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At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods.
Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
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Multilayer feedforward networks with a non-polynomial activation function can approximate any function
M. Leshno, V. Lin, A. Pinkus, and S. Schocken · 1993
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Bayesian Learning for Neural Networks
R. M. Neal · 1996
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Nonlinear component analysis as a kernel eigenvalue problem
B. Schölkopf, A. Smola, and K.-R. Müller · 1998
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Some Gronwall Type Inequalities and Applications
S. S. Dragomir · 2003
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Kernel Methods for Pattern Analysis
J. Shawe-Taylor and N. Cristianini · 2004
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Random features for large-scale kernel machines
A. Rahimi and B. Recht · 2008
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Kernel methods for deep learning
Y. Cho and L. K. Saul · 2009
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Strictly and non-strictly positive definite functions on spheres
T. Gneiting · 2013
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Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Y. N. Dauphin, R. Pascanu, C. Gulcehre, K. Cho, S. Ganguli, and Y. Bengio · 2014
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Generative Adversarial Networks
I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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On the saddle point problem for non-convex optimization
R. Pascanu, Y. N. Dauphin, S. Ganguli, and Y. Bengio · 2014
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The Loss Surfaces of Multilayer Networks
A. Choromanska, M. Henaff, M. Mathieu, G. B. Arous, and Y. LeCun · 2015
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Toward deeper understanding of neural networks: The power of initialization and a dual view on expressivity
A. Daniely, R. Frostig, and Y. Singer · 2016
Empirical analysis of the hessian of over-parametrized neural networks
L. Sagun, U. Evci, V. U. Güney, Y. Dauphin, and L. Bottou · 2017
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Understanding deep learning requires rethinking generalization
C. Zhang, S. Bengio, M. Hardt, B. Recht, and O. Vinyals · 2017
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To understand deep learning we need to understand kernel learning
M. Belkin, S. Ma, and S. Mandal · 2018
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Gaussian process behaviour in wide deep neural networks
A. G. de G. Matthews, J. Hron, M. Rowland, R. E. Turner, and Z. Ghahramani · 2018
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Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach
R. Karakida, S. Akaho, and S.-i. Amari · 2018
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Deep neural networks as gaussian processes
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Sample-then-optimize posterior sampling for bayesian linear models
A. G. de G. Matthews, J. Hron, R. E. Turner, and Z. Ghahramani · 2017
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Geometry of neural network loss surfaces via random matrix theory
J. Pennington and Y. Bahri · 2017
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J. H. Lee, Y. Bahri, R. Novak, S. S. Schoenholz, J. Pennington, and J. Sohl-Dickstein · 2018
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A mean field view of the landscape of two-layer neural networks
S. Mei, A. Montanari, and P.-M. Nguyen · 2018
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