How can we ensure a machine consistently reaches correct states during learning? This paper presents a condition ensuring that a learning process visits the target set infinitely often, with near certainty. Easy to verify, this condition applies to numerous well-known learning rules, spanning the perceptron, continuous energy functions, Kohonen rule, and committee machine. 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. The utility of this method is demonstrated through its application to four types of learning processes. This method helps show that the process enters this target set. 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.
Published in Neural Computation, this article aligns with the journal’s focus on theoretical and computational aspects of neural networks and learning systems. By providing a verifiable condition for ensuring that learning processes reach correct states, this research contributes to the ongoing development of more robust machine learning algorithms.