Learning Simple Arithmetic Procedures

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Abstract
Rumelhan et al. (1986b) proposed a model of how symbolic processing may be achieved by parallel distributed processing (PDP) networks. Their idea is tested by training two types of recurrent networks to learn to add two numbers of arbitrary lengths. This turned out to be a fruitful exercise. We demonstrate: (1) that networks can learn simple programming constructs such as sequences, conditional branches and while loops; (2) that by lsquo;going sequential’ in this manner, we are able to process artibrarily long problems; (3) a manipulation of the training environment, called combined subset training (CST), that was found to be necessary to acquire a large training set; (4) a power difference between simple recurrent networks and Jordan networks by providing a simple procedure that one can learn and the other cannot.