On the design of Hopfield Neural Networks: Synthesis of hopfield type associative memories

In this research paper, it is proved that it is impossible to design a Hopfield Neural Network with orthogonal stable states ( corners of hypercube ) when the total number of neurons in the network ( dimension of network ) is odd. Also linear algebraic structure of associative memory synthesized by Hopfield is discussed. Using Hadamard matrix of suitable dimension, an algorithm to synthesize real valued Hopfield neural network is discussed. The design of a certain complex Hopfield neural network is addressed and solved. Also, synthesis of real and complex Hopfield type associative memories is discussed. This synthesis enables choice of stable states and the corresponding values of energy function.