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The arithmetic complexity of tensor contractions
Citation key CDM-The-Arithmetic-Complexity-Of-Tensor-Contractions
Author Florent Capelli and Arnaud Durand and Stefan Mengel
Title of Book Proceedings Symposium on Theoretical Aspects of Computer Science (STACS) 2013
Year 2013
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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