Analogy between Markov chain and the asynchronous memory recall process of Hebbian-type associative memory

Analytical techniques related to the Markov chain are utilized to study the capacity and recall probability of Hebbian-type associative memory (HAM). The concept is based on the analogy between the Markov chain and the asynchronous iterative memory recall process of HAM. Calculation of the limiting zero state probability of a birth-death process of incorrect bits of the probe leads to a faithful estimation of the recall probability for a given HAM. Results obtained show a strong resemblance to those obtained by J. J. Hopfield (1982). However, time-consuming computational simulation requirements can be avoided by the proposed method. Moreover, it has been shown that the recall probability of a given HAM is independent of the initial Hamming distance between the probe and the nearest memory state as the number of asynchronous recall iterations tends to infinity.