Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

Understand

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 possible.
• Second, we leverage recent advances in machine learning to design a new optimization algorithm for this problem.