A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. A quaternion-valued Hopfield neural network (QHNN) with a twin-multistate activation function was proposed to reduce the number of weight parameters of CHNN. Dual connections (DCs) are introduced to the QHNNs to improve the noise tolerance. The DCs take advantage of the noncommutativity of quaternions and consist of two weights between neurons. A QHNN with DCs provides much better noise tolerance than a CHNN. Although a CHNN and a QHNN with DCs have the samenumber of weight parameters, the storage capacity of projection rule for QHNNs with DCs is half of that for CHNNs and equals that of conventional QHNNs. The small storage capacity of QHNNs with DCs is caused by projection rule, not the architecture. In this work, the ebbian rule is introduced and proved by stochastic analysis that the storage capacity of a QHNN with DCs is 0.8 times as many as that of a CHNN.

中文翻译：

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具有双连接的四元数值 Hopfield 神经网络的存储容量。

复值 Hopfield 神经网络 (CHNN) 是一种多态 Hopfield 模型。提出了具有双多态激活函数的四元数值 Hopfield 神经网络 (QHNN) 以减少 CHNN 的权重参数数量。QHNN 中引入了双连接 (DC) 以提高噪声容限。DC 利用四元数的非对易性，并由神经元之间的两个权重组成。带有 DC 的 QHNN 提供比 CHNN 更好的噪声容限。虽然一个 CHNN 和一个带有 DC 的 QHNN 具有相同数量的权重参数，但是带有 DC 的 QHNN 的投影规则的存储容量是 CHNN 的一半，并且等于传统 QHNN 的投影规则。带有 DC 的 QHNN 的小存储容量是由投影规则而不是架构引起的。在这项工作中，