Recurrence methods in the analysis of learning processes

The goal of most learning processes is to bring; a machine into a set of "c orrect" states. In practice, however, it may be difficult to show that the process enters this target set. We present a condition that ensures that th e process visits the target set infinitely often almost surely. This condit ion is easy to verify and is true for many well-known learning rules. To de monstrate the utility of this method, we apply it to four types of learning processes: the perceptron, learning rules governed by continuous energy fu nctions, the Kohonen rule, and the committee machine.