A Differentiable Transition Between Additive and Multiplicative Neurons
This addresses the computational inefficiency in neural network design for researchers and practitioners, though it appears incremental as it builds on existing methods for combining operations.
The paper tackles the problem of combining additive and multiplicative neural units without fixed assignments or discrete optimization, which increases computational complexity, by introducing a parameterizable transfer function based on non-integer functional iteration that allows differentiable adjustment 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. However, this leads to 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.