Sparse autoregressive neural networks for classical spin systems

IF 6.3 2区 物理与天体物理 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Machine Learning Science and Technology Pub Date : 2024-06-20 DOI:10.1088/2632-2153/ad5783
Indaco Biazzo, Dian Wu and Giuseppe Carleo
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Abstract

Efficient sampling and approximation of Boltzmann distributions involving large sets of binary variables, or spins, are pivotal in diverse scientific fields even beyond physics. Recent advances in generative neural networks have significantly impacted this domain. However, these neural networks are often treated as black boxes, with architectures primarily influenced by data-driven problems in computational science. Addressing this gap, we introduce a novel autoregressive neural network architecture named TwoBo, specifically designed for sparse two-body interacting spin systems. We directly incorporate the Boltzmann distribution into its architecture and parameters, resulting in enhanced convergence speed, superior free energy accuracy, and reduced trainable parameters. We perform numerical experiments on disordered, frustrated systems with more than 1000 spins on grids and random graphs, and demonstrate its advantages compared to previous autoregressive and recurrent architectures. Our findings validate a physically informed approach and suggest potential extensions to multivalued variables and many-body interaction systems, paving the way for broader applications in scientific research.
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经典自旋系统的稀疏自回归神经网络
对涉及大量二元变量集或自旋的玻尔兹曼分布进行高效采样和逼近,在各种科学领域甚至物理学之外都至关重要。生成神经网络的最新进展对这一领域产生了重大影响。然而,这些神经网络通常被视为黑盒子,其架构主要受计算科学中数据驱动问题的影响。为了弥补这一不足,我们引入了一种名为 TwoBo 的新型自回归神经网络架构,专门用于稀疏的双体相互作用自旋系统。我们直接将玻尔兹曼分布纳入其架构和参数中,从而提高了收敛速度、自由能精度和可训练参数。我们对网格和随机图上超过 1000 个自旋的无序、受挫系统进行了数值实验,证明了它与之前的自回归和递归架构相比所具有的优势。我们的研究结果验证了这种物理方法,并建议将其扩展到多值变量和多体相互作用系统,从而为其在科学研究中的广泛应用铺平道路。
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来源期刊
Machine Learning Science and Technology
Machine Learning Science and Technology Computer Science-Artificial Intelligence
CiteScore
9.10
自引率
4.40%
发文量
86
审稿时长
5 weeks
期刊介绍: Machine Learning Science and Technology is a multidisciplinary open access journal that bridges the application of machine learning across the sciences with advances in machine learning methods and theory as motivated by physical insights. Specifically, articles must fall into one of the following categories: advance the state of machine learning-driven applications in the sciences or make conceptual, methodological or theoretical advances in machine learning with applications to, inspiration from, or motivated by scientific problems.
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