Learning to infer transitively: ranking symbols on a mental line in premotor cortex.

Transitive inference (TI) is a form of deductive reasoning that allows to infer unknown relations among premises. Cognitive resolution of this task is thought to involve a mental linear workspace, usually referred to as the "mental line," organizing stimuli sequentially based on their ranks. Here, we introduce the Geometric Mental Line (GML) model for TI task solution, defining the mental line direction as the linear combination of the symbols representations weighted by their ranks. This model can be adapted to specific task designs and implemented in a linear dynamical system approximating more biologically-realistic recurrent neural networks. Tuning few key parameters, the GML model can successfully replicate the behavioral effects observed in monkeys and its unfolded dynamics offers insights into the neural organization of stimuli representations during the task. Therefore, a crucial question arises: does the GML model faithfully capture the geometry of neural activity? Specifically, does a neuronal "mental line" exist, and if so, where is it encoded and learned in the brain? This work explores the role of dorsal premotor cortex (PMd) in representing the GML, challenging the assumption that this region solely represents motor planning, and showing its involvement in encoding task-relevant information, such as symbols representations. Our results provide evidence that PMd plays a key role in manipulating these representations, efficiently transforming the ordinal knowledge into a proper motor decision. The GML implemented in PMd is predictive of animal behavior, forecasting the decision both in correct and error trials and explaining the reaction times distribution. Moreover, we found striking evidence that the representations of the stimuli are plastic: the learning process leads to a realignment of the GML to the motor decision axis, elucidating an optimization strategy pursued by the PMd which eventually shrinks the solution dimensionality, as predicted by our GML model.