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.
Recurrence methods in the analysis of learning processes
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