# Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy

arXiv: https://arxiv.org/abs/2207.14314 · HTML: https://mlsanity.com/paper/2207.14314/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Minimal Gated Unit for Recurrent Neural Networks](https://mlsanity.com/paper/1603.09420/) (2016)
- [Mutual Information Scaling and Expressive Power of Sequence Models](https://mlsanity.com/paper/1905.04271/) (2019)
- [Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz](https://mlsanity.com/paper/2011.08657/) (2020)

## Built on by (most cited first, 6 of 6)

- [Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice](https://mlsanity.com/paper/2405.20384/) (2024)
- [Investigating Topological Order using Recurrent Neural Networks](https://mlsanity.com/paper/2303.11207/) (2023)
- [Hyperbolic recurrent neural network as the first type of non-Euclidean neural quantum state ansatz](https://mlsanity.com/paper/2505.22083/) (2025)
- [Adaptive Neural Quantum States: A Recurrent Neural Network Perspective](https://mlsanity.com/paper/2507.18700/) (2025)
- [New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures](https://mlsanity.com/paper/2604.24337/) (2026)
- [Two-dimensional Hyperbolic RNN Neural Quantum State](https://mlsanity.com/paper/2606.25600/) (2026)

## Abstract (arXiv)

Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these architectures were shown to be powerful ansatze to approximate the ground state of quantum systems. Here, we build over the results of [Phys. Rev. Research 2, 023358 (2020)] and construct a more powerful RNN wave function ansatz in two dimensions. We use symmetry and annealing to obtain accurate estimates of ground state energies of the two-dimensional (2D) Heisenberg model, on the square lattice and on the triangular lattice. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to 14 × 14 on the triangular lattice.