用低秩近似初始化因子机，提升量子退火求解组合优化的精度。
Initialization Method for Factorization Machine Based on Low-Rank Approximation for Constructing a Corrected Approximate Ising Model
- 用低秩近似替代随机初始化，提升因子机对伊辛模型的逼近能力。
- 数值实验表明，该方法在多种伊辛模型上均保持高精度逼近效果。
- 适合研究黑箱组合优化与伊辛机加速求解的科研人员参考。
本文提出一种基于低秩近似的因子机（FM）初始化方法，可高精度逼近给定的近似伊辛模型。该方法被应用于基于因子机的量子退火（FMQA）求解黑箱组合优化问题。尽管热启动（warm-start）有望提升FMQA性能，但其最优初始化方式尚未明确。为此，本文比较了随机初始化与低秩近似初始化，并通过数值实验确定后者更适用于热启动。进一步结合随机矩阵理论分析发现，该初始化方法的逼近精度不受具体伊辛模型影响。研究成果将推动伊辛机在黑箱组合优化领域的应用进展。
原文摘要 · Abstract (English)
This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using a factorization machine (FM), a machine learning model. The construction of an Ising models using an FM is applied to black-box combinatorial optimization problems using factorization machine with quantum annealing (FMQA). It is anticipated that the optimization performance of FMQA will be enhanced through an 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 initialization methods based on random initialization and low-rank approximation, and then identifies a suitable one for use with warm-start in FMQA through numerical experiments. Furthermore, the properties of the initialization method by the low-rank approximation for the FM 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 advancements of research in the field of black-box combinatorial optimization through the use of Ising machines.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。