The arithmetic complexity of tensor contractions

Florent Capelli; Arnaud Durand; Stefan Mengel

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arXiv · 1209.4865

The arithmetic complexity of tensor contractions

Florent Capelli·Arnaud Durand·Stefan Mengel

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Abstract

We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits. This gives a natural and robust characterization of this complexity class that despite its naturalness is not very well understood so far.

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Florent Capelli, Arnaud Durand, Stefan Mengel. 2012-09-21. The arithmetic complexity of tensor contractions. https://arxiv.org/abs/1209.4865

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