This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using the Factorization Machine (FM), a machine learning model. The construction of Ising models using FM is applied to the combinatorial optimization problem using the factorization machine with quantum annealing. It is anticipated that the optimization performance of FMQA will be enhanced through the implementation of the warm-start method. Nevertheless, the optimal initialization method for leveraging the warm-start approach in FMQA remains undetermined. Consequently, the present study compares a number of initialization methods and identifies the most appropriate for use with a warm-start in FMQA through numerical experimentation. Furthermore, the properties of the proposed FM initialization method are analyzed using random matrix theory, demonstrating that the approximation accuracy of the proposed method is not significantly influenced by the specific Ising model under consideration. The findings of this study will facilitate the advancement of combinatorial optimization problem-solving through the use of Ising machines.

翻译：本文提出一种初始化方法，能够使用机器学习模型因子分解机（FM）以高精度近似给定的近似伊辛模型。利用因子分解机构建伊辛模型的方法，已通过结合量子退火的因子分解机应用于组合优化问题。预计通过实施热启动方法，FMQA的优化性能将得到提升。然而，在FMQA中利用热启动方法的最佳初始化策略尚未明确。因此，本研究比较了多种初始化方法，并通过数值实验确定了最适合在FMQA中配合热启动使用的方案。此外，利用随机矩阵理论分析了所提出的FM初始化方法的特性，证明该方法的近似精度不会显著受特定伊辛模型选择的影响。本研究成果将推动基于伊辛机的组合优化问题求解技术的发展。