Fetching the paper…
Reading the bibliography…
Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data.
Kenneth G. Wilson, “Renormalization group and critical phenomena. i. renormalization group and the kadanoff scaling picture,” Phys. Rev. B 4
1971
Earlier work this paper cites.
Kenneth G. Wilson, “Problems in physics with many scales of length,” Scientific American , 158–179 (1979)
1979
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics 144
1992
Earlier work this paper cites.
Steven R. White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Stellan Östlund and Stefan Rommer, “Thermodynamic limit of density matrix renormalization,” Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
Barry Friedman, “A density matrix renormalization group approach to interacting quantum systems on cayley trees,” Journal of Physics: Condensed Matter 9
1997
Earlier work this paper cites.
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller, “Nonlinear component analysis as a kernel eigenvalue problem,” Neural Computation 10
1998
Earlier work this paper cites.
Bernhard Schölkopf, Ralf Herbrich, and Alex Smola, “A generalized representer theorem,” in Computational learning theory (Springer, 2001) pp. 416–426
2001
Earlier work this paper cites.
B. Scholkopf and A. Smola, Learning with kernels: Support Vector Machines, regularization, optimization, and beyond (MIT Press, 2001)
2001
Earlier work this paper cites.
Guifré Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, “Renormalization algorithms for quantum-many body systems in two and higher dimensions,” cond-mat/0407066 (2004)
2004
Earlier work this paper cites.
U. Schollwöck, “The density-matrix renormalization group,” Rev. Mod. Phys. 77
2005
Earlier work this paper cites.
Y.-Y. Shi, L.-M. Duan, and G. Vidal, “Classical simulation of quantum many-body systems with a tree tensor network,” Phys. Rev. A 74
2006
Earlier work this paper cites.
Ian P. McCulloch, “From density-matrix renormalization group to matrix product states,” J. Stat. Mech. , P10014 (2007)
2007
Earlier work this paper cites.
Michael Levin and Cody P. Nave, “Tensor renormalization group approach to two-dimensional classical lattice models,” Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix product state representations,” Quantum Info. Comput. 7
2007
Earlier work this paper cites.
2008
Earlier work this paper cites.
R. Orús and G. Vidal, “Infinite time-evolving block decimation algorithm beyond unitary evolution,” Phys. Rev. B 78
2008
Earlier work this paper cites.
Garnet Kin-Lic Chan, “Density matrix renormalization group lagrangians,” arxiv:0804.1755 (2008)
2008
Earlier work this paper cites.
M. Bañuls, D. Pérez-García, M.M. Wolf, F. Verstraete, and J.I. Cirac, “Sequentially generated states for the study of two-dimensional systems,” Phys. Rev. A 77
2008
Earlier work this paper cites.
Ali Rahimi and Benjamin Recht, “Random features for large-scale kernel machines,” in Advances in Neural Information Processing Systems 20 , edited by J. C. Platt, D. Koller, Y. Singer, and S. T. Roweis (Curran Associates, Inc., 2008) pp. 1177–1184
2008
Earlier work this paper cites.
Dumitru Erhan, Yoshua Bengio, Aaron Courville, and Pascal Vincent, “Visualizing higher-layer features of a deep network,” University of Montreal (2009)
2009
Cited alongside, same era.
G. Evenbly and G. Vidal, “Algorithms for entanglement renormalization,” Phys. Rev. B 79
2009
Cited alongside, same era.
W. Hackbusch and S. Kühn, “A new scheme for the tensor representation,” Journal of Fourier Analysis and Applications 15
2009
Cited alongside, same era.
Norbert Schuch, Ignacio Cirac, and David Pérez-García, “Peps as ground states: Degeneracy and topology,” Annals of Physics 325
2010
Cited alongside, same era.
E. M. Stoudenmire and Steven R. White, “Minimally entangled typical thermal state algorithms,” New Journal of Physics 12
2010
Cited alongside, same era.
2016
Later among the works it cites.
Nadav Cohen, Or Sharir, and Amnon Shashua, “On the expressive power of deep learning: A tensor analysis,” 29th Annual Conference on Learning Theory , 698–728 (2016)
2016
Later among the works it cites.
2016
Later among the works it cites.
2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Marcus Cramer, Martin B. Plenio, Steven T. Flammia, Rolando Somma, David Gross, Stephen D. Bartlett, Olivier Landon-Cardinal, David Poulin, and Yi-Kai Liu, “Efficient quantum state tomography,” Nature Communications 1
2010
Cited alongside, same era.
U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics 326
2011
Cited alongside, same era.
I. Oseledets, “Tensor-train decomposition,” SIAM Journal on Scientific Computing 33
2011
Cited alongside, same era.
Brian Swingle, “Entanglement renormalization and holography,” Phys. Rev. D 86
2012
Cited alongside, same era.
Masahiro Nozaki, Shinsei Ryu, and Tadashi Takayanagi, “Holographic geometry of entanglement renormalization in quantum field theories,” Journal of High Energy Physics 2012
2012
Cited alongside, same era.
Andrew J. Ferris and Guifre Vidal, “Perfect sampling with unitary tensor networks,” Phys. Rev. B 85
2012
Cited alongside, same era.
Michele Dolfi, Bela Bauer, Matthias Troyer, and Zoran Ristivojevic, “Multigrid algorithms for tensor network states,” Phys. Rev. Lett. 109
2012
Cited alongside, same era.
2016
Later among the works it cites.
2016
Later among the works it cites.
Serena Bradde and William Bialek, “ PCA
2016
Later among the works it cites.
Patrick Hayden, Sepehr Nezami, Xiao-Liang Qi, Nathaniel Thomas, Michael Walter, and Zhao Yang, “Holographic duality from random tensor networks,” Journal of High Energy Physics 2016
2016
Later among the works it cites.
2016
Later among the works it cites.
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
2017
Closest in time.
Han Xiao, Kashif Rasul, and Roland Vollgraf, “Fashion- MNIST
2017
Closest in time.
Alessandro Rudi, Luigi Carratino, and Lorenzo Rosasco, “ FALKON
2017
Closest in time.