Analysis of fundamental issued for retrieval in neural network memories of Hopfield type

The Hamming distance commonly used in digital computing as a measure of closeness among binary vectors of equal lengths and consisting of two logical states is discussed in the context of neural network computing. A measure of distance dependent on the contributory bits of +1´s or -1´s present in a pair of vectors of equal length defined over the field of real numbers is described. The threshold conditions suggested by J. J. Hopfield (1982) and many others are analyzed as related to the unipolar and bipolar binaries, and certain modifications to these functions are shown to be contradictory and nonunique. The conditions for the occurrence of a zero during the iterative process for retrieval as well as for improved retrieval of information when some bits are missing or are in error in the probe vectors are described