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

Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data