Citation: | ZHANG Junwei and LI Zhao, “Quantum Contextuality for Training Neural Networks,” Chinese Journal of Electronics, vol. 29, no. 6, pp. 1178-1184, 2020, doi: 10.1049/cje.2020.10.003 |
I. Goodfellow, Y. Bengio, A. Courville, et al., "Deep learning", Cambridge:MIT press, 2016.
|
Y. Bengio, "Learning deep architectures for AI", Now Publishers Inc, 2009.
|
W.U. Yujia, L.I. Jing, S. Chengfang, et al., "Words in Pairs Neural Networks for Text Classification", Chinese Journal of Electronics, Vol.29, No.3, pp.491-500, 2020.
|
Y. Bengio, "Practical recommendations for gradient-based training of deep architectures", Neural networks:Tricks of the trade, Berlin, Heidelberg, pp.437-478, 2012.
|
L.N. Smith, "Cyclical learning rates for training neural networks", IEEE Winter Conference on Applications of Computer Vision, pp.464-472, 2017.
|
Y. Dauphin, H.D. Vries and Y. Bengio, "Equilibrated adaptive learning rates for non-convex optimization", Advances in neural information processing systems, pp.1504-1512, 2015.
|
C. Gulcehre, M. Moczulski and Y. Bengio, "Adasecant:robust adaptive secant method for stochastic gradient", arXiv preprint arXiv:1412.7419, 2014.
|
A. Krogh and J.A. Hertz, "A simple weight decay can improve generalization", Advances in neural information processing systems. pp.950-957, 1992.
|
P. Kurzyński, R. Ramanathan and D. Kaszlikowski, "Entropic test of quantum contextuality", Physical review letters, Vol.109, No.2, pp.020-404, 2012.
|
A. Cabello, S. Severini and A. Winter, "Graph-theoretic approach to quantum correlations", Physical review letters, Vol.112, No.4, pp.040-401, 2014.
|
J.B. Vega, N. Delfosse, D.E. Browne, et al., "Contextuality as a resource for models of quantum computation with qubits", Physical review letters, Vol.119, No.12, pp.120-505, 2017.
|
A.W. Simmons, "How (Maximally) Contextual Is Quantum Mechanics?", Quantum, Probability, Logic. Springer, Cham, pp.505-519, 2020.
|
A. Grudka, K. Horodecki, M. Horodecki, et al., "Quantifying contextuality", Physical review letters, Vol.112, No.12, pp.120-401, 2014.
|
S. Mansfield, "The Mathematical Structure of Non-locality and Contextuality", 2013.
|
A. Cabello, S. Severini and A. Winter, "(Non-) contextuality of physical theories as an axiom", arXiv preprint arXiv:1010.2163, 2010.
|
S. Kochen, and E.P. Specker, "The problem of hidden variables in quantum mechanics", The logico-algebraic approach to quantum mechanics. Springer, Dordrecht, pp.293-328, 1975.
|
S. Popescu and D. Rohrlich, "Quantum nonlocality as an axiom", Foundations of Physics, Vol.24, No.3, pp.379-385, 1994.
|
H.W. Lin, M. Tegmark and D. Rolnick, "Why does deep and cheap learning work so well?", Journal of Statistical Physics, Vol.168, No.6, pp.1223-1247, 2017.
|
K. Horodecki, M. Horodecki, P. Horodecki, et al., "Contextuality offers device-independent security", arXiv preprint arXiv:1006.0468, 2010.
|
L.I. Panchi and Z. Ya, "Model and algorithm of sequencebased quantum-inspired neural networks", Chinese Journal of Electronics, Vol.27, No.1, pp.9-18, 2018.
|
B.R. La Cour, "Quantum contextuality in the Mermin-Peres square:A hidden-variable perspective", Physical Review A, Vol.79, No.1, pp.012-102, 2009.
|
A.Y. Khrennikov, "Contextual approach to quantum formalism", Springer Science Business Media, 2009.
|
M. Kleinmann, O. Gühne, J.R. Portillo, et al., "Memory cost of quantum contextuality", New Journal of Physics, Vol.13, No.11, pp.113-011, 2011.
|
K. Svozil, "How much contextuality?", Natural Computing, Vol.11, No.2, pp.261-265, 2012.
|
A. Grudka, K. Horodecki, M. Horodecki, et al., "Quantifying contextuality", Physical review letters, Vol.1121, No.2, pp.120-401, 2014.
|
A.A. Klyachko, M.A. Can, S. Binicioğlu, et al., "Simple test for hidden variables in spin-1 systems", Physical review letters, Vol.101, No.2, pp.020-403, 2008.
|
S. Kochen and E.P. Specker, "The problem of hidden variables in quantum mechanics", The logico-algebraic approach to quantum mechanics. Springer, Dordrecht, pp.293-328, 1975.
|
S. Yu and C.H. Oh, "State-independent proof of KochenSpecker theorem with 13 rays", Physical review letters, Vol.108, No.3, pp.030-402, 2012.
|
L. Lovász, "On the Shannon capacity of a graph", IEEE Transactions on Information theory, Vol.25, No.1, pp.1-7, 1979.
|
M. Grötschel, L. Lovász and A. Schrijver, "The ellipsoid method and its consequences in combinatorial optimization", Combinatorica, Vol.1, No.2, pp.169-197, 1981.
|
Y. LeCun, C. Cortes and C.J. Burges, "MNIST handwritten digit database", http://yann.lecun.com/exdb/mnist, 2010-7-23.
|
H. Xiao, K. Rasul and R. Vollgraf, "Fashion-mnist:a novel image dataset for benchmarking machine learning algorithms", arXiv preprint arXiv:1708.07747, 2017.
|