  Different neural network architectures can be unsupervisedly or supervisedly
trained to represent quantum states. We explore and compare different
strategies for the supervised training of feed forward neural network quantum
states. We empirically and comparatively evaluate the performance of feed
forward neural network quantum states in different phases of matter for
variants of the architecture, for different hyper-parameters, and for two
different loss functions, to which we refer as \emph{mean-squared error} and
\emph{overlap}, respectively. We consider the next-nearest neighbor Ising model
for the diversity of its phases and focus on its paramagnetic, ferromagnetic,
and pair-antiferromagnetic phases. We observe that the overlap loss function
allows better training of the model across all phases, provided a rescaling of
the neural network.
