Cycles in symmetric sequence processing
Fernando Lucas Metz, W. K. Theumann · AIP conference proceedings · 2007
The competition between pattern reconstruction and sequence processing is studied here in an exactly solvable feed‐forward layered neural network model of binary units and patterns near saturation. We show results for both symmetric and asymmetric sequence processing, either one competing with pattern reconstruction represented by a Hebbian interaction, in order to compare these two kinds of sequence processing. Phase diagrams of stationary states are obtained and a new phase of cycles of period two is found for a weak Hebbian term in the case of symmetric sequence processing, independently of the number of condensed patterns c which have macroscopic overlaps with the states of the network. In contrast, the stability of these cycles depends strongly on c. These results are in contrast with those for the competition between a Hebbian interaction and an asymmetric sequence processing interaction, in which the period of the cycles is c and the stability of these solutions does not depend on c. The dynamics of the macroscopic overlaps in the stationary cyclic phase is analyzed in both models.