Sampling two-dimensional spin systems with transformers
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915970670395392 |
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| author | Białas, Piotr Korcyl, Piotr Stebel, Tomasz Stefański, Adam Zapolski, Dawid |
| author_facet | Białas, Piotr Korcyl, Piotr Stebel, Tomasz Stefański, Adam Zapolski, Dawid |
| contents | Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be computationally inefficient. In this work, we propose a novel approach to transformer-based neural samplers in which we generate not a single spin per step but groups of spins. As an additional improvement, we construct a model of approximated probabilities, further improving the efficiency of the algorithm. Despite our approach being computationally heavier than dense networks or CNN-based approaches, we were able to sample larger systems of up to $180 \times 180$ spins in case of the Ising model. The Effective Sample Size of our sampler is $\sim 20$ times larger than that of the previous state-of-the-art neural sampler when trained for the $128 \times 128$ Ising model at critical temperature. Finally, we also test our algorithm on the 2D Edwards-Anderson model, where we train $64\times 64$ spin systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sampling two-dimensional spin systems with transformers Białas, Piotr Korcyl, Piotr Stebel, Tomasz Stefański, Adam Zapolski, Dawid Disordered Systems and Neural Networks Statistical Mechanics Machine Learning High Energy Physics - Lattice Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be computationally inefficient. In this work, we propose a novel approach to transformer-based neural samplers in which we generate not a single spin per step but groups of spins. As an additional improvement, we construct a model of approximated probabilities, further improving the efficiency of the algorithm. Despite our approach being computationally heavier than dense networks or CNN-based approaches, we were able to sample larger systems of up to $180 \times 180$ spins in case of the Ising model. The Effective Sample Size of our sampler is $\sim 20$ times larger than that of the previous state-of-the-art neural sampler when trained for the $128 \times 128$ Ising model at critical temperature. Finally, we also test our algorithm on the 2D Edwards-Anderson model, where we train $64\times 64$ spin systems. |
| title | Sampling two-dimensional spin systems with transformers |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Machine Learning High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2604.27738 |