Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
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 most conventional iterative numerical schemes (e.g., Jacobi method), which exhibit faster convergence for higher frequencies for various scientific computing problems. With a simple theory, we illustrate that this F-Principle results from the 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 randomized dataset.
Keywords
Cite
@article{arxiv.1901.06523,
title = {Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks},
author = {Zhi-Qin John Xu and Yaoyu Zhang and Tao Luo and Yanyang Xiao and Zheng Ma},
journal= {arXiv preprint arXiv:1901.06523},
year = {2024}
}
Comments
Paper is published in Communications in Computational Physics