A symbolic interpretation for back-propagation networks

This article constructs a solution for a very common architecture of pattern associators: the backpropagation networks and shows how Zadeh's possibility theory brings a formal structure to the output interpretation of the connection matrix.

Abstract

Two main problems for the neural network (NN) paradigm are discussed: the output value interpretation and the symbolic content of the connection matrix. In this article, we construct a solution for a very common architecture of pattern associators: the back-propagation networks. First, we show how Zadeh's possibility theory brings a formal structure to the output interpretation. Properties and practical applications of this theory are developed. Second, a symbolic interpretation for the connection matrix is proposed by designing of an algorithm. By accepting the NN training examples as input this algorithm produces a set of implication rules. These rules accurately model the NN behavior. Moreover, they allow to understand it, especially in the cases of generalization or interference.