Ranking and serial thinking: a geometric solution

A general mathematical description of the way the brain encodes ordinal knowledge of sequences is still lacking. Coherently with the well-established idea of mixed selectivity in high-dimensional state spaces, we conjectured the existence of a linear solution for serial learning tasks. In this theoretical framework, the neural representation of the items in a sequence are read out as ordered projections along a suited "geometric" mental line learned via classical conditioning (delta rule learning). We show that the derived model explains all the behavioral effects observed in humans and other animal species performing the transitive inference task in presence of noisy sensory information and stochastic neural activity. This result is generalized to the case of recurrent neural networks performing motor decision, where the same geometric mental line is learned showing a tight correlation with the motor plan of the responses. Network activity is then eventually modulated according to the symbolic distance of presented item pairs, as observed in associative cortices of  nonhuman primates. Serial ordering is thus predicted to emerge as a linear mapping between sensory input and behavioral output, highlighting a possible pivotal role of motor-related associative cortices in the transitive inference task.