深度神经网络中的普适性：基于林德贝格交换原理的 approach
概率论
2026-05-05 v1 机器学习
机器学习
摘要
We consider the infinite-width limit of a fully connected deep neural network with general weights, and we prove quantitative general bounds on the -Wasserstein distance between the network and its infinite-width Gaussian limit, under appropriate regularity assumptions on the activation function. Our main tool is a Lindeberg principle for Deep Neural Networks, which we use to successively replace the weights on each layer by Gaussian random variables.
引用
@article{arxiv.2605.02771,
title = {Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle},
author = {Filippo Giovagnini and Sotirios Kotitsas and Marco Romito},
journal= {arXiv preprint arXiv:2605.02771},
year = {2026}
}
备注
22 pages, 2 figures