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

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. 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. We demonstrate this architecture on sets of simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model. 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 is applicable to arbitrary lattice data, paving the way for new physical insights from machine learning studies of experimental and numerical data.