Uniformity in learning structures

TL;DR

This paper investigates how removing the nonisomorphism assumption in algebraic structure learning affects the equivalence of Ex-learning and Bc-learning criteria.

Contribution

It analyzes the impact of dropping the nonisomorphism condition on the uniform equivalence of two key learning paradigms.

Findings

Ex-learning and Bc-learning are not always equivalent without the nonisomorphism assumption.

The paper identifies conditions under which the two learning criteria diverge.

It extends understanding of learning frameworks on algebraic structures.

Abstract

The standard framework for studying learning problems on algebraic structures assumes that the structures in the target family are pairwise nonisomorphic. Under this assumption, the most widely investigated learning criterion--Ex-learning--becomes inherently equivalent to the well-known paradigm of Bc-learning. This paper explores what happens when the nonisomorphism requirement is removed and analyzes the extent to which these two learning criteria remain uniformly equivalent.