Representation of abstract quantitative rules applied to spatial and numerical magnitudes in primate prefrontal cortex

Abstract

Processing quantity information based on abstract principles is central to intelligent behavior. Neural correlates of quantitative rule selectivity have been identified previously in the prefrontal cortex (PFC). However, whether individual neurons represent rules applied to multiple magnitude types is unknown. We recorded from PFC neurons while monkeys switched between "greater than/less than" rules applied to spatial and numerical magnitudes. A majority of rule-selective neurons responded only to the quantitative rules applied to one specific magnitude type. However, another population of neurons generalized the magnitude principle and represented the quantitative rules related to both magnitudes. This indicates that the primate brain uses rule-selective neurons specialized in guiding decisions related to a specific magnitude type only, as well as generalizing neurons that respond abstractly to the overarching concept "magnitude rules."

Figure 1.

Rule-coding hypotheses. Two competing hypotheses can be formulated for the coding of quantitative rules applied to two magnitude types. A, Hypothesis 1: the brain may treat different rules as independent principles and encode rules related to numerical or spatial magnitudes separately. B, Hypothesis 2: the brain might emphasize the overarching principle “greater than/less than” in the two protocols and share neurons that represent the instruction to choose the smaller amount of magnitude (fewer items, shorter lines) or the larger amount of magnitude (more items, longer lines), respectively.

Figure 2.

Task-switching protocol based on quantitative rules. A, Rules applied to magnitude line length. Monkeys grasped a lever and maintained central fixation throughout the trial until test phase. A sample line length was shown and followed by a working memory delay (delay1). Then, a rule cue indicated either the “greater than” or “less than” rule. Each rule was indicated by cues of two different sensory modalities (red circle or white circle with water for the “greater than” rule, blue circle or white circle without water for the “less than” rule). After a second delay (delay2), a test line length appeared and the monkeys were required to release the bar if the length of the test line was longer in “greater than” trials and to keep holding the bar if the test length was shorter. Conversely, the monkeys had to release the bar if the first test image displayed a shorter line length than the sample image in “less than” trials. B, Rules applied to magnitude numerosity. The same behavioral protocol was used as in A, but monkeys had to judge whether a test numerosity was greater or less than the sample numerosity based on the rule. In each session, magnitude types, magnitude values, rules, and rule cues were presented pseudorandomized.

Figure 3.

Behavioral performance. A, Performance of monkey E (left) and monkey O (right) during electrophysiological recordings in the line-length protocol (standard and control protocols pooled). Columns represent percentage correct responses for the “greater than” and “less than” task. B, Performance for both monkeys in the numerosity protocol. C, Performance of both monkeys in control and standard trials for the quantitative rules applied to the two different magnitude types.

Figure 4.

Responses of example neurons. A, Lateral view of a monkey brain showing the anatomical location of the recording site. We recorded from the right dorsolateral PFC of two monkeys. AS indicates arcuate sulcus; CS, central sulcus; LF, lateral fissure; PS, principal sulcus. B, C, Neuronal responses of a generalizing rule-selective example neuron preferring the “less than” rule in the line-length protocol (left) and the numerosity protocol (right). Top: Neuronal responses plotted as dot-raster histograms (each dot represents an action potential and spike trains are sorted and color coded according to the rules and rule cues). Bottom: Spike density functions (activity averaged over all trials and smoothed by a 150 ms Gaussian kernel). Rule selectivity was regardless of which cue signified the rule and which magnitude protocol was used. Only responses to correct trials are shown. D, Neuron that differentiated between rules in trials with line-length stimuli as magnitude, but not in trials with numerosity stimuli. E, Neuron that was rule selective when the rule was applied to numerosity, but not when the rule was applied to line length.

Figure 5.

Proportions of rule-selective neurons. The Venn diagram depicts the percentages of rule-selective cells for either of the two magnitude types alone (rule specialists) or in conjunction (rule generalists) relative to all 68 rule-selective neurons.

Figure 6.

Quality and temporal evolution of rule selectivity. A, Top: Frequency histogram of AUROC values of neurons encoding abstract quantitative rules for line-length stimuli during correct trials. Bottom: Temporal evolution of rule-selective signals in the delay2 period for the line-length magnitude rule-selective neurons. Each row in the color map represents the time course of rule-selective coding (AUROC value) for an individual neuron. Neurons are sorted according to their rule preference (“greater than” rule in red with AUROC values larger than 0.5 and “less than” rule in blue with AUROC values smaller than 0.5) and latency of significant rule selectivity (white line in the color map). B, Frequency histogram (top) and temporal evolution of AUROC values (bottom) of rule-selective neurons selective to the numerosity rules.

Figure 7.

Behavioral relevance of rule-selective activity. A, Discharge rates of one example neuron during the delay2 period for correct and error trials. B, Mean AUROC values for error trials compared with correct trials (pooled across magnitudes). Error bars represent SEM. *p < 0.01.