On the Activation Function Dependence of the Spectral Bias of Neural Networks. (arXiv:2208.04924v2 [cs.LG] UPDATED)

Neural networks are universal function approximators which are known to
generalize well despite being dramatically overparameterized. We study this
phenomenon from the point of view of the spectral bias of neural networks. Our
contributions are two-fold. First, we provide a theoretical explanation for the
spectral bias of ReLU neural networks by leveraging connections with the theory
of finite element methods. Second, based upon this theory we predict that
switching the activation function to a piecewise linear B-spline, namely the
Hat …

arxiv bias function lg networks neural networks