Exact Classification with Two-Layered Perceptrons

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3667 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3667 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3667 archive 351 disk0/00/00/36/49 2016-01-15 02:01:55 2021-08-27 17:14:14 2016-01-15 02:01:55 monograph show 2 Aarts E.H.L. Zwietering P.J. Wessels J. AL1368 Exact Classification with Two-Layered Perceptrons pub iis_met prog_mda We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset. 1992-07 published WP-92-049 WP-92-049 10 2510 public working_paper IIASA, Laxenburg, Austria 22 FALSE info:eu-repo/semantics/book