EVEN ON FINITE TEST SETS SMALLER NETS MAY PERFORM BETTER

For feedforward multilayered neural nets we state conditions on the tr ansfer function f under which such nets are uniquely defined by their mappings (up to trivial manipulations). More important we give suffici ent conditions on f such that for two arbitrary structures having diff erent numbers of layers there is a finite test set S on which the opti mal smaller net performs better. That is there exist weights and thres holds for the smaller structure such that the resulting net has an err or (with respect to S) which is less than that of the bigger net, no m atter how the weights and thresholds are chosen for the latter. (C) 19 97 Elsevier Science Ltd. All Rights Reserved.