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

• URL: http://arxiv.org/abs/2006.10739v1
• Date: Thu, 18 Jun 2020 17:59:11 GMT
• Title: Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
• Authors: Matthew Tancik, Pratul P. Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T. Barron, Ren Ng
• Abstract summary: We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron to learn high-frequency functions. Results shed light on advances in computer vision and graphics that achieve state-of-the-art results.
• Score: 69.62456877209304
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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