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We study tensor networks as a model of arithmetic computation for evaluating multilinear maps.
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Which problems have strongly exponential complexity?
Russell Impagliazzo, Ramamohan Paturi, and Francis Zane · 2001
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Günter Rote · 2001
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The complexity of tensor calculus
Carsten Damm, Markus Holzer, and Pierre McKenzie · 2002
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Counting H-colorings of partial k-trees
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Algorithms and complexity results for #SAT and Bayesian inference
Fahiem Bacchus, Shannon Dalmao, and Toniann Pitassi · 2003
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On the complexity of fixed parameter clique and dominating set
Friedrich Eisenbrand and Fabrizio Grandoni · 2004
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Group-theoretic algorithms for matrix multiplication
Henry Cohn, Robert D. Kleinberg, Balázs Szegedy, and Christopher Umans · 2005
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Tamara G. Kolda · 2006
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Martin Beaudry and Markus Holzer · 2007
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Finding, minimizing, and counting weighted subgraphs
Virginia Vassilevska Williams and Ryan Williams · 2013
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Counting thin subgraphs via packings faster than meet-in-the-middle time
Andreas Björklund, Petteri Kaski, and Łukasz Kowalik · 2014
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Powers of tensors and fast matrix multiplication
François Le Gall · 2014
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states
R. Orús · 2014
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Matrix multiplication, trilinear decompositions, APA algorithms, and summation
Victor Y. Pan · 2014
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Faster identification of optimal contraction sequences for tensor networks
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Fourier meets Möbius: fast subset convolution
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Leslie G. Valiant · 2008
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Graphical models, exponential families, and variational inference
Martin J Wainwright, Michael I Jordan, et al · 2008
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Robert N. C. Pfeifer, Jutho Haegeman, and Frank Verstraete · 2014
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If the current clique algorithms are optimal, so is Valiant’s parser
Amir Abboud, Arturs Backurs, and Virginia Vassilevska Williams · 2015
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On traces of tensor representations of diagrams
Alexander Schrijver · 2015
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Finding four-node subgraphs in triangle time
Virginia Vassilevska Williams, Joshua R. Wang, Richard Ryan Williams, and Huacheng Yu · 2015
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Below all subsets for some permutational counting problems
Andreas Björklund · 2016
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A complete dichotomy rises from the capture of vanishing signatures
Jin-Yi Cai, Heng Guo, and Tyson Williams · 2016
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The arithmetic complexity of tensor contraction
Florent Capelli, Arnaud Durand, and Stefan Mengel · 2016
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Andrzej Cichocki, Namgil Lee, Ivan V. Oseledets, Anh Huy Phan, Qibin Zhao, and Danilo P. Mandic · 2016
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