Activation functions enabling the addition of neurons and layers without altering outcomes

TL;DR

This paper introduces a new class of activation functions that allow adding neurons or layers to neural networks without changing their outputs, enabling more flexible network modifications.

Contribution

We propose a novel class of activation functions based on subdivision theory that preserve network outputs when inserting neurons or layers.

Findings

Activation functions enable layer and neuron addition without output change.

Introduction of spline activation functions with practical implementation details.

Theoretical foundation based on subdivision schemes.

Abstract

In this work, we propose activation functions for neuronal networks that are refinable and sum the identity. This new class of activation functions allows the insertion of new layers between existing ones and/or the increase of neurons in a layer, both without altering the network outputs. Our approach is grounded in subdivision theory. The proposed activation functions are constructed from basic limit functions of convergent subdivision schemes. As a showcase of our results, we introduce a family of spline activation functions and provide comprehensive details for their practical implementation.