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Stability Conditions of Bicomplex-Valued Hopfield Neural Networks
Neural Computation ( IF 2.9 ) Pub Date : 2021-02-01 , DOI: 10.1162/neco_a_01350
Masaki Kobayashi 1
Affiliation  

Hopfield neural networks have been extended using hypercomplex numbers. The algebra of bicomplex numbers, also referred to as commutative quaternions, is a number system of dimension 4. Since the multiplication is commutative, many notions and theories of linear algebra, such as determinant, are available, unlike quaternions. A bicomplex-valued Hopfield neural network (BHNN) has been proposed as a multistate neural associative memory. However, the stability conditions have been insufficient for the projection rule. In this work, the stability conditions are extended and applied to improvement of the projection rule. The computer simulations suggest improved noise tolerance.

中文翻译:

双复值Hopfield神经网络的稳定性条件

Hopfield 神经网络已经使用超复数进行了扩展。双复数的代数,也称为可交换四元数,是一个 4 维数系统。由于乘法是可交换的,因此与四元数不同,线性代数的许多概念和理论(例如行列式)都是可用的。已经提出了双复合值 Hopfield 神经网络 (BHNN) 作为多状态神经联想记忆。然而,投影规则的稳定性条件已经不足。在这项工作中,稳定性条件被扩展并应用于改进投影规则。计算机模拟表明改进的噪声容限。
更新日期:2021-02-01
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