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Existing approaches to combine both additive and multiplicative neural unitseither use a fixed assignment of operations or require discrete optimization todetermine what function a neuron should perform. This leads either to aninefficient distribution of computational resources or an extensive increase inthe computational complexity of the training procedure.  We present a novel, parameterizable transfer function based on themathematical concept of non-integer functional iteration that allows theoperation each neuron performs to be smoothly and, most importantly,differentiablely adjusted between addition and multiplication. This allows thedecision between addition and multiplication to be integrated into the standardbackpropagation training procedure.

A Neural Transfer Function for a Smooth and Differentiable Transition Between Additive and Multiplicative Interactions