Information packing in associative memory models

Using a structured approach to the Hopfield model of associative memory, we address the question of maximal information packing. We show that input binary vectors which are orthogonal to one another are not guaranteed to form a faithful set, i.e., a set which generates the same output. We point out the importance of the binary product operation in sorting out the faithful sets. We prove that any binary basis has a total binary product proportional to the unit vector. We construct examples of faithful sets by requiring that certain subsets be forbidden to have a total binary product proportional to the unit vector.