Google DeepMind improves matrix multiplication exponent with AlphaEvolve

Google DeepMind's AlphaEvolve, an evolutionary coding agent built on its Gemini architecture, has refined the matrix multiplication exponent omega from 2.371339 to 2.371177, marking the tightest bound ever placed on the theoretical limit and the first meaningful progress in decades. The improvement, detailed in an arXiv paper, was achieved with contributions from academics Josh Alman and Virginia Vassilevska Williams. AlphaEvolve previously improved 4x4 complex matrix multiplication from 49 to 48 scalar multiplications and delivered a 23% speedup on a Gemini training kernel in 2025.

Via igmguru.com Google DeepMind improves matrix multiplication exponent with AlphaEvolve The AI-driven breakthrough tightens the theoretical bound on how efficiently matrices can be multiplied, marking the first meaningful progress in decades Matrix multiplication is one of those foundational operations that silently runs the modern world. Every time a neural network trains, a physics simulation renders, or a search engine ranks pages, matrices are being multiplied somewhere underneath the hood. And for over half a century, mathematicians have been trying to figure out the theoretical speed limit for doing it. Google DeepMind just nudged that limit a little lower. Using AlphaEvolve, an evolutionary coding agent built on top of its Gemini architecture, DeepMind’s research team refined the matrix multiplication exponent, known in the literature simply as omega or just “w” , from 2.371339 down to 2.371177. The improvement was detailed in an arXiv paper. The difference looks tiny. It is not. Why a decimal shift matters more than it looks To understand why shaving off a few digits in the fourth decimal place of an exponent is a big deal, you need a quick detour into what omega actually represents. When you multiply two n-by-n matrices using the straightforward method you learned in school, the number of operations scales as n cubed, meaning omega equals 3. In 1969, Volker Strassen showed you could do better, proving that omega could be pushed below 2.808 by reducing the number of multiplications needed for a 2×2 matrix block. The new bound of 2.371177 represents the tightest constraint ever placed on omega, improving on the previous best of 2.371339. Key contributors to the work include Google DeepMind researchers alongside academics Josh Alman and Virginia Vassilevska Williams. AlphaEvolve: the tool behind the result AlphaEvolve was first announced by Google DeepMind on May 14, 2025. Unlike traditional code-generation tools that tweak individual functions, AlphaEvolve is designed to evolve entire codebases through an iterative, AI-guided process. It leverages DeepMind’s Gemini models to propose, test, and refine algorithmic improvements at a scale that would be impractical for human researchers working alone. The system had already demonstrated its chops before tackling the omega problem. In its initial applications, AlphaEvolve improved the multiplication of 4×4 complex-valued matrices by reducing the number of required scalar multiplications from 49 to 48. That was the first improvement over Strassen’s original algorithm since 1969. On the practical side, DeepMind reported that AlphaEvolve delivered a 23% speedup on a Gemini training kernel in 2025, along with a 1% reduction in overall training time. Disclosure: This article was edited by Editorial Team. For more information on how we create and review content, see our Editorial Policy https://cryptobriefing.com/editorial-policy/ .