Information Storage Capacity of Incompletely Connected Associative Memories

The memory capacities for auto- and hetero-associative incompletely connected memories are calculated. First, the capacity is computed for fixed parameters of the system. Optimization yields a maximum capacity between 0.53 and 0.69 for hetero-association and half of it for auto-association, improving previous results. The maximum capacity requires sparse input and output patterns and grows with increasing connectivity of the memory. Furthermore, parameters can be chosen in such a way that the information content per pattern asymptotically approaches 1. 1 Introduction Tasks like voice or face recognition are quite difficult to realize with conventional computer systems, even for the most powerful of them. On the contrary, these tasks are easily performed by the human brain despite its highly inferior computation speed. This indicates that it is rather a conceptual problem of the conventional computer model and one could ask for alternatives. An important difference to the human brain..