XY Neural Networks

TL;DR

This paper introduces a novel approach to constructing deep learning architectures inspired by the XY model from statistical mechanics, aiming to perform complex tasks like speech recognition and visual processing.

Contribution

It presents a universal, robust, and transparent methodology for building neural network structures based on the XY model's nonlinear blocks, extending their applicability beyond physical systems.

Findings

Successfully modeled complex classification tasks

Developed a flexible framework for XY-based neural networks

Achieved high performance in speech and visual recognition tasks

Abstract

The 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 the 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), allows many possible extensions while at the same time preserving the simplicity of the methodology.