用新方法训练振荡伊辛机，让其记忆状态稳定可控。
Training oscillator Ising machines to assign the dynamic stability of their equilibrium points
- 通过能量与稳定性关联，设计可调耦合权重
- 实验验证能准确分配平衡点稳定性
- 适合需要稳定记忆的神经计算系统
我们提出一种神经网络模型，通过合理设定其平衡点（EPs）的动态稳定性，实现类霍普菲尔德的联想记忆。振荡伊辛机（OIM）是理想候选者，因其所有0/π二进制平衡点均具有结构稳定性，且动态稳定性可通过耦合权重调节。传统霍普菲尔德模型需同时考虑平衡点的存在性与稳定性来存储模式，而对OIM而言，由于所有0/π二进制平衡点天然结构稳定，只需关注根据目标模式为这些平衡点分配合适的动态稳定性。本文建立了平衡点稳定性与其哈密顿能量之间的联系，并基于此提出哈密顿正则化特征值对比方法（HRECM），用于训练OIM的耦合权重，以实现对平衡点稳定性的精确调控。最后通过数值实验验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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