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

Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jon Barron, Ren Ng

Spotlight presentation: Orals & Spotlights Track 26: Graph/Relational/Theory
on 2020-12-10T08:00:00-08:00 - 2020-12-10T08:10:00-08:00
Poster Session 6 (more posters)
on 2020-12-10T09:00:00-08:00 - 2020-12-10T11:00:00-08:00
GatherTown: Theory ( Town D2 - Spot A3 )
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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 has impractically slow convergence to high frequency signal components. 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.

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