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arXiv · 2103.12598

Bounds on complexity of matrix multiplication away from CW tensors

Roser Homs·Joachim Jelisiejew·Mateusz Michałek·Tim Seynnaeve
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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.

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Roser Homs, Joachim Jelisiejew, Mateusz Michałek, Tim Seynnaeve. 2021-03-23. Bounds on complexity of matrix multiplication away from CW tensors. https://arxiv.org/abs/2103.12598

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