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
on 2020-12-10T08:00:00-08:00 - 2020-12-10T08:10:00-08:00
Toggle Abstract Paper (in Proceedings / .pdf)
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.