Encoding A Priori Information In Feedforward Networks

Theoretical results and practical experience indicate that feedforward networks are very good at approximating a wide class of functional relationships. Training networks to approximate functions takes place by using exemplars to find interconnect weights that maximize some goodness of fit criterion. Given finite data sets it can be important in the training process to take advantage of any a priori information regarding the underlying functional relationship to improve the approximation and the ability of the network to generalize. This paper describes methods for incorporating a priori information of this type into feedforward networks. Two general approaches, one based upon architectural constraints and a second upon connection weight constraints form the basis of the methods presented. These two approaches can be used either alone or in combination to help solve specific training problems. Several examples covering a variety of types of a priori information, including information a..

Polymorphic Equilibrium in Advertising

This article is concerned with the possibility that natural selection can lead to an evolutionarily stable equilibrium where otherwise identical profit maximizing firms follow distinctly different strategies. In biology such occurrences are called polymorphic equilibrium. We develop a model of nonprice competition and from this model two classes of polymorphic equilibria arise. In the first class, advertising by expanding market demand can create a niche large enough to sustain entry by nonadvertising firms. Thus, otherwise identical firms following advertising and no advertising strategies can coexist with equal profits in a polymorphic equilibrium The second class of polymorphic equilibria includes the case where advertising does not expand market demand and instead only affects market shares. The article concludes with a discussion of the implications that polymorphism has for empirical work in economics.