Learning to infer transitively: serial ordering on a mental line in premotor cortex

Transitive inference (TI) is a form of deductive reasoning that allows to infer unknown relationships among premises. It is hypothesized that this cognitive task is accomplished by mapping stimuli onto a linear workspace, referred to as the mental line, based on their arbitrarily assigned ranks. However, open questions remain: does this mental line have a neural correlate, and if so, where and how is it represented and learned in the brain? In this study, we investigate the role of monkeys dorsal premotor cortex (PMd) in encoding the hypothesized mental line during the acquisition of item relationships. Our findings provide evidence that the TI task can be solved through a linear transformation of the neural representations of arbitrarily ranked items. We show that PMd multi-unit activity organizes along a theoretically informed direction, implementing a geometrical solution that effectively explains animal behavior. Our results suggest that the premotor cortex plays a crucial role in integrating item representations into a geometric mental line, where the symbolic distance (i.e., rank difference) between items influences the related motor decisions. Furthermore, we observe an ongoing learning process characterized by a rotation of this mental line, which aligns to the linear manifold where motor plan unfolds. This elucidates a cortical optimization strategy based on the statistical structure of the task.