A model of Hopfield-type octonion neural networks and existing conditions of energy functions
Yasuaki Kuroe, Hitoshi Iima · 2016
Recently, models of neural networks in the real domain have been extended into the high dimensional domain such as the complex number and quaternion domain, and several high-dimensional models have been proposed. These extensions are generalized by introducing Clifford algebra (geometric algebra). In this paper we extend conventional real-valued models of recurrent neural networks into the octonion domain and discuss their dynamics. The octonions represent a particular extension of the quaternions which also represent a particular extension of the complex numbers, They have 7 imaginary parts and do not belong to Clifford algebra. We present a model of fully connected recurrent neural networks, which are extensions of the real-valued Hopfield type neural networks to the octonion domain. We study dynamics of the models from the point view of existence conditions of an energy function. We derive existence conditions of an energy function for the Hopfield type octonion neural networks.