A new result in theoretical computer science shows a practical role for artificial intelligence that is narrower—and more consequential—than simply asking a model to produce a proof. Researchers from Google DeepMind, Carnegie Mellon University, Columbia University, and MIT report a lower upper bound on the number of operations needed to multiply very large matrices. Their preprint, submitted on August 17, combines a redesigned mathematical optimization, GPU-scale computation, and code evolved with AlphaEvolve.
The new bound is expressed through the matrix-multiplication exponent, known as omega. The team reports omega below 2.371177, improving the previous record of 2.371339. The decimal change is small, but the result concerns asymptotic complexity: how the required work grows as matrices become arbitrarily large. It does not mean today’s laptops or AI accelerators will suddenly multiply ordinary matrices faster.
What changed in the search
For decades, progress on this problem has relied on variants of the laser method, a mathematical framework that turns matrix multiplication into a structured search over tensor decompositions. The immediate obstacle was not a missing chatbot answer. It was a difficult non-convex optimization inside a computer-assisted proof.
The previous best result, published by SIAM and available through arXiv, used what researchers call combination-loss analysis and reached 2.371339. The new team retained that mathematical foundation but changed how its optimization was represented and solved. Instead of treating the task as an irregular graph whose nodes exchange updates, it reorganized the computation into tensors that could run in parallel.
That engineering choice expanded the search from a recursion level with roughly 25,000 optimizable parameters to one with nearly seven million. The researchers used JAX, automatic differentiation, the Adam optimizer, and techniques associated with optimal transport to make the larger problem tractable. Gradient descent alone produced most of the improvement over the prior record.
Where AlphaEvolve entered
AlphaEvolve did not replace the mathematical theorem or certify its own output. Google DeepMind describes the system as a coding agent that proposes program changes, runs them against automated evaluators, and evolves the most promising candidates. In this project, the program being evolved was the optimizer itself.
Each candidate optimization program took about five hours on a single graphics processor to produce a value for omega, according to the preprint. AlphaEvolve then searched for code changes that pushed that value lower. An “evolving constructions” feature let each generation begin from the best solution point inherited from its parent program. The authors say gradient-based optimization improved the former record by about 0.000097; adding the evolved optimizer increased the total improvement to about 0.000162.
Analysis: AI was useful because the score was strict
The important pattern is the division of labor. Humans supplied the theorem, the legal search space, the representation, and the standard for a valid result. Conventional optimization navigated millions of continuous parameters. AlphaEvolve modified code inside that pipeline. A separate verifier then checked the final construction.
This is a stronger model for AI-assisted mathematics than treating fluent reasoning as evidence. The search system could explore because every candidate faced a precise numerical objective. Yet a good score was not accepted as proof. The researchers rounded the floating-point solution into rational numbers, evaluated derived quantities with exact rational arithmetic, and bounded logarithms in the conservative direction so numerical error could not manufacture the claimed inequality.
The result also draws a useful boundary around the headline. Matrix multiplication underpins machine learning, graphics, simulation, and many other workloads, but an asymptotic upper bound is not the same as a deployable algorithm. Constants, memory traffic, hardware structure, numerical stability, and matrix size determine whether a theoretical method is practical. The paper establishes that a lower growth rate is mathematically achievable; it does not benchmark a production kernel.
A record, and a map of the remaining gap
The chronology clarifies both the achievement and its scale. The listed record moved from 2.371866 to 2.371552, then to 2.371339, and now to 2.371177. The new paper says its gain is comparable in magnitude to many advances made during the past four decades. But the ideal lower limit is 2, and the authors caution that substantially larger progress will probably require new mathematical ideas rather than further tuning of the same framework.
That makes this less a story about AI solving matrix multiplication than about AI helping scientists interrogate a larger version of a rigorously defined search. The contribution is credible because exploration and verification remain separate. AlphaEvolve widened the hunt for an optimizer; exact arithmetic decided whether the resulting claim survived.
Sources: The research preprint “Improving the matrix multiplication exponent with modern optimization and AlphaEvolve”; the SIAM paper “More Asymmetry Yields Faster Matrix Multiplication”; Google DeepMind’s technical overview of AlphaEvolve.
Featured image: A Cray-2 supercomputer at NASA Ames Research Center. Credit: NASA / Wade Sisler via Wikimedia Commons. License: Public domain (PD-USGov-NASA). Modification: center-cropped to 16:9 and resized.
