Title: Witnessing Adversarial Training in Reproducing Kernel Hilbert Spaces,
Abstract: Modern implicit generative models such as generative adversarial networks
(GANs) are generally known to suffer from instability and lack of
interpretability as it is difficult to diagnose what aspects of the target
distribution are missed by the generative model. In this work, we propose a
theoretically grounded solution to these issues by augmenting the GAN's loss
function with a kernel-based regularization term that magnifies local
discrepancy between the distributions of generated and real samples. The
proposed method relies on so-called witness points in the data space which are
jointly trained with the generator and provide an interpretable indication of
where the two distributions locally differ during the training procedure. In
addition, the proposed algorithm is scaled to higher dimensions by learning the
witness locations in a latent space of an autoencoder. We theoretically
investigate the dynamics of the training procedure, prove that a desirable
equilibrium point exists, and the dynamical system is locally stable around
this equilibrium. Finally, we demonstrate different aspects of the proposed
algorithm by numerical simulations of analytical solutions and empirical
results for low and high-dimensional datasets.