@Article{CiCP-28-1746,
author = {John Xu , Zhi-QinZhang , YaoyuLuo , TaoXiao , Yanyang and Ma , Zheng},
title = {Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {5},
pages = {1746--1767},
abstract = {<p style="text-align: justify;">We study the training process of Deep Neural Networks (DNNs) from the
Fourier analysis perspective. We demonstrate a very universal Frequency Principle
(F-Principle) — DNNs often fit target functions from low to high frequencies — on
high-dimensional benchmark datasets such as MNIST/CIFAR10 and deep neural networks such as VGG16. This F-Principle of DNNs is opposite to the behavior of Jacobi
method, a conventional iterative numerical scheme, which exhibits faster convergence
for higher frequencies for various scientific computing problems. With theories under an idealized setting, we illustrate that this F-Principle results from the smoothness/regularity of the commonly used activation functions. The F-Principle implies
an implicit bias that DNNs tend to fit training data by a low-frequency function. This
understanding provides an explanation of good generalization of DNNs on most real
datasets and bad generalization of DNNs on parity function or a randomized dataset.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0085},
url = {http://global-sci.org/intro/article_detail/cicp/18395.html}
}