  Existing approaches to combine both additive and multiplicative neural units
either use a fixed assignment of operations or require discrete optimization to
determine what function a neuron should perform. This leads either to an
inefficient distribution of computational resources or an extensive increase in
the computational complexity of the training procedure.
  We present a novel, parameterizable transfer function based on the
mathematical concept of non-integer functional iteration that allows the
operation each neuron performs to be smoothly and, most importantly,
differentiablely adjusted between addition and multiplication. This allows the
decision between addition and multiplication to be integrated into the standard
backpropagation training procedure.
