288 pp. per issue
6 x 9, illustrated
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Neural Computation

March 2017, Vol. 29, No. 3, Pages 861-866
(doi: 10.1162/NECO_a_00931)
© 2017 Massachusetts Institute of Technology
Solving Nonlinearly Separable Classifications in a Single-Layer Neural Network
Article PDF (132.52 KB)

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.