Strongly non-U-shaped language learning results by general techniques

Abstract

In learning, a semantic or behavioral U-shape occurs when a learner first learns, then unlearns, and, finally, relearns, some target concept.

This paper introduces two general techniques and applies them especially to syntactic U-shapes in learning: one technique to show when they are necessary and one to show when they are unnecessary. The technique for the former is very general and applicable to a much wider range of learning criteria. It employs so-called self-learning classes of languages which are shown to characterize completely one criterion learning more than another.

We apply these techniques to show that, for set-driven and rearrangement-independent learning, any kind of U-shapes is unnecessary. Furthermore, we show that U-shapes are necessary in a strong way for iterative learning, contrasting with an earlier result by Case and Moelius that semantic U-shapes are unnecessary for iterative learning.