Neural networks with adaptive spline activation function

In this paper a new neural network architecture, based on an adaptive activation function, called generalized sigmoidal neural network (GSNN), is proposed. The activation functions are usually sigmoidal but other functions, also depending on some free parameters, have been studied and applied. Most approaches tend to use relatively simple functions (as adaptive sigmoids), primarily due to computational complexity and difficulties hardware realization. The proposed adaptive activation function, built as a piecewise approximation with suitable cubic splines, can have arbitrary shape and allows to reduce the overall size of the neural networks, trading connection complexity with activation function complexity.