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

TL;DR

This paper presents a novel approach to accelerate matrix diagonalization by formulating it as decision processes and leveraging scalable architectures, resulting in fewer steps and potential for large-scale applications.

Contribution

It introduces a decision process-based framework for faster matrix diagonalization and demonstrates scalability and efficiency improvements over traditional methods.

Findings

Reduced number of diagonalization steps during training

Efficient inference with scalable architecture

Potential applicability to large matrices

Abstract

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.