There is a widespread misconception that the delta-rule is in some sense guaranteed to work on networks without hidden units. As previous authors have mentioned, there is no such guarantee for classification tasks. We will begin by presenting explicit counterexamples illustrating two different interesting ways in which the delta rule can fail. We go on to provide conditions which do guarantee that gradient descent will successfully train networks without hidden units to perform two-category classification tasks. We discuss the generalization of our ideas to networks with hidden units and to multicategory classification tasks.

It is clear that conventional computers lag far behind organic computers when it comes to dealing with very large data rates in problems such as computer vision and speech recognition.