Forgetting Memories and their Attractiveness

We study numerically the memory which forgets, introduced in 1986 by Parisi by bounding the synaptic strength, with a mechanism which avoid confusion, allows to remember the pattern learned more recently and has a physiologically very well defined meaning. We analyze a number of features of the learning at finite number of neurons and finite number of patterns. We discuss how the system behaves in the large but finite N limit. We analyze the basin of attraction of the patterns that have been learned, and we show that it is exponentially small in the age of the pattern. This is a clearly non physiological feature of the model.