Acknowledgments: The authors would like to thank Shilin Hu and Ying Li for their assistance with the material of Section 4. We would also like to thank the reviewers for their helpful suggestions which contributed signiicantly to the overall quality of the paper. Abstract 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 nd interconnect weights that maximize some goodness of t criterion. Given nite 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 speciic training problems. Several examples covering a variety of types of a priori information, including information about curvature, interpolation points, and output layer interrelationships are presented.