Description of fast matrix multiplication algorithm: ⟨3×4×5:47⟩

Algorithm type

13 X^{2} Y^{2} Z^{2} + 3 X^{3} Y Z + X^{2} Y^{2} Z + 2 X Y^{3} Z + 2 X Y^{2} Z^{2} + 4 X Y Z^{3} + 3 X^{2} Y Z + 8 X Y^{2} Z + 6 X Y Z^{2} + 5 X Y Z

Algorithm definition

The algorithm ⟨3×4×5:47⟩ is taken from:

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. Discovering faster matrix multiplication algorithms with reinforcement learning. Nature, 610(7930):47--53, October 2022. [ DOI | http ]

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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