Generative Autoregressive Neural Networks (ARNNs) have recently demonstrated exceptional results in image and language generation tasks, contributing to the growing popularity of generative models in both scientific and commercial applications. This work presents an exact mapping of the Boltzmann distribution of binary pairwise interacting systems into autoregressive form. The resulting ARNN architecture has weights and biases of its first layer corresponding to the Hamiltonian's couplings and external fields, featuring widely used structures such as the residual connections and a recurrent architecture with clear physical meanings. Moreover, its architecture's explicit formulation enables the use of statistical physics techniques to derive new ARNNs for specific systems. As examples, new effective ARNN architectures are derived from two well-known mean-field systems, the Curie-Weiss and Sherrington-Kirkpatrick models, showing superior performance in approximating the Boltzmann distributions of the corresponding physics model compared to other commonly used architectures. The connection established between the physics of the system and the neural network architecture provides a means to derive new architectures for different interacting systems and interpret existing ones from a physical perspective.
Entanglement and optimization within autoregressive neural quantum states
Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）；Vector Institute（向量研究所）；Politécnico Colombiano JIC（哥伦比亚JIC理工学院）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）
Exact autoregressive sampling of planar Ising spin glasses via the Kac--Ward theory
School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心和现代物理系）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences（中国科学院大学先进交叉科学学院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学科学中心）
Inferring effective interactions and task-related brain states from large-scale neural activity with Restricted Boltzmann Machines
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；INRIA（法国国家数字科学研究所）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Institute for Cross-disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所（CSIC- UIB））；Campus Universitat Illes Balears（巴利阿里群岛大学校园）；Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid（马德里理工大学高等工业工程学院）；GISC - Grupo Interdisciplinar de Sistemas Complejos（复杂系统跨学科小组）；Joseph Henry Laboratories of Physics and Lewis–Sigler Institute, Princeton University（普林斯顿大学约瑟夫·亨利物理实验室和刘易斯-西格勒研究所）；Initiative for the Theoretical Sciences, The Graduate Center, City University of New York（纽约市立大学研究生院理论科学倡议）；IPARCOS, Universidad Complutense de Madrid（马德里康普顿斯大学IPARCOS）
Scalable Physics-Inspired Transformers for Spin Glasses
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（基础与前沿科学研究院，电子科技大学）；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（物理科学与技术学院，北京邮电大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（理论物理研究所，中国科学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学科学学院，杭州先进研究院，UCAS）；School of Physics, University of Electronic Science and Technology of China（物理学院，电子科技大学）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（量子物理与光量子信息重点实验室，教育部，电子科技大学）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（四川省非经典信息科学基础学科研究中心，电子科技大学）
Parisi's solution of the Sherrington--Kirkpatrick model from synchronous Monte Carlo dynamics
The University of Tokyo（东京大学）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理研究所）
