Matrix multiplication exponent lowered to below 2.371177
A reformulated optimization inside the laser method, with AlphaEvolve applied as the final refinement, lowers the best known upper bound on the matrix multiplication exponent from 2.371339 to 2.371177.
- Model
- AlphaEvolve
- Field
- Computer science
- Date
- 2026-08-17
- Human collaborators
- Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii, Abbas Mehrabian, Francisco J. R. Ruiz, Abigail See, Renfei Zhou, Josh Alman, Virginia Vassilevska Williams, Matej Balog
- Problem posed
- 1969 · open 57 yrs
What was found
The best bounds on the matrix multiplication exponent come from combination loss analysis, a refinement of the laser method. The paper makes three changes to the optimization at its core, and AlphaEvolve is only the third: first the problem is reformulated so it can be solved over a larger space than was previously tractable, then a new optimization algorithm is designed using recent machine-learning methods, and then that algorithm is refined with AlphaEvolve. The combination gives an upper bound of 2.371177 against a previous best of 2.371339. The paper is a note reporting a record, not a structural advance: whether the exponent equals 2 is untouched, and nothing here suggests the laser method can reach it.
Novelty check
The exponent has a well-tracked ladder of published upper bounds running through Duan, Wu and Zhou (2022), Vassilevska Williams, Xu, Xu and Zhou (2024) and Alman, Duan, Vassilevska Williams, Xu, Xu and Zhou (2025), and the paper states the prior best as 2.371339 and cites it. No lower published upper bound appears before this note. The result is a new bound rather than a retrieval, and it is an improvement of roughly 1.6 times ten to the minus four, which the authors themselves describe as a small step.
Caveats and known objections
A preprint, unrefereed at entry. A bound of this kind is not the sort of claim a reader can spot-check: the number falls out of a large optimization over laser-method parameters, so reproducing it means re-running the optimization rather than checking a certificate, and no such independent rerun is recorded. Autonomy graded search-scaffold, consistent with the other AlphaEvolve entries here: AlphaEvolve is a human-built evolutionary harness with a language model inside, and in this paper it is the last stage of a pipeline whose first two stages are ordinary human applied mathematics. The author list mixes the DeepMind team with the complexity theorists who set the previous record, which is where the reformulation comes from.
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Entry history (1 event)
- AddedEntered the registry graded Author verified and Search scaffold.
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Cite this entry
whataifound.org. (2026). Matrix multiplication exponent lowered to below 2.371177. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-08-17-matmul-exponentBibTeX
@misc{whataifound-googledeepmind-2026-exponent,
title = {Matrix multiplication exponent lowered to below 2.371177},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Google DeepMind. Verification: Author verified. Autonomy: Search scaffold.},
url = {https://whataifound.org/finding/2026-08-17-matmul-exponent}
}