ヒッツェル,エクハルト   HITZER, Eckhard
  ヒッツェル, エクハルト
   所属   国際基督教大学教養学部 アーツ・サイエンス学科
   職種   上級准教授
言語種別 英語
発行・発表の年月 2011
形態種別 研究論文(研究会,シンポジウム資料等)
査読 査読あり
標題 Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions
執筆形態 単著
掲載誌名 Proceedings of the First SICE Symposium on Computational Intelligence
掲載区分国内
巻・号・頁 pp.23-28
担当範囲 Everything.
著者・共著者 HITZER Eckhard
概要 The Liouville theorem states that bounded holomorphic complex functions are necessarily constant. Holomorphic functions fulfill the socalled Cauchy-Riemann (CR) conditions. The CR conditions mean that a complex z-derivative is independent of the direction. Holomorphic functions are ideal for activation functions of complex neural networks, but the Liouville theorem makes them useless. Yet recently the use of hyperbolic numbers, lead to the construction of hyperbolic number neural networks. We will describe the Cauchy-Riemann conditions for hyperbolic numbers and show that there exists a new interesting type of bounded holomorphic functions of hyperbolic numbers, which are not constant. We give examples of such functions. They therefore substantially expand the available candidates for holomorphic activation functions for hyperbolic number neural networks.