Researchers at Hugging Face have announced a new upper bound for the matrix multiplication exponent, a fundamental constant in computer science that determines the efficiency of matrix multiplication algorithms. The new bound, ω < 2.371177, improves upon the previous best of 2.371339.
The work builds on a technique known as combination loss analysis, which has been the basis for the best bounds on ω since 2022. The authors address the core optimization problem of this approach with three key improvements.
First, they reformulate the optimization problem, allowing it to be solved in a larger setting than previously possible. Second, they leverage recent advances in machine learning to design a new optimization algorithm tailored to this problem. Finally, they refine the algorithm using AlphaEvolve, a tool for evolutionary algorithm discovery.
The combined approach yields the improved bound, marking a small but significant step forward in a long-standing area of theoretical computer science. The paper is available on the Hugging Face papers platform.