Convergence mechanism in associative memory

The convergence of vectors in Hopfield´s neural network is studied in terms of both inner products and Hamming distance. The various phases of vector convergence are revealed progressively. It is shown that Hamming distance does not always predict the convergence of the vectors. Instead, weights are found to play a dominant role in the convergence mechanism. The authors identify the factors that lead to correct convergence, complementary convergence, and nonconvergence for both unipolar and bipolar binary partial input vectors. An optimum mixed-mode representation for the neurons and a new measure of similarity are proposed for Hopfield´s associative memory