Biradial transfer functions.

Wlodzislaw Duch, Norbert Jankowski

The most common transfer functions in neural networks are of the sigmoidal type. In this article other transfer functions are considered. Advantages of simple gaussians, giving hyperelliptical densities, and gaussian bar functions (sums of one-dimensional gaussians) are discussed. Bi-radial functions are formed from products of two sigmoids. Product of M bi-radial functions in N-dimensional parameter space give arbitrarily shaped densities offering great flexibility. Extensions of bi-radial functions are proposed. Bi-radial functions can be used as transfer functions in many neural networks, such as RBF, RAN or FSM systems.

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