Sigmoidal Function Classes for Feedforward Artificial Neural Networks

The role of activation functions in feedforward artificial neural networks has not been investigated to the desired extent. The commonly used sigmoidal functions appear as discrete points in the sigmoidal functional space. This makes comparison difficult. Moreover, these functions can be interpreted as the (suitably scaled) integral of some probability density function (generally taken to be symmetric/bell shaped). Two parameterization methods are proposed that allow us to construct classes of sigmoidal functions based on any given sigmoidal function. The suitability of the members of the proposed class is investigated. It is demonstrated that all members of the proposed class(es) satisfy the requirements to act as an activation function in feedforward artificial neural networks.