Autoassociative Hamming Neural Network

An autoassociative neural network is suggested which is based on the calculation of Hamming distances, while the principle of its operation is similar to that of the Hopfield neural network. Using standard patterns as an example, we compare the efficiency of pattern recognition for the autoassociative Hamming network and the Hopfield network. It is shown that the autoassociative Hamming network successfully recognizes standard patterns with a degree of distortion up to $40\%$ and more than $60\%$, while the Hopfield network ceases to recognize the same patterns with a degree of distortion of more than $25\%$ and less than $75\%$. A scheme of the autoassociative Hamming neural network based on McCulloch – Pitts formal neurons is proposed. It is shown that the autoassociative Hamming network can be considered as a dynamical system which has attractors that correspond to the reference patterns. The Lyapunov function of this dynamical system is found and the equations of its evolution are derived.