Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization
Abstract
Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failure in weak-gradient regimes, limiting their practical use in quantum many-body physics and ab initio quantum chemistry. Here we derive an unbiased direct gradient estimator and introduce the adaptive minimum-variance phase (AMVP) estimator for neural-network variational optimization. By improving the signal-to-noise ratio of weak gradients, these methods enable reliable scientific calculations where training previously failed, while substantially reducing computational cost. The framework enables compact networks to outperform larger and fine-tuned default standard-estimator models with over an order of magnitude less GPU time on correlated flux models, and ultimately exceed the density matrix renormalization group (DMRG) accuracy. It further achieves chemical accuracy in N2 bond breaking and, for the first time, in heavy-element I2 with explicit spin-orbit coupling. These results demonstrate that gradient-estimator design expands the capabilities of neural-network variational methods for accurate scientific computing.
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BibTeX
@misc{xue2026gradientestimator,
title = {{Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization}},
author = {Yi-Ran Xue and Rui Wang and Baigeng Wang and Chenan Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22342},
eprint = {2609.22342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22342},
}
RIS
TY - UNPB
TI - Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization
AU - Yi-Ran Xue
AU - Rui Wang
AU - Baigeng Wang
AU - Chenan Wei
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.22342
UR - https://arxiv.org/abs/2609.22342
AB - Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failure in weak-gradient regimes, limiting their practical use in quantum many-body physics and ab initio quantum chemistry. Here we derive an unbiased direct gradient estimator and introduce the adaptive minimum-variance phase (AMVP) estimator for neural-network variational optimization. By improving the signal-to-noise ratio of weak gradients, these methods enable reliable scientific calculations where training previously failed, while substantially reducing computational cost. The framework enables compact networks to outperform larger and fine-tuned default standard-estimator models with over an order of magnitude less GPU time on correlated flux models, and ultimately exceed the density matrix renormalization group (DMRG) accuracy. It further achieves chemical accuracy in N_2 bond breaking and, for the first time, in heavy-element I_2 with explicit spin-orbit coupling. These results demonstrate that gradient-estimator design expands the capabilities of neural-network variational methods for accurate scientific computing.
ER -