Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
This addresses a spectral bias issue in neural networks for computer vision and graphics, offering a practical solution to improve regression tasks in low-dimensional settings.
The paper tackles the problem of multilayer perceptrons (MLPs) failing to learn high-frequency functions in low-dimensional domains, and shows that using a Fourier feature mapping enables MLPs to achieve state-of-the-art performance in tasks like representing 3D objects and scenes.
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.