Exact Classification with Two-Layer Neural Nets

摘要

This paper considers the classification properties of two-layer networks of McCulloch–Pitts units from a theoretical point of view. In particular we consider their ability to realise exactly, as opposed to approximate, bounded decision regions in R2. The main result shows that a two-layer network can realise exactly any finite union of bounded polyhedra in R2whose bounding lines lie in general position, except for some well-characterised exceptions. The exceptions are those unions whose boundaries contain a line which is “inconsistent,” as described in the text. Some of the results are valid for Rn,n⩾2, and the problem of generalising the main result to higher-dimensional situations is discussed.