Some results on the exact realisation of decision regions using feed-forward networks with a single hidden layer

This paper considers the classification properties of neural networks which incorporate a single hidden layer of nodes whose activation function is a simple step. The main result demonstrates that any finite amount of bounded polyhedra in R², whose bounding lines lie in general position, can be realised exactly as the decision region of such a network apart from some well characterised exceptions. The paper also illustrates the difficulty which arises when we attempt to generalise the main theorem to higher dimensions