A Neural Transfer Function for a Smooth and Differentiable Transition Between Additive and Multiplicative Interactions
This addresses a bottleneck in neural network design for researchers and practitioners by providing a more efficient and trainable approach to combining operations, though it appears incremental as it builds on existing concepts of functional iteration.
The paper tackles the problem of inefficient or computationally expensive methods for combining additive and multiplicative neural units by introducing a parameterizable transfer function that smoothly and differentiably adjusts between addition and multiplication, enabling integration into standard backpropagation training.
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.