  Machine learning models are a powerful theoretical tool for analyzing data
from quantum simulators, in which results of experiments are sets of snapshots
of many-body states. Recently, they have been successfully applied to
distinguish between snapshots that can not be identified using traditional one
and two point correlation functions. Thus far, the complexity of these models
has inhibited new physical insights from this approach. Here, using a novel set
of nonlinearities we develop a network architecture that discovers features in
the data which are directly interpretable in terms of physical observables. In
particular, our network can be understood as uncovering high-order correlators
which significantly differ between the data studied. We demonstrate this new
architecture on sets of simulated snapshots produced by two candidate theories
approximating the doped Fermi-Hubbard model, which is realized in state-of-the
art quantum gas microscopy experiments. From the trained networks, we uncover
that the key distinguishing features are fourth-order spin-charge correlators,
providing a means to compare experimental data to theoretical predictions. Our
approach lends itself well to the construction of simple, end-to-end
interpretable architectures and is applicable to arbitrary lattice data, thus
paving the way for new physical insights from machine learning studies of
experimental as well as numerical data.
