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

arXiv: https://arxiv.org/abs/1503.05724 · HTML: https://mlsanity.com/paper/1503.05724/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2015.

## Built on by (most cited first, 3 of 3)

- [Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs](https://mlsanity.com/paper/2101.08366/) (2021)
- [Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions](https://mlsanity.com/paper/2301.04605/) (2023)
- [Ensemble Mask Networks](https://mlsanity.com/paper/2309.06382/) (2023)

## Abstract (arXiv)

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.