On elemental and configural models of associative learning

• Associative learning models may be either configural or elemental.
• The former attribute associative strength to percepts as wholes.
• The latter attribute associative strengths to separate perceptual elements.
• The author shows that any elemental model can be recast as configural, and vice-versa.
• Thus the two approaches are proved to have the same explanatory power.

The elemental and configural approaches to associative learning are considered fundamentally distinct, with much theoretical and empirical work devoted to determining which one can better account for empirical data. Elemental models assume that each perceptual element is capable of acquiring associative strength independently of other elements. Configural models, on the other hand, assume that associative strength accrues to percepts as wholes. Here I derive a necessary and sufficient condition for an elemental and a configural model to be equivalent, i.e., to always make the same predictions. I then ask when the condition can be fulfilled. I show that it is always possible to construct a configural model equivalent to a given elemental model, provided we broaden somewhat the customary definition of a configural model. Constructing an elemental model equivalent to a given elemental one is possible provided the generalization function of the configural model is positive definite. The latter condition is satisfied by existing configural models. The arguments leading to these conclusions clarify the relationship between elemental and configural models, and show that both approaches have heuristic value for associative learning theory.