Signal AlphaEvolve-Assisted Optimization Improves the Matrix Multiplication Exponent Bound

Summary

This work improves the best known upper bound on the matrix multiplication exponent, denoted omega, which governs the asymptotic complexity of matrix multiplication. The previously best bound came from a refinement of the laser method known as combination loss analysis. The authors reformulate the core optimization problem behind this approach so it can be solved in a broader setting, and design a new optimization algorithm that draws on recent machine learning techniques. They then further refine the result using the AlphaEvolve system. Combining these three steps yields a new bound placing omega below 2.371177. This improves on the previous best published bound of 2.371339.