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Bounds on complexity of matrix multiplication away from CW tensors

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 نشر من قبل Joachim Jelisiejew
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassens laser method and obtain an upper bound $2.431$ on $omega$. We also explain how in certain monomial cases using the laser method directly is less profitable than first degenerating. Our results form possible paths in the search for valuable tensors for the laser method away from Coppersmith-Winograd tensors.



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