# Adaptive Neural Quantum States: A Recurrent Neural Network Perspective

arXiv: https://arxiv.org/abs/2507.18700 · HTML: https://mlsanity.com/paper/2507.18700/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 95 references that are in the map.
- First posted on arXiv 24 Jul 2025.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Net2Net: Accelerating Learning via Knowledge Transfer](https://mlsanity.com/paper/1511.05641/) (2015)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Model Complexity of Deep Learning: A Survey](https://mlsanity.com/paper/2103.05127/) (2021)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Minimal Gated Unit for Recurrent Neural Networks](https://mlsanity.com/paper/1603.09420/) (2016)
- [Scaling Smart: Accelerating Large Language Model Pre-training with Small Model Initialization](https://mlsanity.com/paper/2409.12903/) (2024)
- [Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models](https://mlsanity.com/paper/2101.07243/) (2021)
- [Mutual Information Scaling and Expressive Power of Sequence Models](https://mlsanity.com/paper/1905.04271/) (2019)
- [From Tensor Network Quantum States to Tensorial Recurrent Neural Networks](https://mlsanity.com/paper/2206.12363/) (2022)
- [Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice](https://mlsanity.com/paper/2405.20384/) (2024)
- [Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz](https://mlsanity.com/paper/2011.08657/) (2020)
- [Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy](https://mlsanity.com/paper/2207.14314/) (2022)
- [Investigating Topological Order using Recurrent Neural Networks](https://mlsanity.com/paper/2303.11207/) (2023)
- [When can classical neural networks represent quantum states?](https://mlsanity.com/paper/2410.23152/) (2024)
- [Functional Neural Wavefunction Optimization](https://mlsanity.com/paper/2507.10835/) (2025)
- [Turing Computation with Recurrent Artificial Neural Networks](https://mlsanity.com/paper/1511.01427/) (2015)
- [Explorative Curriculum Learning for Strongly Correlated Electron Systems](https://mlsanity.com/paper/2505.00233/) (2025)

## Built on by (most cited first, 1 of 1)

- [Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States](https://mlsanity.com/paper/2604.08661/) (2026)

## Abstract (arXiv)

Neural-network quantum states (NQS) are powerful neural-network ans"atzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be systematically improvable by increasing the number of parameters. Here we demonstrate an Adaptive scheme to optimize NQSs, through the example of recurrent neural networks (RNN), using a fraction of the computation cost while reducing training fluctuations and improving the quality of variational calculations targeting ground states of prototypical models in one- and two-spatial dimensions. This Adaptive technique reduces the computational cost through training small RNNs and reusing them to initialize larger RNNs. This work opens up the possibility for optimizing graphical processing unit (GPU) resources deployed in large-scale NQS simulations.