Irreversibility of Structure Tensors of Modules

Maciej Wojtala

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arXiv · 2110.01684

Irreversibility of Structure Tensors of Modules

Maciej Wojtala

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Abstract

Determining the matrix multiplication exponent $\omega$ is one of the greatest open problems in theoretical computer science. We show that it is impossible to prove $\omega = 2$ by starting with structure tensors of modules of fixed degree and using arbitrary restrictions. It implies that the same is impossible by starting with $1_A$-generic non-diagonal tensors of fixed size with minimal border rank. This generalizes the work of Bl\"aser and Lysikov [3]. Our methods come from both commutative algebra and complexity theory.

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Maciej Wojtala. 2021-10-04. Irreversibility of Structure Tensors of Modules. https://arxiv.org/abs/2110.01684

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