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.

• Received 31 March 2021
• Revised 12 October 2021
• Accepted 1 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.205435