Using Physics to Explain and Interpret Convolutional Neural Network Solutions of Quantum Spin Problems

Convolutional neural networks (CNNs) have been employed alongside Variational Monte Carlo methods for finding the ground state of quantum spin Hamiltonians. In order to do so, however, a CNN with linearly many variational parameters has to successfully approximate a wavefunction on an exponentially large Hilbert space. We examine the details of how a CNN optimizes learning for spin systems, and the role played by physical symmetries during training. We then also demonstrate a method for using the symmetries of the underlying spin system to propose an improved training algorithm. Finally, we present a mapping between the wavefunctions generated by a one-layer CNN, a Correlator Product State (CPS), and the maximum entropy (MaxEnt) principle, thus providing physical insight as to why the CNN is able to solve this problem efficiently.