  The study of multidimensional discriminator (critic) output for Generative
Adversarial Networks has been underexplored in the literature. In this paper,
we generalize the Wasserstein GAN framework to take advantage of
multidimensional critic output and explore its properties. We also introduce a
square-root velocity transformation (SRVT) block which favors training in the
multidimensional setting. Proofs of properties are based on our proposed
maximal p-centrality discrepancy, which is bounded above by p-Wasserstein
distance and fits the Wasserstein GAN framework with multidimensional critic
output n. Especially when n = 1 and p = 1, the proposed discrepancy equals
1-Wasserstein distance. Theoretical analysis and empirical evidence show that
high-dimensional critic output has its advantage on distinguishing real and
fake distributions, and benefits faster convergence and diversity of results.
