Towards Faster Matrix Diagonalization with Graph Isomorphism Networks and the AlphaZero Framework

Geigh Zollicoffer, Kshitij Bhatta, Manish Bhattarai, Phil Romero, Christian Negre, Anders M. N. Niklasson, Adetokunbo Adedoyin

Keywords: Reinforcement Learning

TL;DR: Identifying the common patterns and improvement necessary for scaling the Jacobi Method using Graph Based Alpha Zero.

Abstract: In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the use of formulating 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 practical applications in scientific and engineering domains

Submission Number: 20