Essentially No Energy Barrier Between Independent Fermionic Neural Quantum State Minima

TL;DR

This paper reveals that neural quantum states have a smooth loss landscape with connected minima, challenging previous beliefs, and introduces a new method to construct low-energy paths between these minima.

Contribution

The authors develop GeoNEB, a novel path optimizer, and demonstrate that independent NQS minima are connected by paths with negligible energy barriers, indicating a more benign loss landscape.

Findings

Independent NQS minima are connected by paths with minimal energy barriers.

The developed GeoNEB method effectively constructs low-energy paths.

The NQS loss landscape is more similar to conventional deep learning than previously thought.

Abstract

Neural quantum states (NQS) have proven highly effective in representing quantum many-body wavefunctions, but their loss landscape remains poorly understood and debated. Here, we demonstrate that the NQS loss landscape is more benign and similar to conventional deep learning than previously thought, exhibiting mode connectivity: independently trained NQS are connected by paths in parameter space with essentially no energy barrier. To construct these paths, we develop GeoNEB, a path optimizer integrating efficient stochastic reconfiguration with the nudged elastic band method for constructing minimum energy paths. For the strongly interacting six-electron quantum dot modeled by a $1.6$M-parameter Psiformer, we find two independent minima with expected energy barrier $\sim10^{-5}$ times smaller than the system's overall energy scale and $\sim10^{-3}$ times smaller than the linear path's barrier. The path respects physical symmetry in addition to achieving low energy, with the angular momentum remaining well quantized throughout. Our work is the first to construct optimized paths between independently trained NQS, and it suggests that the NQS loss landscape may not be as pathological as once feared.