  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.
