Doumas, L. A. A., Hamer, A., Puebla, G., & Martin, A. E.
(2017). A theory of the detection and learning of structured representations of similarity and relative magnitude. In G. Gunzelmann, A. Howes, T. Tenbrink, & E. Davelaar (Eds.), Proceedings of the 39th Annual Conference of the Cognitive Science Society (CogSci 2017) (pp. 1955-1960). Austin, TX: Cognitive Science Society.
Responding to similarity, difference, and relative magnitude (SDM) is ubiquitous in the animal kingdom. However, humans seem unique in the ability to represent relative magnitude (‘more’/‘less’) and similarity (‘same’/‘different’) as abstract relations that take arguments (e.g., greater-than (x,y)). While many models use structured relational representations of magnitude and similarity, little progress has been made on how these representations arise. Models that developuse these representations assume access to computations of similarity and magnitude a priori, either encoded as features or as output of evaluation operators. We detail a mechanism for producing invariant responses to “same”, “different”, “more”, and “less” which can be exploited to compute similarity and magnitude as an evaluation operator. Using DORA (Doumas, Hummel, & Sandhofer, 2008), these invariant responses can serve be used to learn structured relational representations of relative magnitude and similarity from pixel images of simple shapes