Abstract: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.
| Comments: | 15 pages, 7 figures |
| Subjects: | Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat) |
| Cite as: | arXiv:2604.27738 [cond-mat.dis-nn] |
| (or arXiv:2604.27738v1 [cond-mat.dis-nn] for this version) | |
| https://doi.org/10.48550/arXiv.2604.27738 arXiv-issued DOI via DataCite (pending registration) |
From: Dawid Zapolski [view email]
[v1]
Thu, 30 Apr 2026 11:29:28 UTC (908 KB)
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