A Neural Transfer Function for a Smooth and Differentiable Transition Between Additive and Multiplicative Interactions

TL;DR

This paper introduces a novel neural transfer function that enables smooth, differentiable transitions between additive and multiplicative neuron operations, streamlining the integration of mixed interactions into neural networks.

Contribution

A new parameterizable transfer function based on non-integer functional iteration allows neurons to smoothly and differentiably switch between addition and multiplication during training.

Findings

Enables seamless transition between additive and multiplicative operations

Integrates operation choice into standard backpropagation training

Reduces computational complexity compared to previous 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. 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.