A Differentiable Transition Between Additive and Multiplicative Neurons

TL;DR

This paper introduces a differentiable transfer function enabling neural units to smoothly transition between additive and multiplicative operations, simplifying training and operation selection.

Contribution

It proposes a novel, parameterizable transfer function based on non-integer functional iteration that allows neurons to adaptively choose between addition and multiplication during training.

Findings

Enables neurons to smoothly transition between addition and multiplication.

Integrates operation choice into standard backpropagation training.

Reduces computational complexity compared to discrete optimization methods.

Abstract

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.