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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
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Year:    2020

Author:    Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1746–1767

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0085

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1746–1767

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Deep learning training behavior generalization Jacobi iteration Fourier analysis.

Author Details

Zhi-Qin John Xu

Yaoyu Zhang

Tao Luo

Yanyang Xiao

Zheng Ma

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  83. The Rossby Normal Mode as a Physical Linkage in a Machine Learning Forecast Model for the SST and SSH of South China Sea Deep Basin

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