Bounds on complexity of matrix multiplication away from CW tensors

Abstract

We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassen's 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.

v3: final v2: minor changes v1: 14 pages, comments welcome!

References in corpus (1)

• Plethysm and fast matrix multiplication