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.

通过将输入点通过简单的傅里叶特征映射传递，使得多层感知机（MLP）能够学习低维问题领域中的高频函数。研究结果对计算机视觉和图形学领域中使用 MLP 表示复杂 3D 对象和场景的最新进展提供了启示。通过神经切比雪夫核（NTK）文献中的工具，我们展示了标准 MLP 在理论和实践中都无法学习高频的结论。为了克服这种频谱偏差，我们使用傅里叶特征映射将有效的 NTK 转换为带有可调节带宽的平稳核。我们提出了一种选择问题特定的傅里叶特征的方法，极大地提高了 MLP 在与计算机视觉和图形学相关的低维回归任务中的性能。