  Generative adversarial networks (GANs) are an exciting alternative to
algorithms for solving density estimation problems---using data to assess how
likely samples are to be drawn from the same distribution. Instead of
explicitly computing these probabilities, GANs learn a generator that can match
the given probabilistic source. This paper looks particularly at this matching
capability in the context of problems with one-dimensional outputs. We identify
a class of function decompositions with properties that make them well suited
to the critic role in a leading approach to GANs known as Wasserstein GANs. We
show that Taylor and Fourier series decompositions belong to our class, provide
examples of these critics outperforming standard GAN approaches, and suggest
how they can be scaled to higher dimensional problems in the future.
