5、Memory Capacity

How good is the storage prescription (1) at storing the patterns so that they are stable states? Clearly, as the number of patterns m increases, the chances of accurate storage must decrease. In some empirical work in his 1982 paper, Hopfield showed that about half the memories were stored accurately in a net of nodes if . The other patterns did not get stored as stable states. In a more rigorous piece of analysis McCliece et al. (1987) showed theoretically that, if we require almost all the required memories to be stored accurately, then the maximum number of patterns m is . For this gives .

Suppose a pattern which was required to be stored did not, in fact produce a stable state and we start the net in this state. The net must evolve to some stable state and this is usually not related to any of the original patterns used in the prescription. The stable state represents a spurious energy minimum of the system - one that is not there by design.