Abstract
Complex-valued Hopfield neural networks have been extended to several high-dimensional Hopfield neural networks (HDHNNs) using hypercomplex numbers. However, the extensions by hypercomplex numbers are limited. For example, the dimensions of Clifford and Cayley-Dickson algebras are power of two. Group theory provides more various algebras since the orders of groups are any. In this work, Klein four-group is introduced to HDHNNs. It is an abelian group whose order is 4. A Klein Hopfield neural network employs the twin-multistate activation function. We compare the noise tolerance with that of quaternion-valued and commutative quaternion-valued twin-multistate Hopfield neural networks by computer simulations.
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