Memory annihilation of structured maps in bidirectional associative memories

Structured sets comprise Boolean vectors with equal pair-wise Hamming distances, h. An external vector, if it exists at an equidistance of h/2 from each vector of the structured set, is called the centroid of the set. A structured map is a one-one mapping between structured sets. It is a set of associations between Boolean vectors, where both domain and range vectors are drawn from structured sets. Associations between centroids are called centroidal associations. We show that when structured maps are encoded into bidirectional associative memories using outer-product correlation encoding, the memory of these associations are annihilated under certain mild conditions. When annihilation occurs, the centroidal association emerges as a stable association, and we call it an alien attractor. For the special case of maps where h=2, self-annihilation can take place when either the domain or range dimensions are greater than five. In fact, we show that for dimensions greater than eight, as few as three associations suffice for self-annihilation. As an example shows, annihilation occurs even for the case of bipolar decoding which is well known for its improved error correction capability in such associative memory models.