A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910551201808384 |
|---|---|
| author | Rende, Riccardo Viteritti, Luciano Loris Bardone, Lorenzo Becca, Federico Goldt, Sebastian |
| author_facet | Rende, Riccardo Viteritti, Luciano Loris Bardone, Lorenzo Becca, Federico Goldt, Sebastian |
| contents | Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are challenging to optimize using traditional methods, as gradient descent. Stochastic Reconfiguration (SR) has been effective with a limited number of parameters, but becomes impractical beyond a few thousand parameters. Here, we leverage a simple linear algebra identity to show that SR can be employed even in the deep learning scenario. We demonstrate the effectiveness of our method by optimizing a Deep Transformer architecture with $3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square lattice, a challenging benchmark in highly-frustrated magnetism. This work marks a significant step forward in the scalability and efficiency of SR for Neural-Network Quantum States, making them a promising method to investigate unknown quantum phases of matter, where other methods struggle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05715 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States Rende, Riccardo Viteritti, Luciano Loris Bardone, Lorenzo Becca, Federico Goldt, Sebastian Strongly Correlated Electrons Disordered Systems and Neural Networks Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are challenging to optimize using traditional methods, as gradient descent. Stochastic Reconfiguration (SR) has been effective with a limited number of parameters, but becomes impractical beyond a few thousand parameters. Here, we leverage a simple linear algebra identity to show that SR can be employed even in the deep learning scenario. We demonstrate the effectiveness of our method by optimizing a Deep Transformer architecture with $3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square lattice, a challenging benchmark in highly-frustrated magnetism. This work marks a significant step forward in the scalability and efficiency of SR for Neural-Network Quantum States, making them a promising method to investigate unknown quantum phases of matter, where other methods struggle. |
| title | A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2310.05715 |