Lie Algebra-Valued Hopfield Neural Networks

This paper introduces Lie algebra-valued Hopfield neural networks, for which the states, outputs, weights and thresholds are all from a Lie algebra. This type of networks represents an alternative generalization of the real-valued neural networks besides the complex-, hyperbolic-, quaternion-, and Clifford-valued neural networks that have been intensively studied over the last few years. The dynamics of these networks from the energy function point of view is studied by giving the expression of such a function and proving that it is indeed an energy function for the proposed network.