Random dilution in a neural network for biased patterns
M. R. Evans · Journal of Physics A Mathematical and General · 1989
A neural network introduced by Tsodyks and Feigel'man (1988) suitable for the storage of biased patterns is studied in a randomly diluted form. Coupled evolution equations are derived for the two order parameters needed to describe a configuration near to a stored pattern. These equations are studied numerically and are found to exhibit non-linear effects such as spiralling trajectories and limit cycles. The bifurcations by which the transition to no memory occurs are illustrated. It is seen that a nominated pattern may not be within the basin of attraction of the memory fixed point correlated with it. The structure of a memory fixed point is investigated and found to be more complicated than a single configuration. Finally the situation where two patterns are highly correlated is examined and phase boundaries separating the regimes of no memory, undistinguishing memory and distinguishing memory are constructed. Multiple storage of a pattern does not improve its recall without appropriate modification of the thresholding parameter.