Training oscillator Ising machines to assign the dynamic stability of their equilibrium points

TL;DR

This paper introduces a method to train oscillator Ising machines by assigning stability to their equilibrium points, enabling Hopfield-like associative memory with tunable stability for pattern storage.

Contribution

It proposes the Hamiltonian-Regularized Eigenvalue Contrastive Method (HRECM) to train coupling weights for stability assignment in oscillator Ising machines.

Findings

HRECM effectively assigns stability to EPs in OIMs.

Numerical experiments validate the method's effectiveness.

OIMs can store patterns with tunable stability.

Abstract

We propose a neural network model, which, with appropriate assignment of the stability of its equilibrium points (EPs), achieves Hopfield-like associative memory. The oscillator Ising machine (OIM) is an ideal candidates for such a model, as all its $0/\pi$ binary EPs are structurally stable with their dynamic stability tunable by the coupling weights. Traditional Hopfield-based models store the desired patterns by designing the coupling weights between neurons. The design of coupling weights should simultaneously take into account both the existence and the dynamic stability of the EPs for the storage of the desired patterns. For OIMs, since all $0/\pi$ binary EPs are structurally stable, the design of the coupling weights needs only to focus on assigning appropriate stability for the $0/\pi$ binary EPs according to the desired patterns. In this paper, we establish a connection between the stability and the Hamiltonian energy of EPs for OIMs, and, based on this connection, provide a Hamiltonian-Regularized Eigenvalue Contrastive Method (HRECM) to train the coupling weights of OIMs for assigning appropriate stability to their EPs. Finally, numerical experiments are performed to validate the effectiveness of the proposed method.