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For Every Generalization Action, Is There Really An Equal And Opposite Reaction? Analysis of the Conservation Law for Generalization Performance
 Proceedings of the Twelfth International Conference on Machine Learning
, 1995
"... The "Conservation Law for Generalization Performance" [Schaffer, 1994] states that for any learning algorithm and bias, "generalization is a zerosum enterprise." In this paper we study the law and show that while the law is true, the manner in which the Conservation Law adds up generalization ..."
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The "Conservation Law for Generalization Performance" [Schaffer, 1994] states that for any learning algorithm and bias, "generalization is a zerosum enterprise." In this paper we study the law and show that while the law is true, the manner in which the Conservation Law adds up generalization performance over all target concepts, without regard to the probability with which each concept occurs, is relevant only in a uniformly random universe. We then introduce a more meaningful measure of generalization, expected generalization performance. Unlike the Conservation Law's measure of generalization perfor mance (which is, in essence, defined to be zero), expected generalization performance is conserved only when certain symmetric properties hold in our universe. There is no reason to believe, a priori, that such symmetries exist; learning algorithms may well ex hibit nonzero (expected) generalization per forlllance.