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

arXiv: https://arxiv.org/abs/2006.10739 · HTML: https://mlsanity.com/paper/2006.10739/

## Key facts

- Cited by 2,200 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

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## Abstract (arXiv)

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.