Improving matrix multiplication exponent with optimization and AlphaEvolve

Researchers using a machine-learning-guided optimization algorithm called AlphaEvolve have improved the upper bound on the matrix multiplication exponent to ω < 2.371177, surpassing the previous best of 2.371339. The team, including authors from the paper submitted to arXiv on 17 Aug 2026, reformulated the core optimization problem and combined modern optimization techniques with AlphaEvolve to achieve this result.

Computer Science Data Structures and Algorithms Submitted on 17 Aug 2026 Title:Improving the matrix multiplication exponent with modern optimization and AlphaEvolve View PDF /pdf/2608.16884 HTML experimental https://arxiv.org/html/2608.16884v1 Abstract:The current best bounds on the matrix multiplication exponent $\omega$ are obtained through a refinement of the laser method called combination loss analysis Duan et al., 2022; Williams et al., 2024; Alman et al., 2025 . In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously possible. Second, we leverage recent advances in machine learning to design a new optimization algorithm for this problem. Finally, we refine the resulting optimization algorithm with AlphaEvolve. Our combined approach yields an upper bound of $\omega$ < 2.371177, improving the previous best bound of 2.371339. Current browse context: cs.DS References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs https://info.arxiv.org/labs/index.html .