Description of fast matrix multiplication algorithm: ⟨5×5×5:93⟩

Algorithm type

X^{3} Y^{2} Z + 32 X^{2} Y^{2} Z^{2} + X^{2} Y Z^{3} + X Y^{3} Z^{2} + X^{2} Y^{2} Z + X^{2} Y Z^{2} + X Y^{2} Z^{2} + 11 X^{2} Y Z + 11 X Y^{2} Z + 11 X Y Z^{2} + 22 X Y Z

Algorithm definition

The algorithm ⟨5×5×5:93⟩ is taken from:

Jakob Moosbauer and Michael Poole. Flip graphs with symmetry and new matrix multiplication schemes. Technical report, arXiv, February 2025. [ arXiv ]

Algorithm description

Algorithm symmetries

The following group of 3 isotropies acts as a permutation group on algorithm tensor representation:

maple tensor representation (compressed by bzip2);

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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