Title: Identifying Product Order with Restricted Boltzmann Machines,
Abstract: Unsupervised machine learning via a restricted Boltzmann machine is an useful
tool in distinguishing an ordered phase from a disordered phase. Here we study
its application on the two-dimensional Ashkin-Teller model, which features a
partially ordered product phase. We train the neural network with spin
configuration data generated by Monte Carlo simulations and show that distinct
features of the product phase can be learned from non-ergodic samples resulting
from symmetry breaking. Careful analysis of the weight matrices inspires us to
define a nontrivial machine-learning motivated quantity of the product form,
which resembles the conventional product order parameter.