Exact classification with two-layer neural nets inn dimensions Original Research Article

This paper considers the classification capabilities of neural networks which incorporate a single hidden layer of McCulloch-Pitts units. Previous research by the authors has led to a geometric characterisation of bounded sets which can be exactly classified almost everywhere inℝ2. In this paper we extend these results to higher dimensions. The main result gives necessary and sufficient conditions for ann-dimensional set to be classified by such a network, subject to almost all misclassifications being constrained to lie within an arbitrary neighbourhood of the(n − 3)-skeleton of the boundary of the set. A conjecture on necessary and sufficient conditions for a subset ofℝn to be exactly classifiable almost everywhere is also proposed.