Informational capacity and recall quality in sparsely encoded Hopfield-like neural network: Analytical approaches and computer simulation

A sparsely encoded Hopfield-like attractor neural network is investigated analytically and by computer simulation. informational capacity and recall quality are evaluated. Three analytical approaches are used: replica method (RM); method of statistical neurodynamics (SN); and single-step approximation (SS). Computer simulation confirmed the good accuracy of RIM and SN for all levels of network activity. SS is accurate only for large sparseness. It is shown that informational capacity monotonically increases when sparseness increases, while recall quality changes nonmonotonically: initially it decreases and then increases. Computer simulation revealed the main features of network behaviour near the saturation which are not predicted by the used analytical approaches. (C) 1997 Elsevier Science Ltd.