GENERALIZATION IN NEURAL NETWORKS: THE CONTIGUITY PROBLEM.

The problem of constructing a network that will learn concepts from a training set consisting of some fraction of the total number of possible examples of the concept is considered. Without some sort of prior knowledge, this problem is not well defined, since in general there will be many possible concepts that are consistent with a given training set. It is suggested that one way of incorporating prior knowledge is to construct the network such that the structure of the network reflects the structure of the problem environment. Two types of networks (a two-layer slab trained with back propagation and a single high-order slab) are explored to determine their ability to learn the concept of contiguity. It is found that the high-order slab learns and generalizes contiguity very efficiently, whereas the first-order network learns very slowly and shows little generalization capability on the small problems that have been examined.