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Hyperbolic Hopfield neural networks with four‐state neurons
Author(s) -
Kobayashi Masaki
Publication year - 2017
Publication title -
ieej transactions on electrical and electronic engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 30
eISSN - 1931-4981
pISSN - 1931-4973
DOI - 10.1002/tee.22394
Subject(s) - geometric algebra , quaternion , artificial neural network , clifford algebra , hopfield network , algebra over a field , stability (learning theory) , computer science , types of artificial neural networks , recurrent neural network , cellular neural network , hyperbolic function , mathematics , algorithm , pure mathematics , artificial intelligence , geometry , machine learning
In recent years, applications of neural networks with Clifford algebra have become widespread. Clifford algebra is also referred to as geometric algebra and is useful in dealing with geometric objects. Hopfield neural networks with Clifford algebra, such as complex numbers and quaternions, have been proposed. However, it has been difficult to construct Hopfield neural networks by Clifford algebra with positive part of the signature, such as hyperbolic numbers. Hyperbolic numbers are useful algebra to deal with hyperbolic geometry. Kuroe proposed hyperbolic Hopfield neural networks and provided their continuous activation functions and stability conditions. However, the learning algorithm has not been provided. In this paper, we provide two quantized activation functions and the primitive learning algorithm satisfying the stability condition. We also perform computer simulations and compare the activation functions. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.