Publication Date
2025
Document Type
Dissertation/Thesis
First Advisor
Krishtal, Ilya
Degree Name
M.S. (Master of Science)
Legacy Department
Department of Mathematical Sciences
Abstract
Neural networks have become central to modern natural science. One of the key components of these networks is the choice of a suitable activation function. In this manuscript, we explore the selection of an optimal activation function in the context of complex-valued neural networks. We aim to characterize the activation functions $\sigma\colon \mathbb{C} \rightarrow \mathbb{C}$, where each neuron performs the operation $\mathbb{C}^N \rightarrow \mathbb{C}$, defined as: $z \mapsto \sigma(b + w^Tz)$. First, we briefly discuss the real-valued counterpart, including the importance of function approximation and the renowned universal approximation theorem. Subsequently, we examine various criteria for complex activation functions that provide a universal network class for shallow and deep networks.
Recommended Citation
Mondal, Sauvik, "Universality of Complex Valued Neural Networks" (2025). Graduate Research Theses & Dissertations. 8127.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/8127
Extent
48 pages
Language
en
Publisher
Northern Illinois University
Rights Statement
In Copyright
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.
Media Type
Text
