tancik/fourier-feature-networks
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
repo name | tancik/fourier-feature-networks |
repo link | https://github.com/tancik/fourier-feature-networks |
homepage | https://people.eecs.berkeley.edu/~bmild/fourfeat/ |
language | Jupyter Notebook |
size (curr.) | 10237 kB |
stars (curr.) | 290 |
created | 2020-06-16 |
license | MIT License |
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
Project Page | Paper
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
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.