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.
Furthermore REF introduced a parametric activation function to smoothly interpolate the operation a neuron performs on its inputs between addition and multiplication, thus allowing the most appropriate operation to be determined during training.
A Neural Transfer Function for a Smooth and Differentiable Transition Between Additive and Multiplicative Interactions
ArXiv
ArXiv
Mathematics Computer Science