Deep and wide neural networks covariance estimation

It has been recently shown that a deep neural network with i.i.d. random parameters is equivalent to a Gaussian process in the limit of infinite network width. The Gaussian process associated to the neural network is fully described by a recursive covariance kernel determined by the architecture of...

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Detalles Bibliográficos
Autores: Arratia Quesada, Argimiro Alejandro|||0000-0003-1551-420X, Cabaña Nigro, Ana Alejandra, León, José Rafael
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/407308
Acceso en línea:https://hdl.handle.net/2117/407308
https://dx.doi.org/10.1007/978-3-030-61609-0_16
Access Level:acceso abierto
Palabra clave:Neural Networks
Deep neural networks
Gaussian process
Kernels
Hermite polynomials
Xarxes neuronals (Informàtica)
Àrees temàtiques de la UPC::Informàtica
Descripción
Sumario:It has been recently shown that a deep neural network with i.i.d. random parameters is equivalent to a Gaussian process in the limit of infinite network width. The Gaussian process associated to the neural network is fully described by a recursive covariance kernel determined by the architecture of the network, and which is expressed in terms of expectation. We give a numerically workable analytic expression of the neural network recursive covariance based on Hermite polynomials. We give explicit forms of this recursive covariance for the cases of neural networks with activation function the Heaviside, ReLU and sigmoid.