  Motivated by recent progress in applying techniques from the field of
artificial neural networks (ANNs) to quantum many-body physics, we investigate
as to what extent the flexibility of ANNs can be used to efficiently study
systems that host chiral topological phases such as fractional quantum Hall
(FQH) phases. With benchmark examples, we demonstrate that training ANNs of
restricted Boltzmann machine type in the framework of variational Monte Carlo
can numerically solve FQH problems to good approximation. Furthermore, we show
by explicit construction how n-body correlations can be kept at an exact level
with ANN wave-functions exhibiting polynomial scaling with power n in system
size. Using this construction, we analytically represent the paradigmatic
Laughlin wave-function as an ANN state.
