MULTIPLICATIVE CONTEXTS IN ASSOCIATIVE MEMORIES

A system of networks, consisting of a first net that constructs the Kr onecker product between two vectors and then sends it to a second net that sustains a correlation memory, defines a context-dependent associ ative memory. In the real nervous system of higher mammals, the anatom y of the neural connections surely exhibits a considerable amount of l ocal imprecision superimposed on a regular global layout. In order to evaluate the potentialities of the multiplicative devices to constitut e plausible biological models, we analyse the performances of a contex t-dependent memory when the multiplicative net, responsible of the con struction of the Kronecker product, presents an incomplete connectivit y. Our study shows that a large dimensional system is able to support a considerable amount of incompleteness in the connectivity without a great deterioration of the memory. We establish a scaling relationship between the degree of incompleteness, the capacity of the memory, and the tolerance threshold to imperfections in the output. We then analy se some performances that show the versatility of this kind of network to represent a variety of functions. These functions include a contex t-modulated novelty filter, a network that computes logical modalities and an adaptive searching device.