Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation
This work introduces a novel computing paradigm for linear algebra, potentially benefiting fields like scientific computing, but it appears incremental as it applies an existing ONN framework to a new problem type.
The paper tackles the problem of computing inverse matrices using oscillatory neural networks, demonstrating that a linear approximation of the Kuramoto oscillator model yields the inverse matrix solution, with numerical simulations validating the framework and identifying optimal parameter regimes for accuracy.
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.