Thomas Shultz, Jeffrey Elman
Jeffrey L. Elman
Center for Research on Language Department of Cognitive Science
University of California at San Diego
LaJolla, CA 92093-0126 U.S.A.
The non-linear complexities of neural networks make network solutions difficult to understand. Sanger's contribution analysis is here extended to the analysis of networks automatically generated by the cascade(cid:173) correlation learning algorithm. Because such networks have cross connections that supersede hidden layers, standard analyses of hidden unit activation patterns are insufficient. A contribution is defined as the product of an output weight and the associated activation on the sending unit, whether that sending unit is an input or a hidden unit, multiplied by the sign of the output target for the current input pattern. Intercorrelations among contributions, as gleaned from the matrix of contributions x input patterns, can be subjected to principal components analysis (PCA) to extract the main features of variation in the contributions. Such an analysis is applied to three problems, continuous XOR, arithmetic comparison, and distinguishing between two interlocking spirals. In all three cases, this technique yields useful insights into network solutions that are consistent across several networks.