Generalize AML beyond semilattice algebras

Determine whether Algebraic Machine Learning can be implemented using algebraic structures other than semilattices, and establish whether its learning mechanism depends primarily on subdirect decomposition rather than on properties specific to semilattice algebras.

Background

The paper develops Algebraic Machine Learning using atomized semilattices, chosen for their simplicity and expressive power. Its learning mechanism is based on decomposing models into atoms corresponding to subdirectly irreducible components, and the authors suggest that this decomposition may be more fundamental than the particular algebra used.

Extending AML to other algebraic structures would test whether the proposed learning principle is genuinely algebra-independent and could broaden the range of tasks representable within the framework. The paper does not establish this extension and presents it as a hypothesis and expectation.