A parsimonious model for learning order relations provides a principled explanation of diverse experimental data

A cornerstone of higher cognitive function is the ability to learn relations between objects, and to use this relational information for inference. A concrete challenge is learning an order relation, and the use of resulting internal representations for transitive inference. It is known that order relations are represented in the parietal cortex both by a summation code, where the firing rates of neurons indicate the rank of an item in the order, and by a heterogeneous code where neurons are selective for specific rank values. But it remains open how these neural codes are learned. We show that the summation code emerges through a simple rule for synaptic plasticity in a single layer of synaptic connections. The resulting neural representation enables transitive inference and gives rise to the terminal item effect observed in human behavior. We also show that the simultaneous presence of a heterogeneous code gives rise to the commonly observed curvature of 2D projections of fMRI (functional magnetic resonance imaging) signals for items of increasing rank: They tend to lie on a horseshoe-shaped curved line. Our models are supported by a rigorous theory.