A theory of the detection and learning of structured representations of similarity and relative magnitude

Responding to similarity, difference, and relative magnitude is ubiquitous in the animal kingdom. However, humans seem unique in the ability to represent relative magnitude and similarity 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 use these representations assume access to computations of similarity and magnitude a priori. 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 to learn structured relational representations of relative magnitude and similarity from pixel images of simple shapes.