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Tensor Network Complexity of Multilinear Maps

2018
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Innovations in Theoretical Computer Science
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We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as O(n ω+ ) time matrix multiplication, and in addition many other algorithms such as O(n log n) time discrete Fourier transform and O * (2 n ) time for computing the permanent of a matrix. However tensor networks sometimes yield faster algorithms than those that follow from low-rank decompositions. For instance the

doi:10.4230/lipics.itcs.2019.7
dblp:conf/innovations/AustrinKK19
fatcat:t4xmqd4rxfb27lgqzslpxtduli