Optimal storage capacity of neural networks at finite temperatures

Abstract

Gardner's analysis (1989) of the optimal storage capacity of neural networks is extended to study finite-temperature effects. The typical volume of the space of interactions is calculated for strongly diluted networks as a function of the storage ratio alpha , temperature T and the tolerance parameter m, from which the optimal storage capacity alpha c is obtained as a function of T and m. At zero temperature it is found that alpha c=2 regardless of m while alpha c in general increases with the tolerance at finite temperatures. The authors show how the best performance for given alpha and T is obtained, which reveals a first-order transition from high-quality performance to a low-quality one at low temperatures. An approximate criterion for recalling, which is valid near m=1, is also discussed.