Improved ranks found for 207 small matrix formats, 84 new ternary schemes, and 23 new schemes with exponent below log2(7) via extended meta flip graph and serendipitous product search.
Exploiting the Structure in Tensor Decompositions for Matrix Multiplication
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abstract
We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for $6\times 6$ matrix multiplication we reduce the exponent of the recent algorithm by Moosbauer and Poole from $2.8075$ to $2.8019$, while retaining a reasonable leading coefficient.
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2026 1verdicts
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Meta Flip Graph meets Serendipitous Product: new Fast Matrix Multiplication results
Improved ranks found for 207 small matrix formats, 84 new ternary schemes, and 23 new schemes with exponent below log2(7) via extended meta flip graph and serendipitous product search.