利用图同构网络与AlphaZero框架加速矩阵对角化
Towards Faster Matrix Diagonalization with Graph Isomorphism Networks and the AlphaZero Framework
AI总结：
本文将矩阵对角化建模为马尔可夫决策过程，结合图同构网络与AlphaZero框架，在减少对角化步骤的同时实现了对大规模矩阵的可扩展推理，为科学与工程应用提供了更高效的方法。
摘要：
在本文中，我们提出了加速矩阵对角化Jacobi方法的创新途径，具体通过将大规模矩阵对角化建模为半马尔可夫决策过程，以及将小规模矩阵对角化建模为马尔可夫决策过程。此外，我们研究了在不同规模矩阵之间利用可扩展架构的潜力。在短暂的训练期内，我们的方法发现对角化所需步骤数显著减少，并展现出高效的推理能力。重要的是，该方法展示了对大规模矩阵的可能可扩展性，表明其具有广泛适用性的潜力。训练完成后，我们获得了动作-状态概率和转移图，这些图描绘了不同状态之间的转移。这些输出不仅为对角化过程提供了洞见，还为与大规模矩阵相关的成本节约铺平了道路。本研究取得的进展提升了矩阵对角化的有效性和可扩展性，为其在科学与工程领域实际应用中的部署开辟了新的可能性。
英文摘要：
In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix diagonalization as a Markov Decision Process. Furthermore, we examine the potential of utilizing scalable architecture between different-sized matrices. During a short training period, our method discovered a significant reduction in the number of steps required for diagonalization and exhibited efficient inference capabilities. Importantly, this approach demonstrated possible scalability to large-sized matrices, indicating its potential for wide-ranging applicability. Upon training completion, we obtain action-state probabilities and transition graphs, which depict transitions between different states. These outputs not only provide insights into the diagonalization process but also pave the way for cost savings pertinent to large-scale matrices. The advancements made in this research enhance the efficacy and scalability of matrix diagonalization, pushing for new possibilities for deployment in practical applications in scientific and engineering domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
