The inherent capacity of neurons to learn order relations and support abstract reasoning

Brains extract relations between objects and concepts and integrate them into cognitive maps for decision-making. But it remains unclear how they achieve that. Here we present a rigorous theory showing that single neurons can already learn to extract ranks of items in a linear order with a simple local rule for synaptic plasticity. The resulting model explains human brain data on the emergence of cognitive maps from linear orders, accounts for the terminal item effect in transitive inference, and enables rapid reconfiguration of internal representations when new evidence appears. We also present a theoretical explanation for the surprising fact that 2D projections of neural representations of linear orders in the brain are curved rather than linear. Since the model requires only local synaptic plasticity in shallow networks, it is suited for relational learning and fast inference on low-energy edge devices. We demonstrate this on the neuromorphic chip Loihi 2.