2018年5月
Hyperbolic Gradient Operator and Hyperbolic Back-Propagation Learning Algorithms
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
- ,
- 巻
- 29
- 号
- 5
- 開始ページ
- 1689
- 終了ページ
- 1702
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1109/TNNLS.2017.2677446
- 出版者・発行元
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
In this paper, we first extend the Wirtinger derivative which is defined for complex functions to hyperbolic functions, and derive the hyperbolic gradient operator yielding the steepest descent direction by using it. Next, we derive the hyperbolic backpropagation learning algorithms for some multilayered hyperbolic neural networks (NNs) using the hyperbolic gradient operator. It is shown that the use of the Wirtinger derivative reduces the effort necessary for the derivation of the learning algorithms by half, simplifies the representation of the learning algorithms, and makes their computer programs easier to code. In addition, we discuss the differences between the derived Hyperbolic-BP rules and the complex-valued backpropagation learning rule (Complex-BP). Finally, we make some experiments with the derived learning algorithms. As a result, we find that the convergence rates of the Hyperbolic-BP learning algorithms are high even if the fully activation functions are used, and discover that the Hyperbolic-BP learning algorithm for the hyperbolic NN with the split-type hyperbolic activation function has an ability to learn hyperbolic rotation as its inherent property.
- リンク情報
- ID情報
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- DOI : 10.1109/TNNLS.2017.2677446
- ISSN : 2162-237X
- eISSN : 2162-2388
- Web of Science ID : WOS:000430729100024