Looking Under the Hood: How Convolutional Neural Networks Successfully Approximate Quantum Spin Hamiltonians

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. In our work, we look under the black box to understand how the 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, to further investigate how the CNN replicates the essential physics of the target Hamiltonian, we show connections between a one-layer CNN wavefunction ansatz to ansatz from maximum entropy (MaxEnt) distribution as well as to entangled plaquette ansatzes, thus connecting the neural network to concepts from information theory and previous physics VQMC methods.