Google DeepMind AlphaEvolve Sets New Record on Matrix Multiplication Exponent

Researchers from Google DeepMind and several universities have established a new upper bound for the matrix multiplication exponent, reducing it to 2.371177. This achievement refines the laser method by addressing a complex non-convex optimization problem associated with combination loss analysis. The team utilized gradient-based optimization and the Jax framework to scale the computation, handling millions of parameters through hardware parallelization. They further enhanced their results by employing AlphaEvolve, an automated coding agent, to discover more efficient optimization algorithms. To ensure accuracy, the final results were rigorously confirmed using exact rational arithmetic to eliminate potential numerical errors. Their work represents the latest advancement in a decades-long effort to minimize the computational complexity of fundamental algebraic operations.

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