Recurrence Methods in the Analysis of Learning Processes

  • Authors:
  • S. Mendelson;I. Nelken

  • Affiliations:
  • Department of Mathematics, Technion, and Institute of Computer Science, Hebrew University, Jerusalem 91120, Israel;Department of Physiology, Hebrew University–Hadassah Medical School, and the Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem 91120, Israel

  • Venue:
  • Neural Computation
  • Year:
  • 2001

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Abstract

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.