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

2025-07-18

AI Summary

This work addresses the challenge of controlling the dynamic stability of equilibrium points (EPs) in oscillator-based Ising machines (OIMs), which limits their effectiveness as associative memory models. We propose the Hamiltonian-Regularized Eigenvalue Contrast Method (HRECM), which establishes, for the first time, an explicit analytical link between the binary EP stability of OIMs and their Hamiltonian energy. By regularizing coupling weights during training, HRECM enables differentiable, end-to-end optimization of EP stability specifically for target memory patterns. Unlike conventional Hopfield networks—whose robustness relies on hand-crafted energy functions—HRECM directly shapes the eigenvalue spectrum of the Jacobian matrix at EPs, preserving the physical realizability of OIMs while endowing them with Hopfield-like robust pattern storage and retrieval. Numerical experiments demonstrate substantial improvements in memory capacity and noise tolerance.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Metareasoning and Metaheuristics
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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 $0/π$ 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 $0/π$ binary EPs are structurally stable, the design of the coupling weights needs only to focus on assigning appropriate stability for the $0/π$ 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.

Problem

• Training oscillator Ising machines for stable equilibrium points
• Designing coupling weights for Hopfield-like associative memory
• Assigning dynamic stability to binary equilibrium points

Innovation

• Uses oscillator Ising machine for associative memory
• Assigns stability via Hamiltonian energy connection
• Trains weights with Hamiltonian-Regularized Eigenvalue Contrastive Method