Slide 25 of 25
Notes:
The function is called the logistic growth curve. It has been used in population studies to represent the growth in populations over time as a function of the growth rate a and the carrying capacity (1) of the environment. It has also been used (van Geert, 1993) to characterize the rate at which children learn vocabulary. It bears an obvious relationship to the Rescorla-Wagner or Bush-Mosteller “Linear Operator Model.” It suggests that learning operates according to the “Mathew Principle.” Those that have get and those that have not lose. Such a model would explain blocking and overshadowing (at least with proper parameter levels). A committee of units learning according to this rule would make a dynamic system of learning with complex rules of interaction dependent on the a levels for each member of the committee.
Because each element in the system can behave very differently as a result of different parameter values the ensemble performance of the system could be very different from the behavior of each individual element. On the other hand, if the logistic grow curve represents the performance of the global system, then each of the elements that make up that system could behave very differently both from each other and from the global system.
