  Spectral analysis is a powerful tool, decomposing any function into simpler
parts. In machine learning, Mercer's theorem generalizes this idea, providing
for any kernel and input distribution a natural basis of functions of
increasing frequency. More recently, several works have extended this analysis
to deep neural networks through the framework of Neural Tangent Kernel. In this
work, we analyze the layer-wise spectral bias of Deep Neural Networks and
relate it to the contributions of different layers in the reduction of
generalization error for a given target function. We utilize the properties of
Hermite polynomials and Spherical Harmonics to prove that initial layers
exhibit a larger bias towards high-frequency functions defined on the unit
sphere. We further provide empirical results validating our theory in high
dimensional datasets for Deep Neural Networks.
