A GEOMETRICAL ANALYSIS OF ASSOCIATIVE MEMORY

A geometrical method is proposed for analyzing the properties of an au tocorrelation associative memory model. From the present geometrical v iewpoint, the state transition of the model is expressed as dynamics o n a sphere. The method shows that there is a critical memory ratio cor responding to the memory capacity at which the characteristic of the d ynamics on the sphere changes and that the stored vectors are distribu ted around the stored band which is the intersection between the spher e and deformed sphere defined with the square of the inner states of n eurons. The stored band seperates the sphere into the upper side, wher e initial state vectors in recalling processes are distributed, and th e lower side, where spurious stored vectors are distributed. The metho d gives a geometrical picture of the dynamical behaviour in recalling processes: the state vector starts from the upper side and falls into the stored vector around the stored band or into some spurious stored vector on the lower side. Based on this picture, it is explained that Morita's partial reverse method of enhancing the memory capacity makes state vectors in the lower side unstable and stored vectors around th e stored band stable. (C) 1998 Elsevier Science Ltd. All rights reserv ed.