Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities indicate how the hidden and output layers sizes affect the Gaussian behaviour of the network and quantitatively recover the distributional convergence results in the wide limit, i.e., if all the hidden layers sizes become large.

QUANTITATIVE GAUSSIAN APPROXIMATION OF RANDOMLY INITIALIZED DEEP NEURAL NETWORKS

Trevisan, D.
2022-01-01

Abstract

Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities indicate how the hidden and output layers sizes affect the Gaussian behaviour of the network and quantitatively recover the distributional convergence results in the wide limit, i.e., if all the hidden layers sizes become large.
2022
Basteri, A.; Trevisan, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1259527
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