# Matrix Diagonalization as a Board Game: Teaching an Eigensolver the Fastest Path to Solution

arXiv: https://arxiv.org/abs/2306.10075 · HTML: https://mlsanity.com/paper/2306.10075/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 16 Jun 2023.

## Builds on (most cited first, 3 of 3)

- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach](https://mlsanity.com/paper/2002.02600/) (2020)

## Built on by (most cited first, 2 of 2)

- [Accelerating Matrix Diagonalization through Decision Transformers with Epsilon-Greedy Optimization](https://mlsanity.com/paper/2406.16191/) (2024)
- [Towards Faster Matrix Diagonalization with Graph Isomorphism Networks and the AlphaZero Framework](https://mlsanity.com/paper/2407.00779/) (2024)

## Abstract (arXiv)

Matrix diagonalization is at the cornerstone of numerous fields of scientific computing. Diagonalizing a matrix to solve an eigenvalue problem requires a sequential path of iterations that eventually reaches a sufficiently converged and accurate solution for all the eigenvalues and eigenvectors. This typically translates into a high computational cost. Here we demonstrate how reinforcement learning, using the AlphaZero framework, can accelerate Jacobi matrix diagonalizations by viewing the selection of the fastest path to solution as a board game. To demonstrate the viability of our approach we apply the Jacobi diagonalization algorithm to symmetric Hamiltonian matrices that appear in quantum chemistry calculations. We find that a significant acceleration can often be achieved. Our findings highlight the opportunity to use machine learning as a promising tool to improve the performance of numerical linear algebra.