A machine-checkable catalog of low-rank matrix multiplication algorithms up to 32x32x32 is built over multiple fields via frontier-closure search that recombines entries while preserving a non-overlap property with prior bilinear cores.
On symmetries of the Strassen algorithm
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abstract
We consider the famous Strassen algorithm for fast multiplication of matrices. We show that this algorithm has a nontrivial finite group of automorphisms of order 36 (namely the direct product of two copies of the symmetric group on 3 symbols), or even 72, if we consider "extended" Strassen algorithm. This is an indirect evidence that the (unknown at present) optimal algorithm for multiplication of two size 3 by 3 matrices also may have a large automorphism group, and this may be a fruitful idea for a search of such an algorithm. In the beginning we give a brief introduction to the subject, to make the text accessible for specialists in the representation theory of finite groups.
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2026 1verdicts
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A catalog of fast matrix multiplication algorithms with frontier-closure search
A machine-checkable catalog of low-rank matrix multiplication algorithms up to 32x32x32 is built over multiple fields via frontier-closure search that recombines entries while preserving a non-overlap property with prior bilinear cores.