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

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-05-01 DOI:10.1016/j.cam.2025.116730

Sergio López-Ureña

引用次数: 0

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.

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激活功能可以在不改变结果的情况下增加神经元和层

在这项工作中，我们提出了神经元网络的激活函数，这些函数是可细化的，并对恒等式求和。这类新的激活函数允许在现有层之间插入新的层和/或增加一层中的神经元，两者都不会改变网络的输出。我们的方法以细分理论为基础。所提出的激活函数由收敛细分格式的基本极限函数构造而成。为了展示我们的结果，我们介绍了一系列样条激活函数，并提供了它们实际实现的全面细节。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.