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A paper posted August 17, 2026 establishes ω < 2.371177, improving the previous best known bound of ω < 2.371339. The team used AlphaEvolve, Google DeepMind's AI-based optimizer, as a final refinement step in a broader mathematical optimization pipeline.
What the source says
The ten authors are Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii, Abbas Mehrabian, Francisco J. R. Ruiz, Abigail See, Renfei Zhou, and Matej Balog, alongside theoretical computer scientists Josh Alman and Virginia Vassilevska Williams, who established the prior ω < 2.371339 record. The method reformulates the laser method's combination loss analysis to allow optimization in a larger solution space than was previously feasible. Recent machine learning advances were used to develop a novel optimization algorithm, which was then refined with AlphaEvolve. The new bound improves on the previous best by approximately 0.000162.
Why it matters
The matrix multiplication exponent ω governs the asymptotic complexity of matrix multiplication, and tighter bounds propagate to linear algebra, graph algorithms, and any computation reducible to matrix products. The improvement is small in absolute terms, but each step closer to 2, the conjectured true value of ω, has historically required new mathematical techniques. This paper reformulates a well-established framework to work in a larger search space, then applies AlphaEvolve to find a better solution within it. The presence of Alman and Williams, who hold the prior record, places this result at the direct leading edge of the field rather than adjacent to it.