  Generative-adversarial networks (GANs) have been used to produce data closely
resembling example data in a compressed, latent space that is close to
sufficient for reconstruction in the original vector space. The Wasserstein
metric has been used as an alternative to binary cross-entropy, producing more
numerically stable GANs with greater mode covering behavior. Here, a
generalization of the Wasserstein distance, using higher-order moments than the
mean, is derived. Training a GAN with this higher-order Wasserstein metric is
demonstrated to exhibit superior performance, even when adjusted for slightly
higher computational cost. This is illustrated generating synthetic antibody
sequences.
