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The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions.
1903
Earlier work this paper cites.
C. Baldassi, F. Pittorino, and R. Zecchina, Proceedings of the National Academy of Sciences 117
1905
Earlier work this paper cites.
C. Baldassi, E. M. Malatesta, and R. Zecchina, Physical Review Letters 123
1907
Earlier work this paper cites.
1908
Earlier work this paper cites.
S. Goldt, M. Mézard, F. Krzakala, and L. Zdeborová, Physical Review X 10
1909
Earlier work this paper cites.
W. Kibble, Mathematical Proceedings of the Cambridge Philosophical Society 41
1945
Earlier work this paper cites.
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables , Vol. 55 (US Government printing office, 1948)
1948
Earlier work this paper cites.
T. M. Cover, IEEE transactions on electronic computers , 326 (1965)
1965
Earlier work this paper cites.
M. Mézard, G. Parisi, and M. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications , Vol. 9 (World Scientific Publishing Company, 1987)
1987
Earlier work this paper cites.
E. Gardner, Journal of Physics A: Mathematical and General 21
1988
Earlier work this paper cites.
E. Gardner and B. Derrida, Journal of Physics A: Mathematical and General 21
1988
Earlier work this paper cites.
G. Cybenko, Mathematics of control, signals and systems 2
1989
Earlier work this paper cites.
K. Hornik, M. Stinchcombe, H. White, et al. , Neural networks 2
1989
Earlier work this paper cites.
G. Mitchison and R. Durbin, Biological Cybernetics 60
1989
Earlier work this paper cites.
This divergence is slow, with α c ∼ l o g K \alpha_{c}\sim\sqrt{\mathop{log}\nolimits K} Monasson and Zecchina 1995 ; Mitchison and Durbin 1989 ; we provide a detailed discussion of this and other finite-size effects in Appendix A
1989
Earlier work this paper cites.
J. Hertz, A. Krogh, and R. G. Palmer, Introduction to the Theory of Neural Computation (CRC Press, 1991)
1991
Earlier work this paper cites.
E. Barkai, D. Hansel, and H. Sompolinsky, Physical Review A 45
1992
Earlier work this paper cites.
A. Engel, H. Köhler, F. Tschepke, H. Vollmayr, and A. Zippelius, Physical Review A 45
1992
Earlier work this paper cites.
R. Monasson and R. Zecchina, Physical Review Letters 75
1995
Cited alongside, same era.
R. Urbanczik, Journal of Physics A: Mathematical and General 30
1997
Cited alongside, same era.
V. I. Bogachev, Gaussian measures (American Mathematical Society, 1998)
1998
Cited alongside, same era.
R. H. Byrd, J. C. Gilbert, and J. Nocedal, Mathematical Programming 89
2000
Cited alongside, same era.
A. Engel and C. Van den Broeck, Statistical mechanics of learning (Cambridge University Press, 2001)
2001
Cited alongside, same era.
B. Willmore and D. J. Tolhurst, Network: Computation in Neural Systems 12
2001
Cited alongside, same era.
D. Breuer, M. Timme, and R.-M. Memmesheimer, Physical Review X 4
2014
Later among the works it cites.
D. P. Kingma and J. Ba, arXiv preprint arXiv:1412.6980 (2014)
2014
Later among the works it cites.
Y. LeCun, Y. Bengio, and G. Hinton, Nature 521
2015
Later among the works it cites.
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems,” (2015), software available from tensorflow.org
2015
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2002
Cited alongside, same era.
D. Pollard, A user’s guide to measure theoretic probability , Vol. 8 (Cambridge University Press, 2002)
2002
Cited alongside, same era.
M. Talagrand, Spin glasses: a challenge for mathematicians: cavity and mean field models , Vol. 46 (Springer Science & Business Media, 2003)
2003
Cited alongside, same era.
P. Poirazi, T. Brannon, and B. W. Mel, Neuron 37
2003
Cited alongside, same era.
M. Shcherbina and B. Tirozzi, Communications in Mathematical Physics 234
2003
Cited alongside, same era.
A. Mozeika, B. Li, and D. Saad, Physical Review Letters 125
2004
Cited alongside, same era.
Later among the works it cites.
2016
Later among the works it cites.
2016
Later among the works it cites.
I. Goodfellow, Y. Bengio, and A. Courville, Deep learning (MIT press, 2016)
2016
Later among the works it cites.
P. Ramachandran, B. Zoph, and Q. V. Le, arXiv preprint arXiv:1710.05941 (2017), arXiv:1710.05941
2017
Later among the works it cites.
2018
Later among the works it cites.
M. Belkin, D. Hsu, S. Ma, and S. Mandal, Proceedings of the National Academy of Sciences 116
2019
Later among the works it cites.
In the published version of their Letter, Baldassi et al. 2019 reported a value of α 1-RSB ≃ 2.92 \alpha_{\textrm{1-RSB}}\simeq 2.92 . After the appearance of our work in preprint form, they found that this result was incorrect (see Appendix F
2019
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2019
Later among the works it cites.
2019
Later among the works it cites.
A. Payeur, J.-C. Béïque, and R. Naud, Current Opinion in Neurobiology 58
2019
Later among the works it cites.
L. Zdeborová, Nature Physics 16
2020
Closest in time.
P. Poirazi and A. Papoutsi, Nature Reviews Neuroscience 21
2020
Closest in time.
A. Gidon, T. A. Zolnik, P. Fidzinski, F. Bolduan, A. Papoutsi, P. Poirazi, M. Holtkamp, I. Vida, and M. E. Larkum, Science 367
2020
Closest in time.