Encoding of Spatial Attention by Primate Prefrontal Cortex Neuronal Ensembles

Behavioral performance

We trained two adult monkeys (Macaca mulatta), R and S, to maintain their gaze on a central fixation point while covertly attending to one of two white, peripherally presented, moving RDPs presented on a dark background. In a given trial, the RDPs appeared simultaneously and moved in the same direction, changing colors after a variable time. Based on a color rule (Lennert and Martinez-Trujillo, 2011, 2013), the monkeys had to identify and attend to the target RDP while ignoring the other RDP (distractor). Briefly, we taught the animals an arbitrarily arranged ordinal hierarchy of six isoluminant colors. In each trial, the higher-ranking colored RDP was the target. The animals were rewarded for releasing a button after correctly detecting a brief motion direction change in the target, ignoring distractor changes (Fig. 1A and Methods).

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Figure 1.

Behavioral task and performance. A, Example trial of color scale task and hierarchy of colors used (inset). The monkeys initiated a trial by fixating on the central point while pressing a button. After this initial fixation period, two white moving RDPs appeared peripherally of the fixation point and changed to two different colors after a random interval. The animals had to identify the higher-ranking color (the target) and allocate their attention to it before the color cue was extinguished and the RDPs returned to white. The monkeys had to maintain central fixation and covert attention until there was a brief motion direction change in the relevant stimulus. In 50% of the trials, the distractor changed before the target, in those cases, the monkeys had to keep pushing the button as only a release after the target change was rewarded with juice. B, Percentage of hits, errors, and mean response time for monkey R (black bars) and monkey S (white bars). Averaged across all color combinations. Error bars denote standard deviation across sessions.

Both monkeys learned the task and performed above chance level (50%) in all experimental sessions (Fig. 1B, left panel; 87.6% correct trials in monkey R and 64.97% correct trials in monkey S, respectively). Most error trials of both monkeys were responses to the distractor (false alarms) rather than failures to respond (misses; Fig. 1B, middle panel). The latter indicates that the animals indeed attended to the target and ignored the distractor but also that the task was challenging for the animals. Monkey R had a better performance and faster reaction times than monkey S (Fig. 1B, right panel, 327 and 436 ms, respectively). Unless stated otherwise, we considered only correct trials for our analyses of neuronal responses.

Neuronal selectivity

While the animals performed the task, we recorded the responses of a total of 556 units (single units and multiunits) in monkey S (5 sessions) and 525 in monkey R (4 sessions) using 96-channel microelectrode (Utah) arrays chronically implanted in the left area 8A, located on the cortical surface between the posterior end of the principal sulcus and the knee of the arcuate sulcus (Petrides, 2005). Our arrays were located slightly dorsal to the principal sulcus (Fig. 2A). Of those recorded, 853 units (79%) showed significantly different firing rates during the color cue presentation and/or the postcue epoch compared with a window of 700 ms centered at stimulus onset (Wilcoxon rank-sum test; p < 0.05^a). The variables of interest in the following analyses were the allocation of spatial attention and the direction of the stimuli; therefore, we concentrated on the postcue or attentional period in which the stimuli on the screen did not change color or direction.

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Figure 2.

Implantation sites of the arrays and single-unit activity. A, Schematic macaque brain with area 8 a highlighted according to Petrides (2005) and implantation sites. Photographs were taken during the implantation procedure. Principal and arcuate sulci are indicated. B, Single-cell examples obtained from monkey R illustrating mean normalized responses (ordinate) to different stimulus conditions as a function of time from stimulus onset (left abscissa) and color change onset (right abscissa). Schematic shows the position of the units on the array. Prominent landmarks are indicated. C, Single-cell examples obtained from monkey S for the same conditions. Shading represents SEM (±) at each time point.

To examine the tuning of single units, we used a 2-way ANOVA with target location and motion direction as factors (p < 0.05^b). Fig. 2B shows an example unit (recorded from monkey R) that responded more strongly when the target location was contralateral to the recording site (left panel), or when the RDP’s motion direction was down (right panel). Similarly, Fig. 2C shows an example unit (recorded from monkey S) responding more strongly on trials when the target stimulus was presented ipsilaterally (left panel), or when the RDPs’ motion direction was up (right panel). These units were recorded from different electrodes in the array (see schematics in Fig. 2A), and they encode the target location (red squares) and motion direction (green squares), respectively.

We next examined the proportions of selectivity for the attended location (location selective) and the stimulus’ motion direction (direction selective) in the entire population (Fig. 3A). In monkey R (left panel), we identified 56% of the units (285 of 462) to be selective for at least one of the two variables, attended location and motion direction. Of those, 59% (36% ± 4.38% of the total population) were location selective, 28% (17% ± 3.45%) were direction selective, and 13% (8% ± 2.52%) showed selectivity for both attended location and direction. To determine whether these proportions were different from those expected by chance, we compared them to those obtained using a randomization procedure (chance estimate). For the randomization procedure, we used the same trials and units as in the original data but shuffled the trial labels. In monkey R, the proportion of location selective cells predicted by chance was 4.94%, which was significantly smaller than that found in the real population (χ² test, p = 8.29 ×10^{−10 c}). Similarly, the proportion of direction-selective units was significantly smaller in the randomized population than in the real data (5.04%, χ² test, p = 0.002^d), as well as the proportion of units encoding both variables (0.23%, χ² test, p = 0.004^e).

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Figure 3.

Proportions of selective single units. A, Proportions of selective units were obtained using two-way ANOVA with the factors target location and motion direction in monkey R (right) and monkey S (right) during the postcue period. The markers represent the proportions of selective units found in the population (blue, location; yellow, direction; orange, selectivity for both); the error bars represent 95% confidence intervals. Shading indicates proportion found in data with shuffled trial labels. Asterisks mark significant differences in proportions compared to chance proportions (***, p < 0.001; **, p < 0.05, χ²-test). The majority of selective cells found in monkey R were location selective, and the majority of selective cells found in monkey S were direction selective. B, Timeline of the monkeys’ training. At the time of recording the task presented in this paper (ColorScale Task 2), monkey R had received exclusive training on a spatial attention task involving a color scale (Lennert and Martinez-Trujillo, 2011; 2013). Despite a 2.5-yr pause between the two tasks, monkey R performed the task very well. After its initial training, monkey S was extensively trained on delayed-match-to-sample tasks involving motion directions (for example, Mendoza-Halliday et al., 2014). Monkey S had a >4-yr break from a color scale task, during which it became an expert for motion direction tasks. C, We tracked the proportion of selective electrodes/channels per recording session in each animal to see whether the distributions were approximately stable over time. To test the spatial clustering hypothesis, each electrode’s categorical selectivity of on example session was mapped into the array for monkey R (D) and monkey S (E). Left panels: colors indicate whether units on an electrode were selective. White channels had no activity; black channels indicate unwired electrodes. Right panels: magnitude of spatial clustering of preferred stimuli in monkey R (D) and S (E). Black line depicts Moran’s I (metric of spatial autocorrelation) calculated over increasing spatial scales. Gray shaded area represents chance values.

In monkey S (Fig. 3A, right panel), 49% of the units (191 of 391) were classified as selective for the attended location or direction. The majority of cells, 77% (38% ± 4.8% of the total population), were direction selective, 17% (8% ± 2.75%) were location selective, and 6% (3% ± 1.71%) were both location and direction selective. The proportion of direction-selective units was significantly higher than expected by chance (5.21%, χ² test, p = 4.13 ×10^{−10 g}), whereas the proportion of location selective units was not significantly different from that found in a randomized population (9.39%, χ² test, p = 0.6972^f). The proportion of units selective for both features was also not different from chance (0.21%, χ² test, p = 0.1016^h). To assess whether the (nonsignificant) proportion of units that did have location selectivity showed a true effect, we compared the size of the isolated effect in the original data with that in the shuffled data by computing an index of sensitivity (D′). The magnitude of the effect was similar in both groups of units (Wilcoxon rank-sum test, p = 0.553). Thus, it is unclear whether the effect isolated in the original data was a true effect of attention that is present in a small number of units or reflected noise in our data. With the current analysis, we cannot fully reject the latter scenario.

The distributions of selectivities were different in the two animals. Whereas animal R had a larger proportion of units selective for the attended location than units selective for motion direction, animal S showed an inverse pattern. One possible explanation for this result is that the animals had different training histories and because selectivity in the LPFC for different features may be affected by experience; thus exposure to different tasks may have shaped neuronal selectivities in a different manner for each animal. To investigate this issue, we plotted the training history of the animals (Fig. 3B). Monkey R was extensively trained and participated in other experiments using a similar color-rank order task shown in Fig. 1. In this task, although motion direction is important to detect the response cue, the spatial location of the target is of primary importance, i.e., the animals had to decide whether the right or left RDP was the target. On the other hand, monkey S had first been trained in the same task, but before undergoing testing in the current experiments, it was extensively trained in various match-to-sample tasks that required matching the direction of two moving RDPs or Gabor patches. In those tasks, location was an irrelevant variable for determining what the target was: only motion direction was important (Mendoza-Halliday et al., 2014). Using an ANOVA with the factors target location and motion direction on the averaged activity recorded on each electrode, we tracked the distribution of selective channels over the recording sessions in each animal (Fig. 3C). Our goal was to examine whether the proportions of selective cells were relatively stable over time. Interestingly, from one session to the next, there were only few channels with significant tuning in common, but overall there were very similar distributions of selectivities (see color bars). This suggests that the selectivity was stable over recording time and the difference between animals was not due to an outlier session. Thus, it is possible that the differences in neuronal selectivities are due to differences in training history between animals. However, another equally possible explanation is that the area we recorded from was slightly different in both animals and the proportion of units may change depending on the relative location of the arrays. To test this hypothesis, we wanted to assess whether there was significant spatial clustering and/or even a difference therein. We mapped the preferred location or motion direction of an electrode onto its cortical position (the left panels in Fig. 3D,E show representative example sessions for each monkey). To examine whether neurons with similar preferences were anatomically clustered (Fig. 3D,F, right panels), we used Moran’s I, a metric of spatial autocorrelation, and compared it to the 95th percentile range of chance values obtained by shuffling the electrodes’ preference labels 1000 times. Although some neurons with similar preferences were isolated from nearby electrodes, in general the analysis revealed no significant clustering neurons selective for attended location or stimulus motion direction in the areas covered by the arrays in the two monkeys. The lack of spatial clustering as well as the similar position (i.e., position of the arrays relative to the sulci) led us to favor the training history hypothesis to explain the differences in neuronal selectivity between animals.

To examine the population activity profiles, we pooled the responses of units selective for the attended location and motion direction. Because units could be selective for one location (i.e., ipsilateral or contralateral) or motion direction (i.e., up or down), we pooled units after aligning their responses to their preferred direction or location. To gauge the latency and magnitude of the difference in response to preferred and nonpreferred stimuli, we performed a paired t test on the responses of the selective units using time bins of 20 ms. The latency was determined as the first of five consecutive significant bins (p < 0.05) and the magnitude as the mean t-value across all bins. The difference between responses to the preferred (red) and nonpreferred (blue) target location is more pronounced in monkey R than in monkey S (t = 12.36 ± 5.09ⁱ and 4.15 ± 1.61,ⁱ respectively; Fig. 4A,B, left panels). On the other hand, the difference in the responses to the preferred (orange) and nonpreferred (green) direction seems to be less distinct between the two animals (t = 7.14 ± 2.98^j and 11.41 ± 3.57^j for monkey R and S, respectively; Fig. 4A,B, right panels). One detail in this figure is that in the two animals, the discrimination between motion directions (time when the responses to the preferred and nonpreferred directions diverge; Fig. 4A,B, left panels, black arrow; 320 and 260 ms after stimulus onset for monkey R and S, respectively) appears to start earlier than the discrimination between the attended and unattended locations (time where responses to attended and unattended locations start diverging; Fig. 4A,B, right panels, black arrow; 228 and 48 ms after color cue onset in monkey R and S, respectively). This is likely because information about the stimulus direction was available to the animal earlier than information about the target location. In other words, the animals probably identified the motion direction earlier and then directed their attention to the target and ignored the distractor.

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Figure 4.

Population selectivities. Mean normalized population responses (ordinate) as a function of time from trial event onsets (abscissas) in monkey R (A) and monkey S (B). Left: the population of location-selective cells (n = 167 and n = 32) shows an increased response when the target is in the preferred location (red) after color cue onset (left dashed line) compared with trials in which the target is in the nonpreferred location (blue). Right: the population of direction selective cells (n = 80 and n = 147) shows an increased response in trials with the preferred motion direction (orange) compared with the response in trials with the nonpreferred direction (green). Shading represents SEM (±) at each time point. Arrows indicate the onset of separability between the two curves, determined as the time point when the data in at least five consecutive bins of 20 ms were significantly different from each other (paired t test, p < 0.05).

These results indicate that average population responses are modulated by attended location and the stimulus motion direction in both animals. However, the degree to which the populations do so is different between the animals, particularly for the case of spatial attention. This is also concordant with the higher behavioral performance in monkey R relative to monkey S.

Decoding attended location and motion direction from neuronal ensembles

We used a binary linear classifier, support vector machine (Cortes and Vapnik, 1995; SVM), to decode spatial attention and the stimuli’s motion direction independently from ensembles of simultaneously recorded task-related units in each session. We used the SVM as a proxy to assess the ability of a downstream entity (single neuron or neuronal ensemble) to read out the information from the recorded LPFC neuronal ensemble. Decoding accuracy was assessed using a cross-validation procedure in which 90% of the data were used for training and the remaining 10% for testing (10-fold cross-validation; see Methods).

The amount of information encoded by a neuronal ensemble has been shown to vary with the number of units in the ensemble (Tremblay et al., 2015). To investigate this issue, we used two different procedures of progressively building (adding units to) neuronal ensembles and obtained a decoder performance value for each ensemble size and composition. First, we decoded from each single unit independently and sorted the units based on their performance from highest to lowest. Then, we built neuronal ensembles (e.g., n = 2, 3, 4, … 94) by iteratively adding the next-best-performing unit (Fig. 5A, left, best single unit ensemble or BSU method). Second, we used a variation of this method: in each iteration, instead of adding the next-best-performing single unit to the ensemble, we added the unit that maximized the decoder’s performance when added to the ensemble. In this procedure, the existing ensemble of size n is paired with each one of the remaining units that have not been added, and a value of decoding accuracy for all n + 1 ensembles is obtained. The n + 1 ensemble that yielded the highest decoding was chosen. Then we kept this best-performing ensemble of n + 1 units and repeated the procedure (Fig. 5A, right). Note that applying this procedure does not search for the entire space of possible n-size ensembles, which was computationally unreachable in reasonable time. We refer to this building method as the best ensemble (BE; see also Methods).

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Figure 5.

Ensemble building procedure. A, We ranked individual units based on their information content, as assessed by SVM and then, starting with the most informative unit, either iteratively added the next best unit to the ensemble (BSU procedure) or looped through the remaining units to identify which pair yielded the highest performance, then looped through the remaining units to identify the best trio, etc. (BE procedure). B, Example session from monkey R when decoding target location. The decoding accuracy in percentage is shown as a function of ensemble size for both building procedures (green, BE; magenta, BSU). Decoding accuracy expected by chance is shown in gray for BSU and in black for BE. Circular markers indicate the individual units’ decoding accuracy and the order in which they get added to the ensemble. Colored markers mark selectivity for the decoded feature. The red line connects the markers that make up the BSU ensemble, and the green line connects those that make up the BE ensemble. C, Example session from monkey S when decoding motion direction.

The difference between these two procedures is that in the BSU procedure, performance of individual units dictates which unit is added to the ensemble. If the main factor that determines performance is the coding properties of individual units, this procedure should yield the best decoding performance with fewer units. On the other hand, in the BE procedure, the contribution of a unit to information coding by the entire ensemble determines its ensemble membership. In other words, the BE procedure takes into account not only the performance of the added unit considered in isolation but how the added unit interacts with the rest of the ensemble. If the tuning properties of individual units, and not the interactions, solely determine the ensemble performance, these two procedures should lead to identical ensembles of n units in each iteration (for all ensemble sizes).

Fig. 5B,C shows the results of two example sessions when decoding attended location in monkey R and motion direction in monkey S, respectively. The green lines indicate the decoding performance using the BE building method as a function of ensemble size, and the magenta lines indicate it for the BSU building method. The black and gray lines denote chance levels, obtained by shuffling the trial labels, for the BE and BSU ensembles, respectively. The circular markers show the individual units’ decoding performances in the order in which they were added to the ensembles. Colored markers indicate whether a unit was selective for either a target (attended) location (blue) or motion direction (yellow). For the BSU building method, we see, as anticipated, a steady decline in individual units’ decoding performances (red lines), whereas for the BE method, sometimes low performing/untuned units were added before high performing/tuned ones (green lines). Importantly, both ensemble methods consistently yield higher decoding accuracy than the best single-unit decoding accuracy (first unit on the x-axis or ensemble with n = 1). Note that the lines converge at the maximum ensemble size: for this n, the ensembles are the same and hence the decoding accuracy should be similar.

Next, we confirmed these results at the population level (Fig. 6). Because the number of units we recorded varied between sessions, we considered the minimum ensemble size for our analyses (n = 94 in monkey R and n = 61 in monkey S), truncated the data accordingly, and plotted the average across sessions. We compared the decoder performance of the different ensemble types (magenta for BSU and green for BE) with the average performances based on surrogate data in which the trial labels were randomized 10 times and new ensembles for each shuffle were built (gray for shuffled BSU and black for shuffled BE) and with ensembles for which the trial labels had been permutated within condition 100 times, i.e., removing the simultaneity of recordings and effectively removing noise correlations (dashed lines). The lines inside the table on top of the plots indicate ensemble sizes that were significantly different from each other for the different comparisons (BE vs. shuffled, BSU vs. shuffled, BE vs. decorrelated BE, and BSU vs. decorrelated BSU).

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Figure 6.

Decoding from neuronal ensembles using SVM. We decoded target location (A, B) and motion direction (C, D) during the postcue epoch from monkey R and S, respectively. The SVM’s performance (left ordinate) is shown as a function of ensemble size (abscissa). We truncated the plots to show only the performance for the minimum number of units across sessions. Green lines indicate decoding from BE ensembles, and magenta indicates BSU ensembles. Average decoding performance from ensembles built out of shuffled data are shown in black (BE) and gray (BSU). Dashed lines represent decoding from BE and BSE ensembles when noise correlations had been removed by shuffling trials within the same condition. Shading over the lines indicates SEM (±) for each ensemble size. The lines in the table on top indicate which ensemble sizes were significantly different from each other (p < 0.05) for the indicated comparisons. Circular markers indicate the individual units’ decoding performance once they got added to the ensembles. The right ordinate indicates decoding performance for the maximum ensemble sizes averaged across sessions. We compared median SVM performance of the ensembles that had produced the highest decoding accuracy for each stimulus class independently in monkey R (E) and monkey S (F). Error bars represent standard deviations across recording sessions.

When we decoded target location, the performance of all BSU sizes for monkey R (Fig. 6A) was significantly higher than chance performance (exact test, p < 0.01^k). Similarly, the performance of 93 of 94 BE ensemble sizes was also higher than chance (exact test, p < 0.01^l). Removing noise correlations from the ensembles reduced decoding accuracy for smaller ensembles (n < 40) using the BE method (paired t test, 0.0091 < p < 0.0489^m) and had no effect on BSU ensembles (p > 0.2074ⁿ). For monkey S (Fig. 6B), we found the same trend across all BE ensemble sizes, although the exact tests failed to reach statistical significance (p > 0.08^p). The same was true for the BSU ensembles (p > 0.2400^o). Removing noise correlations had similar effects as in monkey R: it decreased decoding performance in the majority of BE ensembles (57/61, paired t test, 1.59 × 10⁻⁴ < p < 0.0495^q) and only in few BSU ensembles (2/61, 0.0373 < p < 0.0499^r). One reason we did not see a statistically significant difference between the data-based ensembles and those built on random data may be that the ensembles had different compositions that might have affect the comparison negatively. Nonetheless, our data indicate that even in monkey S, there is a systematic trend that relatively small and heterogeneous neuronal ensembles can encode stimulus information, even when the proportion of single units tuned for that feature in the ensemble is low. This may be due to the linear classifier weighing the contribution of different neurons to information coding unequally, as well as to the ability of the classifier to use information about the correlation structure of the neuronal ensemble. Note that the curve corresponding to the BE method in monkey S (green) reaches a maximum and then decreases as more neurons are added. This is likely because of the finite number of trials in our sample and the relatively low selectivity of neurons for the attended location. A small number of trials yields a too-high feature-to-instance ratio (i.e., neuron-to-trial). This leads to overfitting and consequently a decay in mean decoding accuracy (Trunk, 1979; Guyon and Elisseeff, 2003; Kanitscheider et al., 2015). In fact, the average decoding performance for the maximum possible BE ensemble size per recording session is not significantly different from chance (Fig. 6B, right ordinate, exact test, p = 0.8000^s).

When examining decoding of motion direction, almost all BSU ensemble sizes for monkey R were significantly above chance (Fig. 6C, 89/94, exact test, p < 0.01^t), and all ensemble sizes in monkey S were (Fig. 6D, exact test, p < 0.01).^u The BE also yielded significantly above-chance performances across 91 of 94 ensemble sizes in monkey R and across 60 of 61 ensemble sizes in monkey S (exact tests, p < 0.01^v and p < 0.01,^w respectively). Removing noise correlations again had a decreasing effect on most of the BE ensembles in both animals (paired t test, 1.43 × 10⁻⁴ < p < 0.0469^x and 6.19 × 10⁻⁵ < p < 0.0458^y for monkeys R and S, respectively) and yielded mostly no change in the BSU ensembles.

When decoding attended location using the BE method, we found higher decoding accuracy across all ensemble sizes in monkey R than in monkey S (unpaired t test, 5.69 ×10⁻⁷ ≤ p ≤ 2.99 ×10^{−4 z}). In contrast, when decoding motion direction using the BE, performance was better in monkey S relative to monkey R (unpaired t test, 2.74 ×10⁻⁶ ≤ p ≤ 0.0080^bb). The same was true when examining the BSU ensembles (unpaired t test, 1.05 ×10⁻⁵ ≤ p ≤ 4.02 ×10^{−4 aa} for location decoding and 1.46 ×10⁻⁵ ≤ p ≤ 0.0191^cc for direction decoding). These results follow the same trend as the differences in proportions of selective cells between animals (Fig. 3A). Notably, we were able to decode more information from either ensemble type than from the best single units (dots in all panels). This corroborates that ensembles encode substantially more information than the best single units and therefore than any measurement derived from statistics based on single-unit performance (e.g., average, median, or maximum performance across single units).

To more closely examine the differences in decoding performance between the BSU and BE ensemble-building methods, we assessed the maximum performances linked to each ensemble building method for both features (see Tables 2 and 3). It is important to note that in this analysis, the maximum performance is not necessarily equivalent to the performance of the full ensemble (see right ordinate axis in Figure 6A–D). Here, we defined maximum decoding performance as the average maximum decoding accuracy across recording sessions in the plotted ensemble sizes. The full ensemble does not necessarily yield the highest decoding performance, because our training/testing set has a finite number of trials. As mentioned earlier, training on finite data can lead to overfitting and suboptimal decoding accuracy (Trunk, 1979; Guyon and Elisseeff, 2003; Kanitscheider et al., 2015). The maximum performance can be considered as a low boundary estimate in the information encoded by the neuronal ensemble we recorded from.

When decoding target location in monkey R (Fig. 6E), the best BE returned slightly higher median decoding accuracy than the best BSU (89.19% ± 3.07 and 88.00% ± 5.26, respectively), yet this difference was not statistically significant (Wilcoxon signed-rank, p = 0.1250^dd). Similarly, when decoding motion direction, the best BE yielded a higher median accuracy (72.62% ± 3.42) than the best SU (70.10% ± 4.57), but this difference again did not reach statistical significance (Wilcoxon signed-rank, p = 0.1250^ff).

When decoding target location in monkey S (Fig. 6F), the best BE generated higher median decoding accuracy than the best BSU (60.93% ± 2.05 and 57.32% ± 2.26, respectively). This difference did not reach statistical significance (Wilcoxon signed-rank, p = 0.0625^ee). The same was true for the decoding of motion direction (median best BE = 89.38% ± 1.66, median best BSU = 87.10% ± 2.21; Wilcoxon rank-sum, p = 0.0625^gg). In summary, when we analyzed each animal separately, we found a small trend for the median decoding accuracy to be higher when using the BE ensemble building method, but it did not reach statistical significance.

However, when pooling data across animals (n = 9, Tables 2 and 3, compare second and fourth columns) we found that BE method yielded significantly higher maximum performance than the BSU method for both attended location and motion direction (Wilcoxon signed-rank test, p = 0.0039^hh for target location and p = 0.0039ⁱⁱ for motion direction).

Effect of ensemble size on decoding performance

One interesting observation in Fig. 6A–D is that as ensembles increase in size, there is a fast increase in performance for small sizes that seems to reach an asymptote for ensembles of ∼20 units or less. This suggests that maximum classification performance can be achieved with ensembles that are substantially smaller than the largest possible ensemble size. It also suggests that the information brought about by adding more neurons to an ensemble can be negligible. To closely examine this issue, we computed the ensemble sizes at which the maximum performance was achieved, as well as the ensemble size at which 90% of that maximum performance was achieved for both the BE and the BSU methods (Tables 2 and 3).

In some ensembles, the number of neurons needed to achieve maximum performance is smaller than the number of neurons needed to achieve 90% of that performance (Table 2, monkey Sd5). This is because the best decoding performance as achieved by a single neuron, and adding more neurons lowered the performance. These ensembles were more the exception than the rule. They usually have lower performance than the rest of the ensembles, which can be explained by the progressive addition of noisy neurons that are poorly tuned and detrimental to the correlation structure.

We pooled the indices across monkeys and across direction and location ensembles (Tables 2 and 3) and compared ensemble sizes for maximum performance and 90% of maximum performance. The latter was done to have a second estimate that does not depend on a single measurement that could be due to a peak in performance at a given ensemble size. The BE method reached maximal decoding accuracy at smaller ensemble sizes than the BSU method (Wilcoxon signed-rank, p = 0.0198^jj). The BE method also yielded 90% of maximum decoding accuracy at smaller ensemble sizes compared to the BSU method (Wilcoxon signed-rank, p = 0.0293^kk). Overall, our results indicate that BE ensembles reach their best decoding performances at smaller ensemble sizes. This is also in line with our previously mentioned result (Fig. 6B), which indicated that significant differences between BE and the shuffled counterparts were found at relatively small ensemble sizes.

Decoding accuracy and behavior

One important question is whether the information encoded by neuronal ensembles in the LPFC contributes to task performance. If it does, one would anticipate that fluctuations in ensemble performance correlate with fluctuations in the animals’ performance. We decoded the attended location using the neuronal activity from the BE ensembles that had generated the maximal decoding performance for different trial outcomes: all trials, hit trials only, relevant error trials [misses (no response) and false positives (response to change in distractor stimulus)], and false positives only. In monkey R, the average decoding performance across all trials was 83.11% (SD 4.79; Fig. 7A, black bar), which was significantly higher than chance decoding (exact test, p < 0.01^ll) but slightly lower than the performance using hit trials only (87.40% ± 4.27, white bar; exact test to compare to chance, p < 0.01ⁿⁿ) whereas the decoder performed at chance level when using error trials (50.72% ± 7.80, exact test, p = 0.4300,^pp dark gray bar) or only false-positive trials (47.09% ± 10.24, exact test, p = 0.4600,^rr light gray bar).

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Figure 7.

Relationship between decoding accuracy and monkeys’ behavior. We used the BE ensemble with the highest decoding accuracy to decode target location from the neuronal activity during different trial outcomes (black, averaged across all trials; white, correct trials only; dark gray, error trials; light gray, false positives only) independently for monkey R (A) and monkey S (B). Error bars represent standard deviations across recording sessions. Asterisks mark significant differences in mean accuracy compared to chance decoding accuracy (***, p < 0.001, *, p < 0.05; exact test). We repeated this analysis for motion direction in monkey R (C) and monkey S (D).

When we decoded target location from the data obtained from monkey S, we actually did not reach higher-than-chance performance when considering all trials (52.84% ± 1.44, exact test, p = 0.2840^mm; Fig. 7B, black bar). However, when considering hit trials only, the decoder’s performance was slightly but significantly better than chance (white bar, 56.28% ± 1.92; exact test, p = 0.0160^oo). When decoding from error trials, the performance was again at chance level [48.95% ± 3. 68, exact test, p = 0.3760^qq and 50.44% ± 3.19, p = 0.6600^ss for error trials (dark gray bar) and false positives only (light gray bar), respectively].

We repeated this analysis for the feature motion direction. In monkey R, the decoder’s performance was above chance when considering all trial outcomes (Fig. 7C, black bar) and correct trials only (white bar; 66.68% ± 3.71 and 69.01% ± 4.15, respectively; exact test, p < 0.01^tt,vv). When considering all error trials (dark gray bar), the performance dropped to chance level (53.38% ± 4.17; exact test, p = 0.5500^xx). Similarly, when decoding from false-positive trials, performance was at chance level (52.01% ± 13.23; exact test, p = 0.3850^zz).

In monkey S, the decoding accuracy remained high regardless of behavioral performance (Fig. 7D). When decoding from all trials, the mean performance was 86.03% ± 2.16 (black bar). When using hit trials only (white bar), there was a slight increase to 86.98% ± 1.79, and when using error trials (dark gray bar), it dropped to 82.52% ± 3.61, which is very similar to the decoding performance when considering false positives only (83.08% ± 4.82, light gray bar). In all cases, the decoder performed above chance level (exact test, p < 0.01^uu,ww,yy,aaa).

These results indicate that in both animals there is a similar relationship between the behavior of the monkey and the encoding efficiency of LPFC neuronal ensembles, with the effect being more pronounced for the allocation of spatial attention.