A model of Hopfield-type octonion neural networks and existing conditions of energy functions
A model of Hopfield-type octonion neural networks and existing conditions of energy functions
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Hopfield型八元神经网络模型及能量函数存在条件
DOI：
10.1109/ijcnn.2016.7727778
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
H. Iima
中科院分区：
文献类型：
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作者：
Y. Kuroe;H. Iima
近年来，神经网络在实数域的模型已经扩展到复数、四元数域等高维领域，并提出了几种高维模型。这些推广是通过引入Clifford代数(几何代数)来推广的。本文将递归神经网络的传统实值模型推广到八元数域，并讨论了它们的动力学问题。八元数代表四元数的一个特殊扩张，也代表复数的一个特殊扩张，它们有7个虚部，不属于Clifford代数。我们提出了一种全连通递归神经网络模型，它是实值Hopfield型神经网络在八元数域上的推广。我们从能量函数存在条件的角度来研究模型的动力学。给出了Hopfield型八元数神经网络能量函数存在的条件。
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.
DOI：
10.1109/tnn.2006.872154
发表时间：
2003
期刊：
--
影响因子：
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作者：
廣瀬 明
通讯作者：
廣瀬 明