Constructing near-tight wavelet frames by neural networks
Xin Li · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
Suppose that (sigma) is a sigmoidal function which is the activation function of a neural network. Under certain assumptions on the derivatives of (sigma) , we show that a simple linear combination of dilates and translates of (sigma) generates a near tight wavelet frame for L2(R), which is then used in constructing approximation to multivariate functions by neural networks with one hidden layer.