SYNTOLOGY HomeExplorerAtlasCodeMethodologyAboutDevelopersFeedPricing
Paper · 1901.06523 · 2019

Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 8 functions out of this paper's own repositories and ran 7 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
xuzhiqin1990/F-Principle reimplementation 4 of 5
xuzhiqin1990/mscalednn reimplementation 3 of 3
FunctionStatusWhere it lives
func0 Ran xuzhiqin1990/F-Principle/main_1d_20190924.py
pointer only (licence: NONE) · get_code("c567a9e22918a4b2")
getWeightNorm Ran xuzhiqin1990/F-Principle/BasicFunc.py
pointer only (licence: NONE) · get_code("eaec3a6ad43de50b")
getWeightNormLayer Ran xuzhiqin1990/F-Principle/BasicFunc.py
pointer only (licence: NONE) · get_code("47f4b6968afd11b4")
rand_bd Ran xuzhiqin1990/mscalednn/exp/sin_M/62178/code.py
pointer only (licence: NONE) · get_code("829510e90192ce5e")
rand_it Ran xuzhiqin1990/mscalednn/exp/sin_M/62178/code.py
pointer only (licence: NONE) · get_code("06d6c667e46ee123")
sigmoid Ran xuzhiqin1990/F-Principle/main_1d_20190924.py
pointer only (licence: NONE) · get_code("2d3e248be1323d2c")
u Ran xuzhiqin1990/mscalednn/exp/sin_M/62178/code.py
pointer only (licence: NONE) · get_code("71f9d808a0cde4de")
plot_w Not yet run xuzhiqin1990/F-Principle/BasicFunc.py
pointer only (licence: NONE) · get_code("cc48b19eaf790f9e")

Repositories linked to this paper

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

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.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("1901.06523")
get_code_for_paper("1901.06523")
have("1901.06523")

Connect an agent — have() is free.