Working memory representation of empty sets in the primate parietal and prefrontal cortices

For the brain, representing empty sets as a precursor to zero is a challenge because it requires the active coding of a quantitative category that, by definition, contains no items. Recent neurophysiological recordings show that empty sets are distinctively encoded by neurons in the primate ventral intraparietal area (VIP) and the prefrontal cortex (PFC). However, how empty sets are represented in working memory is unknown. We simultaneously recorded from VIP and PFC while rhesus monkeys performed a delayed numerosity matching task that required the maintenance of numerosities in memory for a brief period. Countable numerosities (1-4) and empty sets ('numerosity 0') were included as stimuli. Single neurons in PFC, and to a lesser extent neurons in VIP, actively encoded empty sets during the delay period. In both cortical areas, empty sets were progressively differentiated from countable numerosities with time during the ongoing trial. Moreover, the tuning of neuron populations in VIP and PFC shifted dynamically towards empty sets so that they became increasingly overrepresented in working memory. Compared to VIP, the prefrontal representation of empty sets was more stable in time and more independent of low level visual features. Moreover, PFC activity correlated better with behavioral performance in empty set trials. These findings suggest that the representation of null quantity in working memory relies more on prefrontal and less on parietal processing. Overall, our results show that empty sets are dynamically and distinctly represented in working memory.