，进而对数据的潜在空间分布进行建模，并证明在实验验证中，这种方法显着优于传统的鉴别器架构。