A COMPLEX-VALUED ASSOCIATIVE MEMORY FOR STORING PATTERNS AS OSCILLATORY STATES

A neuron model in which the neuron state is described by a complex num ber is proposed. A network of these neurons, which can be used as an a ssociative memory, operates in two distinct modes: (i) fixed point mod e and (ii) oscillatory mode. Mode selection can be done by varying a c ontinuous mode parameter, nu, between 0 and 1. At one extreme value of nu (= 0), the network has conservative dynamics, and at the other (nu = 1), the dynamics are dissipative and governed by a Lyapunov functio n. Patterns can be stored and retrieved at any value of nu by, (i) a o ne-step outer product rule or (ii) adaptive Hebbian learning. In the f ixed point mode patterns are stored as fixed points, whereas in the os cillatory mode they are encoded as phase relations among individual os cillations. By virtue of an instability in the oscillatory mode, the r etrieval pattern is stable over a finite interval, the stability inter val, and the pattern gradually deteriorates with time beyond this inte rval. However, at certain values of nu sparsely distributed over nu-sp ace the instability disappears. The neurophysiological significance of the instability is briefly discussed. The possibility of physically i nterpreting dissipativity and conservativity is explored by noting tha t while conservativity leads to energy savings, dissipativity leads to stability and reliable retrieval.