On the capacity of associative memories with linear threshold functions

Some important features of various known constructions of associative memories based on linear threshold functions are analyzed. Two important features are dealt with: (a) the ability to select an arbitrary set of desired memory vectors and design a network for this set; (b) the sizes and shapes of the domains of attraction of the desired memory vectors and their relation to various design parameters. The static capacity for randomly chosen desired memories is also analyzed. Two extremal examples of sets of desired memories are then analyzed in detail. For spectral schemes with randomly chosen O[N /ln N] memories, it is shown that almost all of the Hamming sphere around each memory is directly attracted