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Moosbauer and Poole have recently shown that the multiplication of two $5\times 5$ matrices requires no more than 93 multiplications in the (possibly non-commutative) coefficient ring, and that the multiplication of two $6\times 6$ matrices requires no more than 153 multiplications.
Discovering faster matrix multiplication algorithms with reinforcement learning
Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert, Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Francisco J. R. Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, David Silver, Demis Hassabis, and Pushmeet Kohli · 2022
Earlier work this paper cites.
Flip graphs for matrix multiplication
Manuel Kauers and Jakob Moosbauer · 2023
Earlier work this paper cites.
Search Techniques for Matrix Algorithms
Jakob Moosbauer · 2023
Earlier work this paper cites.
Adaptive flip graph algorithm for matrix multiplication
Yamato Arai, Yuma Ichikawa, and Koji Hukushima · 2024
Cited alongside, same era.
Some new non-commutative matrix multiplication algorithms of size ( n , m , 6 ) (n,m,6)
Manuel Kauers and Jakob Moosbauer · 2025
Cited alongside, same era.
Flip graphs with symmetry and new matrix multiplication schemes
Jakob Moosbauer and Michael Poole · 2025
Closest in time.
Yet another catalogue of fast matrix multiplication algorithms
Alexandre Sedoglavic · 2025
Closest in time.
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