Understanding and eliminating spurious modes in variational Monte Carlo using collective variables

TL;DR

This paper investigates the problem of spurious modes in neural network-based variational Monte Carlo methods for quantum systems, and proposes a collective-variable-based penalization to improve training robustness and accuracy.

Contribution

It introduces a novel penalization technique using collective variables to prevent spurious modes in neural VMC, enhancing reliability and generalizability.

Findings

Spurious modes cause unreliable energy estimates in neural VMC.

Collective-variable penalization effectively suppresses spurious modes.

The method improves energy estimate accuracy and is computationally inexpensive.

Abstract

The use of neural network parametrizations to represent the ground state in variational Monte Carlo (VMC) calculations has generated intense interest in recent years. However, as we demonstrate in the context of the periodic Heisenberg spin chain, this approach can produce unreliable wave function approximations. One of the most obvious signs of failure is the occurrence of random, persistent spikes in the energy estimate during training. These energy spikes are caused by regions of configuration space that are over-represented by the wave function density, which are called ``spurious modes'' in the machine learning literature. After exploring these spurious modes in detail, we demonstrate that a collective-variable-based penalization yields a substantially more robust training procedure, preventing the formation of spurious modes and improving the accuracy of energy estimates. Because the penalization scheme is cheap to implement and is not specific to the particular model studied here, it can be extended to other applications of VMC where a reasonable choice of collective variable is available.