# Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach

arXiv: https://arxiv.org/abs/2602.21797 · HTML: https://mlsanity.com/paper/2602.21797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 1 of 1)

- [A Refined Laser Method and Faster Matrix Multiplication](https://mlsanity.com/paper/2010.05846/) (2020)

## Abstract (arXiv)

Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, textscStrassenNet, which reproduces the Strassen algorithm for 2× 2 multiplication. Across many independent runs the network always converges to a rank-7 tensor, thus numerically recovering Strassen's optimal algorithm. We then train the same architecture on 3× 3 multiplication with rank r∈19,dots,23. Our experiments reveal a clear numerical threshold: models with r=23 attain significantly lower validation error than those with r≤ 22, suggesting that r=23 could actually be the smallest effective rank of the matrix multiplication tensor 3× 3. We also sketch an extension of the method to border-rank decompositions via an varepsilon--parametrisation and report preliminary results consistent with the known bounds for the border rank of the 3× 3 matrix--multiplication tensor.