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There is a recent and growing literature on large-width asymptotic and non-asymptotic properties of deep Gaussian neural networks (NNs), namely NNs with weights initialized as Gaussian distributions.
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Bounds on Moments of Certain Random Variables
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The path resistance method for bounding the smallest nontrivial eigenvalue of a laplacian
S. Guattery, F. Thomson Leighton, and G.L. Miller · 1999
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S4 classes for distributions
P. Ruckdeschel, M. Kohl, T. Stabla, and F. Camphausen · 2006
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Fluctuations of eigenvalues and second order Poincaré inequalities
S. Chatterjee · 2009
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Second order poincaré inequalities and clts on wiener space
I. Nourdin, G. Peccati, and G. Reinert · 2009
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Normal approximation with Malliavin calculus: from Stein’s method to universality
I. Nourdin and G. Peccati · 2012
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Normal approximation on poisson spaces: Mehler’s formula, second order poincaré inequalities and stabilization
G. Last, G. Peccati, and M. Schulte · 2016
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Deep convolutional networks as shallow gaussian processes
A. Garriga-Alonso, C. Rasmussen, and L. Aitchison · 2018
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Gaussian process behaviour in wide deep neural networks
A. Matthews, J. Hron, M. Rowland, R.E. Turner, and Z. Ghahramani · 2018
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Bayesian deep convolutional networks with many channels are gaussian processes
R. Novak, L. Xiao, Y. Bahri, J. Lee, G. Yang, J. Hron, D.A. Abolafia, J. Pennington, and J. Sohl-dickstein · 2018
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Finite size corrections for neural network gaussian processes
J. Antognini · 2019
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On the asymptotics of wide networks with polynomial activations
K. Aitken and G. Gur-Ari · 2020
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Deep Stable neural networks: large-width asymptotics and convergence rates
S. Favaro, S. Fortini, and S. Peluchetti · 2022
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Rate of convergence of polynomial networks to gaussian processes
A. Klukowski · 2022
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transport: Computation of Optimal Transport Plans and Wasserstein Distances , 2022
D. Schuhmacher, B. Bähre, C. Gottschlich, V. Hartmann, F. Heinemann, and B. Schmitzer · 2022
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Normal approximation of random gaussian neural networks
N. Apollonio, D. De Canditiis, G. Franzina, P. Stolfi, and G.L. Torrisi · 2023
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A quantitative functional central limit theorem for shallow neural networks
Valentina Cammarota, Domenico Marinucci, Michele Salvi, and Stefano Vigogna · 2023
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A. Andreassen and E. Dyer · 2020
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An improved second-order poincaré inequality for functionals of gaussian fields
A. Vidotto · 2020
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Tensor programs I: Wide feedforward or recurrent neural networks of any architecture are gaussian processes
G. Yang · 2020
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Large-width functional asymptotics for deep Gaussian neural network
D. Bracale, S. Favaro, S. Fortini, and S. Peluchetti · 2021
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Non-asymptotic approximations of neural networks by gaussian processes
R. Eldan, D. Mikulincer, and T. Schramm · 2021
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Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks
A. Basteri and D. Trevisan · 2022
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Deep neural networks as gaussian processes
J. Lee, Y. Bahri, R. Novak, S. Schoenholz, J. Pennington, and J. Sohl-Dickstein
Cited in the paper.
S. Favaro, B. Hanin, D. Marinucci, I. Nourdin, and G. Peccati · 2023
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Random neural networks in the infinite width limit as Gaussian processes
B. Hanin · 2023
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Wide deep neural networks with gaussian weights are very close to gaussian processes
D. Trevisan · 2023
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Gaussian random field approximation via Stein’s method with applications to wide random neural networks
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Deep neural networks with dependent weights: Gaussian process mixture limit, heavy tails, sparsity and compressibility
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