Thresholding, Hamming distance, unipolar/bipolar binaries, and retrieval in neural network based memories

The use of a bipolar retrieval key has the effect of doubling the length of the probe vector and making the number of +1's equal to the number of -1's in the stored vectors, even if the original stored vectors have an unequal number of +1's and -1's. The threshold conditions suggested by Hopfield and many others are examined, and certain proposed modifications to these functions are shown to be contradictory and nonunique. The concept of Hamming distance is discussed in the context of neural network computing, and a new 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.<>