On the fundamental properties of fully quaternionic hopfield network

Choosing an appropriate activation function is a challenging problem in quaternionic neural networks, due to the analyticity in quaternionic domain. This paper presents a Hopfield-type neural network with an activation function with quaternionic equivalent of tanh function. This activation function is obtained by incorporating so-called “local analyticity” on quaternionic domain and the recent results on complex-valued activation functions. The stability of the network is shown by proving monotonic decrease of energy with the changes of neuron states.