Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks
Machine Learning
2023-09-25 v2 Probability
Machine Learning
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.
Cite
@article{arxiv.2203.07379,
title = {Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks},
author = {Andrea Basteri and Dario Trevisan},
journal= {arXiv preprint arXiv:2203.07379},
year = {2023}
}