AlphaEvolve Lowers Matrix Multiplication Exponent Record to 2.371177

A new upper bound for computing’s core operation

The theoretical speed limit for matrix multiplication has moved again. Google DeepMind researchers and academic collaborators lowered the upper bound on the matrix multiplication exponent, ω, from 2.371339 to below 2.371177. The numerical improvement is only 0.000162, but matrix multiplication underpins graphics, scientific computing, and machine learning, making this a meaningful change to a long-running record in complexity theory.

“A new record for omega (ω<2.371177) … is the result of a great team effort between Google DeepMind, our academic collaborators, and our Gemini-powered coding agent AlphaEvolve.”

The statement comes from the source post by Pushmeet Kohli, a paper co-author and Google DeepMind researcher whose account regularly discusses the lab’s algorithmic and scientific work. Google DeepMind’s official account also reposted the result, connecting the researcher’s standalone explanation to the lab.

Where AlphaEvolve entered the proof pipeline

The linked paper explains that the strongest recent bounds come from combination loss analysis, a refinement of the laser method. The team first reformulated the central optimization problem so it could be solved in a larger setting. It then designed a new optimization algorithm with modern machine-learning methods and used AlphaEvolve to refine the resulting construction.

AlphaEvolve is better understood as a search and coding system than as a chatbot supplying a finished theorem. Gemini models propose programs, automated evaluators score them, and evolutionary search iterates on stronger candidates. Human researchers still defined the mathematical framework, selected the objective, and assembled the argument. The paper has ten authors across DeepMind and academic institutions, so the result measures a human-agent research workflow rather than autonomous theorem discovery.

The exponent ω describes the approximate O(n^ω) operation count required to multiply two n-by-n matrices. A better theoretical exponent does not mean production GPU kernels become faster immediately. Algorithms that establish asymptotic records can carry large constants and intricate structures that make them impractical at ordinary sizes. Even so, a lower bound affects the theoretical limits of many graph, algebra, and optimization problems that reduce to matrix multiplication.

What to watch

The paper is a version-one preprint submitted on August 17, 2026, so peer review, independent numerical checking, and reproduction of the optimization are the immediate tests. Beyond verification, watch whether researchers can reuse the reformulation and AlphaEvolve workflow on other combinatorial or complexity problems. A further reduction in ω would show that this was not a one-off parameter search but a repeatable method for extending mathematical frontiers.