Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

Excerpt

arXiv:2608.16884v1 Announce Type: cross Abstract: The current best bounds on the matrix multiplication exponent $\omega$ are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously poss