This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during diagonalization with the Jacobi algorithm, leading to significant speedups compared to the traditional max-element Jacobi method. To bolster robustness, we integrate an epsilon-greedy strategy, enabling success in scenarios where deterministic approaches fail. This work demonstrates the effectiveness of DTs in complex computational tasks and highlights the potential of reimagining mathematical operations through a machine learning lens. Furthermore, we establish the generalizability of our method by using transfer learning to diagonalize matrices of smaller sizes than those trained.

翻译：本文提出了一种新颖的矩阵对角化框架，将其重新表述为序列决策问题，并应用决策Transformer（DT）的强大能力。我们的方法在雅可比算法对角化过程中确定最优主元选择，相比传统的最大元素雅可比方法实现了显著的加速。为增强鲁棒性，我们引入了ε-贪婪策略，使其在确定性方法失效的场景中仍能成功。这项工作展示了DT在复杂计算任务中的有效性，并凸显了通过机器学习视角重新构想数学运算的潜力。此外，我们通过迁移学习对角化比训练尺寸更小的矩阵，验证了该方法的泛化能力。