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Recurrence Methods in the Analysis of Learning Processes

Department of Mathematics, Technion, and Institute of Computer Science, Hebrew University, Jerusalem 91120, Israel

I. Nelken

Department of Physiology, Hebrew University–Hadassah Medical School, and the Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem 91120, Israel

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