Classical XY model is a lattice model of statistical mechanics notable for its universality in the rich hierarchy of the optical, laser, and condensed matter systems. We show how to build complex structures for machine learning based on the XY model's nonlinear blocks. The final target is to reproduce the deep learning architectures, which can perform complicated tasks usually attributed to such architectures: speech recognition, visual processing, or other complex classification types with high quality. We developed a robust and transparent approach for the construction of such models, which has universal applicability (i.e., does not strongly connect to any particular physical system) and allows many possible extensions, while at the same time preserving the simplicity of the methodology.

中文翻译：

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基于经典 XY 模型的神经网络架构

经典 XY 模型是统计力学的晶格模型，以其在光学、激光和凝聚态系统的丰富层次结构中的普遍性而著称。我们展示了如何基于 XY 模型的非线性块为机器学习构建复杂的结构。最终目标是重现深度学习架构，它可以执行通常归因于此类架构的复杂任务：语音识别、视觉处理或其他高质量的复杂分类类型。我们为构建此类模型开发了一种稳健且透明的方法，该方法具有普遍适用性（即，不与任何特定物理系统紧密相连）并允许许多可能的扩展，同时保持方法论的简单性。