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Uniqueness Theorem of ComplexValued Neural Networks with PolarRepresented Activation Function
Masaki KOBAYASHI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E98A
No.9
pp.19371943 Publication Date: 2015/09/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E98.A.1937
Type of Manuscript: PAPER Category: Nonlinear Problems Keyword: complexvalued neural networks, activation function, reducibility, uniqueness theorem,
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Summary:
Several models of feedforward complexvalued neural networks have been proposed, and those with split and polarrepresented activation functions have been mainly studied. Neural networks with split activation functions are relatively easy to analyze, but complexvalued neural networks with polarrepresented functions have many applications but are difficult to analyze. In previous research, Nitta proved the uniqueness theorem of complexvalued neural networks with split activation functions. Subsequently, he studied their critical points, which caused plateaus and local minima in their learning processes. Thus, the uniqueness theorem is closely related to the learning process. In the present work, we first define three types of reducibility for feedforward complexvalued neural networks with polarrepresented activation functions and prove that we can easily transform reducible complexvalued neural networks into irreducible ones. We then prove the uniqueness theorem of complexvalued neural networks with polarrepresented activation functions.

