AlphaEvolve reports new small-matrix multiplication algorithms

What was reported

Google DeepMind introduced AlphaEvolve, an agent that combines proposals from Gemini Flash and Gemini Pro with automated evaluators and an evolutionary search loop.

Among the reported results is an algorithm multiplying two $4\times4$ complex-valued matrices using 48 scalar multiplications. The system also searched more than fifty problems across mathematics and reported improvements to previously known constructions in a subset of those experiments.

Relation to the open problem

Improved constructions for fixed matrix sizes can become ingredients in asymptotic algorithms, but they do not by themselves prove that the matrix-multiplication exponent is two. The distinction between a finite construction and the asymptotic exponent is preserved in the linked problem record.

OpenTCS attributes these claims to the linked public report and does not independently verify the algorithms.