title: Solving Nonlinearly Separable Classifications in a Single-Layer Neural Network.
abstract: Since the work of Minsky and Papert ( 1969 ), it has been understood that single-layer neural networks cannot solve nonlinearly separable classifications (i.e., XOR). We describe and test a novel divergent autoassociative architecture capable of solving nonlinearly separable classifications with a single layer of weights. The proposed network consists of class-specific linear autoassociators. The power of the model comes from treating classification problems as within-class feature prediction rather than directly optimizing a discriminant function. We show unprecedented learning capabilities for a simple, single-layer network (i.e., solving XOR) and demonstrate that the famous limitation in acquiring nonlinearly separable problems is not just about the need for a hidden layer; it is about the choice between directly predicting classes or learning to classify indirectly by predicting features.
authors.affiliation: Department of Psychology, Binghamton University, Binghamton, NY 13903, U.S.A. nconaway@wisc.edu.
authors.forename: Nolan
authors.initials: N
authors.lastname: Conaway
authors.affiliation: Department of Psychology, Binghamton University, Binghamton, NY 13903, U.S.A. kkurtz@binghamton.edu.
authors.forename: Kenneth J
authors.initials: KJ
authors.lastname: Kurtz