Incoming links: AlphaEvolve
DeepMind likes coming up with new improved algorithms for these more specific cases, e.g. it was announced in 2025 that AlphaEvolve found a novel 4x4 complex valued algorithm that uses 48 multiplications.
Bibliography:
- fmm.univ-lille.fr/ attempts to keep an up-to-date list for various sizes
Updates Understanding the state of 3x3 matrix multiplication Updated 2025-05-23 +Created 2025-05-21
After yet another awesome announcement by DeepMind that it had improved theoretical 4x4 matrix multiplication reducing the number of scalar multiplications with its AlphaEvolve system, I decided to have a look at the smallest open size 3x3 to understand what was going on in there.