Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation

TL;DR

This paper introduces a thermodynamics-inspired approach using oscillatory neural networks to compute inverse matrices, demonstrating both theoretical foundations and numerical validation for this novel application.

Contribution

It presents a new method leveraging thermodynamic principles and oscillatory neural networks to solve linear algebra problems, specifically inverse matrices, which was not previously explored.

Findings

The linear approximation of the Kuramoto oscillator model yields inverse matrix solutions.

Numerical simulations confirm the theoretical framework.

Optimal parameter regimes for accurate computation are identified.

Abstract

We describe a thermodynamic-inspired computing paradigm based on oscillatory neural networks (ONNs). While ONNs have been widely studied as Ising machines for tackling complex combinatorial optimization problems, this work investigates their feasibility in solving linear algebra problems, specifically the inverse matrix. Grounded in thermodynamic principles, we analytically demonstrate that the linear approximation of the coupled Kuramoto oscillator model leads to the inverse matrix solution. Numerical simulations validate the theoretical framework, and we examine the parameter regimes that computation has the highest accuracy.