/fourier-feature-networks

Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains

Primary LanguageJupyter NotebookMIT LicenseMIT

Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains

Project Page | Paper

Open Demo in Colab

Matthew Tancik*1, Pratul P. Srinivasan*1,2, Ben Mildenhall*1, Sara Fridovich-Keil1, Nithin Raghavan1, Utkarsh Singhal1, Ravi Ramamoorthi3, Jonathan T. Barron2, Ren Ng1

1UC Berkeley, 2Google Research, 3UC San Diego
*denotes equal contribution

Abstract

Teaser Image

We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP fails to learn high frequencies both in theory and in practice. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.

Code

We provide a demo IPython notebook as a simple reference for the core idea. The scripts used to generate the paper plots and tables are located in the Experiments directory.