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Bicomplex Projection Rule for Complex-Valued Hopfield Neural Networks
Neural Computation ( IF 2.9 ) Pub Date : 2020-11-01 , DOI: 10.1162/neco_a_01320
Masaki Kobayashi 1
Affiliation  

A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should be simplified. In this work, the number of weight parameters is reduced by bicomplex projection rule for CHNNs, which is given by the decomposition of bicomplex-valued Hopfield neural networks. Computer simulations support that the noise tolerance of CHNN with a bicomplex projection rule is equal to or even better than that of quaternion- and bicomplex-valued Hopfield neural networks. By computer simulations, we find that the projection rule for hyperbolic-valued Hopfield neural networks in synchronous mode maintains a high noise tolerance.

中文翻译:

复值 Hopfield 神经网络的双复投影规则

具有多态激活函数的复值 Hopfield 神经网络 (CHNN) 是神经联想记忆的多态模型。权重参数需要大量内存资源。双多态激活函数被引入到四元数和双复数值的 Hopfield 神经网络中。由于它们的架构比 CHNN 复杂得多,因此应该简化架构。在这项工作中,权重参数的数量通过 CHNN 的双复投影规则减少,这是由双复值 Hopfield 神经网络的分解给出的。计算机模拟支持具有双复合投影规则的 CHNN 的噪声容限等于甚至优于四元数和双复合值 Hopfield 神经网络的噪声容限。通过计算机模拟,
更新日期:2020-11-01
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