Fast, Accurate, and Scalable Fermionic Neural Networks via Translation Equivariance
Abstract
We demonstrate that designing a neural quantum state to be an exact eigenstate of the Hamiltonian's symmetries significantly improves both training speed and final variational energy. For the 2D electron gas, we design TorFormer, a neural network wavefunction which is an exact eigenstate of the total momentum. TorFormer describes both the Fermi liquid and Wigner crystal with no supervision and significantly outperforms Psiformer-based references up to large system sizes. For rs = 30.0 and $40.0$ at N=91, we compare TorFormer trained for 8K steps against the previous best NQS, which required 100K training steps. Our improvement to the total energy at rs = 40.0, excluding the trivial Madelung part, is 0.12%---enormous compared to the tiny differences separating phases. Relative to Slater-Jastrow-backflow diffusion Monte Carlo, TorFormer's energy decrease is roughly $9.8$ times that of the previous best NQS. Our work demonstrates that neural quantum states can both accurately and efficiently solve large-scale problems.
Related
- Exact Equivariance from Ordinary Neural Networks for Lattice Many-Body Dynamics
- Premonoidal Semantics and Scalable Diagrammatics of Fermionic Quantum Computing
- AES-Debye: an Accurate, Efficient, and Scalable Engine for Debye Scattering Calculations
- PINN-Phase: Physics-informed neural integration for accurate, generalizable and scalable multiphase-field evolution
- DNNsolver: Accurate and Efficient Deep Learning Modeling of Polarization-Sensitive Diffractive Neural Networks
BibTeX
@misc{dai2026fast,
title = {{Fast, Accurate, and Scalable Fermionic Neural Networks via Translation Equivariance}},
author = {David D. Dai and Yen-Ting Lin and Marin Soljačić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10186},
eprint = {2609.10186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10186},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Fast, Accurate, and Scalable Fermionic Neural Networks via Translation Equivariance
AU - David D. Dai
AU - Yen-Ting Lin
AU - Marin Soljačić
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10186
UR - https://arxiv.org/abs/2609.10186
AB - We demonstrate that designing a neural quantum state to be an exact eigenstate of the Hamiltonian's symmetries significantly improves both training speed and final variational energy. For the 2D electron gas, we design TorFormer, a neural network wavefunction which is an exact eigenstate of the total momentum. TorFormer describes both the Fermi liquid and Wigner crystal with no supervision and significantly outperforms Psiformer-based references up to large system sizes. For r_s = 30.0 and $40.0$ at N=91, we compare TorFormer trained for 8K steps against the previous best NQS, which required 100K training steps. Our improvement to the total energy at r_s = 40.0, excluding the trivial Madelung part, is 0.12%---enormous compared to the tiny differences separating phases. Relative to Slater-Jastrow-backflow diffusion Monte Carlo, TorFormer's energy decrease is roughly $9.8$ times that of the previous best NQS. Our work demonstrates that neural quantum states can both accurately and efficiently solve large-scale problems.
ER -