Description of fast matrix multiplication algorithm: ⟨4×5×5:76⟩

Algorithm type

X2Y3Z2+4X4YZ+23X2Y2Z2+4XYZ4+13XY3Z+8XY2Z2+4XY2Z+4XYZ2+15XYZX2Y3Z24X4YZ23X2Y2Z24XYZ413XY3Z8XY2Z24XY2Z4XYZ215XYZX^2*Y^3*Z^2+4*X^4*Y*Z+23*X^2*Y^2*Z^2+4*X*Y*Z^4+13*X*Y^3*Z+8*X*Y^2*Z^2+4*X*Y^2*Z+4*X*Y*Z^2+15*X*Y*Z

Algorithm definition

The algorithm ⟨4×5×5:76⟩ 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.


Back to main table