A Normalization Circuit Underlying Coding of Spatial Attention in Primate Lateral Prefrontal Cortex

Sensory normalization in LPFC area 8a

In a given attention trial condition, the cue was presented alone at the start of the trial, allowing us to examine the responses of the neurons to single stimuli presented in different quadrants of the visual field. The responses in the fixation trials allowed us to quantify the responses to all the stimuli presented together (Fig. 1A, bottom). Figure 2A shows an example neuron’s response to a lone cue stimulus presented in each of the four quadrants. The cue evoked the strongest response when presented in the upper left visual quadrant, and evoked minimal change from baseline when shown in the other quadrants. When all the stimuli were presented together the response was in between the maximal response to the cue on the upper left quadrant and the responses to the cue in the other quadrants. For each cell, we computed responses during the cue epoch or equivalent time window during fixation trials when the four stimuli were presented together. We tested whether the responses of single neurons to multiple stimuli equaled the sum responses to those stimuli presented alone, as predicted by a linear SUM model (Fig. 2B, SUM, red line). The vast majority of our tuned units’ (232/236; 98%) responses to multiple stimuli were sublinear and resembled those predicted by an average model computation (AVG, green line).

To further explore this issue, we transformed the data in Figure 2B by scaling each unit’s activity by its mean response to the cue that evoked the strongest response (preferred location or stimulus; Fig. 2C). This enabled the comparison of responses to a WTA response model prediction (blue line). WTA can be considered as a form of response normalization wherein a unit’s response to multiple stimuli is equal to its response to the preferred stimulus alone. We computed the RMSE from the data to the prediction of the SUM, AVG, and WTA models. Of these three response configurations, the AVG computation yielded the lowest RMSE (bootstrap t test, p < 10⁴,^a Bonferroni corrected; Fig. 2D). This demonstrates that neurons in area 8A undergo response normalization when multiple stimuli are presented in the visual field and that, from the three models considered, the AVG model best describes the computation.

Spatial tuning and normalization

We divided our sample into two subsets: neurons that produced a maximal response when the single stimuli were presented ipsilateral to the recording hemisphere and neurons that produced a maximal response when the stimulus was presented contralateral to the recording hemisphere (referred to as ipsilateral and contralateral neurons, respectively; Fig. 3A,B). Figure 3C shows the same plot as Figure 2B with each neuron labeled according to its visuospatial tuning. By comparing RMSE between models, we found that both populations of tuned neurons were best described by an AVG response (bootstrap t test on RMSE, p < 10⁻⁴,^b,c Bonferroni corrected). We further quantified the strength of normalization in each neuron using a MSRI, where r_all is a unit’s average response to the four stimuli presented simultaneously, and is its response to a single cue stimulus presented in quadrant i on the screen (i = 1 … 4 for the four quadrants). If a unit’s response to all stimuli (r_all) equals the sum of the responses to each stimulus alone ( ) then MSRI is 0; if r_all is greater than , MSRI is <0; and if r_all is lower than , MSRI is between 0 and 1. For our task with four stimuli, an average (AVG) response would occur when r_all = , and MSRI = 0.75. Although the distributions of MSRI overlap, the average MSRI was greater for ipsilateral neurons (median = 0.78, 95% confidence interval (CI) [0.75,0.81]) than for contralateral neurons (median = 0.70, 95% CI [0.67,0.73]; Mann–Whitney U test, z = 4.32, p = 7.97 × 10⁻⁶;^d Fig. 3D). This indicates a stronger response normalization in ipsilateral than in contralateral units.

Receptive field size and normalization

The difference in normalization between contralateral and ipsilateral neurons could be explained by differing RF properties between units, such as RF size. Here, we consider the RF as the region of the visual field that is modulated by the appearance of the single cue and includes both excitatory (RFe) and inhibitory (RFi) regions. To investigate this issue, we first estimated the size of each unit’s RF (pooling across both RFe and RFi) by examining whether individually presented stimuli in each quadrant modulated the firing rate relative to the pre-stimulus baseline response (paired t test with threshold of α = 0.05, Bonferroni corrected; Fig. 4A; see Materials and Methods). On average, ipsilateral-tuned units had RFs spanning more quadrants (bootstrapped mean ± SD: 2.9 ± 0.1 quadrants) than contralateral-tuned units (2.24 ± 0.09 quadrants, bootstrap t test, p < 10⁻⁴).^e However, the overall size of a unit’s RF was only weakly correlated with its MSRI (Spearman’s ρ = 0.18, bootstrap 95% CI [0.06,0.29], p < 10⁻⁴;^f Fig. 4B), and thus it is unlikely to fully account for the difference in MSRI between the two populations.

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Figure 4.

Receptive field properties. A, Distributions of receptive field sizes (number of quadrants) for ipsilateral and contralateral neurons. A quadrant of the visual field was classified as being part of a unit’s receptive field if a singly presented stimulus in that quadrant elicited a response (excitatory or inhibitory) different from pre-stimulus baseline. B, Corresponding MSRI of units with a given receptive field size. Medians (black vertical lines) were computed using 10,000 bootstrap samples, and gray bars indicate the central 95% CIs of the distribution of medians. CIs for top row: [0.65,0.72], second row: [0.66,0.76], third row: [0.73,0.81], and fourth row: [0.71,0.76]. C, Receptive field configurations. Singly presented stimuli may either excite or suppress neuronal activity relative to baseline. Thus, the receptive field of a given neuron can be (1) purely inhibitory, (2) purely excitatory, or (3) a mixture of both. Neuronal responses (z-scored to baseline) were combined for each of the three possible groups. Preferred responses were the responses to stimuli which elicited the greatest response (or the stimuli which elicited the least amount of suppression, in the case of the purely inhibitory RFs). Non-preferred responses are the average response to the three stimuli, excluding the preferred stimulus. Insets show proportion of ipsilateral-tuned and contralateral-tuned cells in each group. D, MSRI of units with RF compositions shown in C. MSRI was greater in units with a greater proportion of inhibitory receptive quadrants. Each dot is one single unit. Dots are horizontally jittered with reduced opacity for clarity. Vertical length of diamonds are 2.5th and 97.5th percentile CIs of the bootstrapped distributions (10,000 samples) of medians. CIs for purely inhibited cells: [0.79,0.83], cells with a mixture of excited and inhibited activity: [0.73,0.79], and purely excited cells: [0.64,0.68].

It is possible that the difference in normalization between the populations are related to the specific composition of the RF in terms of excitatory and inhibitory regions. Specifically, the suppressed response to many stimuli may depend on whether specific regions of the RF are excitatory (RFe) or inhibitory (RFi). We determined whether a region was excitatory or inhibitory by quantifying the difference in responses between a single cue, and pre-cue baseline when the animal was only fixating the center point with no stimulus present. Indeed, in our recorded population we obtain a heterogeneous sample of RF compositions: purely inhibited (all responses below baseline), purely excited (all responses above baseline) and mixture of the two (Fig. 4C). However, we found a trend for a larger proportion of ipsilateral tuned neurons to be purely inhibited, and an opposite trend of a higher proportion of contralateral neurons to be purely excited that did not reach statistical significance (χ² test p = 0.09^g).

Whereas the size of the RFi was positively correlated with the MSRI (Spearman’s ρ = 0.50 ± 0.05, bootstrap mean ± SD, p < 10⁻⁴),^h the size of a unit’s RFe was negatively correlated with the MSRI (Spearman’s ρ = –0.34 ± 0.06, bootstrap mean ± SD, p < 10⁻⁴).ⁱ Thus, the larger a neuron’s RFi (measured as number of quadrants), the more normalization it exhibited. Conversely, a neuron with a larger RFe was likely to show weaker normalization. In agreement with this result, the median MSRI for neurons with purely RFi was greater than for neurons with purely RFe (bootstrap t tests between MSRI distributions, purely inhibitory vs purely excitatory: p < 10⁻⁴,^j purely inhibited vs mixture: p = 0.012,^k mixture vs purely excitatory: p < 10⁻⁴;^l Fig. 4D). This result suggests that the extension of the RFe and RFi, determined using singly presented stimuli, relates to the amount of response normalization a given neuron undergoes when multiple stimuli are presented. Furthermore, contralateral neurons, with larger RFe regions and smaller RFi regions, undergo less normalization than their ipsilateral counterparts.

Another possibility that may account for the differences in response normalization is that the populations of ipsilateral and contralateral neurons mutually inhibit each other, with the strength of the inhibition being proportional to the size of the neuronal pool. Previous studies have shown that contralateral neurons are more numerous than ipsilateral neurons in this area (Lennert and Martinez-Trujillo, 2013; Bullock et al., 2017). We observe this again in the current study, using the multiunit activity obtained from each electrode to determine its tuning (contralateral or ipsilateral). Figure 5A shows the locations of ipsilateral (cyan) and contralateral (orange) units on the microelectrode array for each animal; a significantly larger proportion of neurons are contralateral compared to ipsilateral (Z test for proportions, H₀: 50% ipsilateral tuned, 50% contralateral tuned; Monkey JL, Z = 10.2, p < 10⁻⁴;^m Monkey F, Z = 8.2, p < 10⁻⁴;ⁿ Fig. 5C) . We also computed Moran’s I, an index of spatial autocorrelation, to quantify clustering of these two groups of neurons on the cortical surface, and observed significant clustering in both animals; neurons of a given type (e.g., contralateral) are more likely to be surrounded by neurons of the same type than by neurons of the opposite type (Fig. 5B, Moran’s I, black line above the gray null distribution). This trend was more evident in animal JL for different cluster radiuses, while in animal F the trend only occurred for small cluster radiuses.

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Figure 5.

Anatomic clustering of spatial tuning. Multielectrode array data from Monkey JL (left column) and Monkey F (right column). A, Multi-unit spatial tuning (ipsilateral or contralateral) on each electrode of the array when using three recording sessions (one per block of 32 electrodes; see Materials and Methods) from each monkey. Black squares are inactive channels, and white squares are channels in which no tuning was present (for details, see Materials and Methods). B, Spatial autocorrelation of tuned clusters on recording array using Moran’s I. Black curves are empirical distributions and gray shaded regions are shuffled 95% null distributions. Although both subjects showed significant clustering at the smallest cluster size, Monkey JL exhibited significant clustering at larger spatial scales than Monkey F. C, Distribution of multi-unit spatial tuning across all recording sessions (12 sessions in Monkey JL, and 11 sessions in Monkey F).

Effects of attention on normalization responses

Stimuli presented during attention trials were identical to those presented during fixation trials. However, after the cue presentation during attention trials, when the four stimuli appear on the screen, the subjects covertly attended toward the cued stimulus in one quadrant while ignoring the three distracters located in the other quadrants (Fig. 1A, top). We characterized neuronal responses when attention was allocated to (1) the stimulus that evoked a stronger response when presented alone (preferred stimulus, attend in), (2) one of the non-preferred stimuli (attend out), and (3) the fixation point, when none of the four stimuli were cued (“fixation”). Ipsilateral and contralateral neuronal responses in these three different attention conditions are shown in Figure 6A.

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Figure 6.

Ipsilateral and contralateral population attention responses. A, Bootstrapped population average SDFs for ipsilateral (left panel) and contralateral populations (right panel). Attend in, attend out, and fixation trial responses are shown in blue, red. and black, respectively. Attend out trial conditions were averaged across the three non-preferred locations. Single neuron spike trains were trial-averaged, convolved with a Gaussian kernel (15-ms SD), z-scored, and finally averaged within each ipsi/contra population. B, Comparison between each unit’s response to a single stimulus presented in its RF center during the cue epoch (x-axis) vs its attend in response during the delay epoch when distracters were present (y-axis). Dotted line is when a unit’s attend in response matches its response when presented that stimulus alone (i.e., WTA response). C, The sum of each unit’s responses to individual stimuli (x-axis) versus attend in responses (y-axis); x-coordinates of each point are identical to those in Figure 2B. D, RMSE for WTA and AVG models during attend in and attend out conditions for ipsilateral-tuned and contralateral-tuned units. For attend out conditions, we used trials where the animals were attending to the quadrants adjacent to a given unit’s preferred quadrant and located in the opposite hemifield. We found similar results using attend out responses for the remaining two quadrants (i.e., either attending to the quadrant diagonal to the preferred quadrant, or the quadrant adjacent to the preferred quadrant and in the same hemifield) as well. RMSE for SUM models were omitted for clarity due to being much greater in magnitude compared to AVG and WTA model RMSE.

Firing rates were on average higher during attend in trials than during attend out trials (Fig. 6A, blue and red lines, respectively). This effect was highly significant for both the ipsilaterally-tuned population (t test, t₍₆₈₎ = 5.5, p = 6.2 × 10⁻⁷)^o and contralaterally-tuned population (t test, t₍₁₆₂₎ = 7.15, p = 2.8 × 10⁻¹¹).^p We found that attend in responses of contralateral neurons, but not ipsilateral neurons, were better described by a WTA model (a linear regression slope of 1 signifies a WTA response; Fig. 6B). The regression slope for contralateral neurons (median slope = 0.89; 95% CI [0.81,0.96]) was greater than that for ipsilateral neurons (median slope = 0.62; 95% CI [0.59,0.65]; bootstrap t test, p < 10⁻⁴).^q Figure 6C shows each unit’s sum of responses to individually presented stimuli versus its response to four stimuli during attend in trials. We computed the RMSE corresponding to each model prediction for contralateral and ipsilateral neurons during both attend in and attend out conditions. Attend in and attend out responses of ipsilateral neurons remained best-described by an AVG model (bootstrap t test on RMSE, attend in p < 10⁻⁴;^r attend out p < 10⁻⁴;^s Fig. 6D). For contralateral units attend out responses were also better described by an AVG model (bootstrap t test on RMSE, AVG vs WTA p = 3 × 10⁻⁴).^t However, contralateral attend in responses were best described by a WTA computation (dashed gray box; bootstrap t test, p = 0.01^u). Thus, when the animals attended to the preferred stimulus, normalization in contralateral units shifted from AVG to WTA.

Dynamics of sustained attention

The previous analyses using firing rates averaged over statically defined time periods of the task overlooks the temporal dynamics of attentional modulation. We investigated this issue by first examining how responses during the attentional period change over time relative to the cue period responses. We scaled each unit’s SDF (Fig. 6A) by the mean response to its preferred stimulus (i.e., maximal response) to yield a time-evolving index. We called this index the WTA index to refer to changes in response during the attentional period relative to the response when the cue is presented alone (Fig. 7). A decrease in WTA index away from 1 indicates a stronger normalization response toward the AVG regime caused by distracters.

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Figure 7.

Single neuron characterization of attention dynamic responses. Bootstrapped average population WTA index (y-axis) over time (x-axis) for (A) attend in and (B) attend out conditions. We computed linear regression slopes (arrows) for the decaying, and sustained attention portions of the curves during time bins denoted by gray bars on the x-axis. Shaded error bars are 1 SD. Each line was computed using 10,000 bootstrap samples.

Both population WTA indices decreased following distracter onset in the attend in condition (Fig. 7A), indicating that responses to all stimuli decreased relative to the single target response. In other words, responses were normalized toward the AVG response on distracter onset. We computed the temporal rate of normalization in the ipsilateral and contralateral populations after distracter onset by fitting straight lines to the time evolving WTA indices (linear regression slopes computed during time bin 1, indicated by the left shaded gray bar along the x-axis; Fig. 7A). The ipsilateral population slope (cyan arrow; time bin 1) was more negative than the contralateral population slope (orange arrow; time bin 1; mean ± SD, ipsilateral: –2.0 ± 0.3 s⁻¹; contralateral: –0.8 ± 0.3 s⁻¹; p = 8 × 10⁻⁴,^v bootstrap t test). This shows that during attend in trials, ipsilateral neurons were more strongly normalized by the appearance of the distracters than contralateral neurons. Approximately 250 ms following this initial response decrease, there was an upward trend (time bin 2, indicated by the right shaded gray bar along the x-axis) toward a WTA response (dashed line), with positive average slopes for each population, not statistically different from one another (orange and cyan arrows aligned with bin 2; ipsilateral-tuned slope: 0.3 ± 0.1 s⁻¹; contralateral slope: 0.4 ± 0.1 s⁻¹; p = 0.18^w, bootstrap t test). This suggests that the rate of response change toward the WTA regime when the animals maintained attention on the target is similar in both populations. However, the degree of suppression (normalization) caused by distracter onset is stronger in ipsilateral neurons.

During attend out trials, neural activity after distracter onset initially moves toward a WTA regime for both populations, however this increase was greater in magnitude for contralateral neurons (comparing means during time bin 1; bootstrap t test, p < 1 × 10⁻⁴;^x Fig. 7B). During attend out trials, since the initial cue was outside the preferred region of each neuron’s RF, the change in normalization during the delay epoch was likely due to a distracter populating the neurons’ RFs. After this initial increase, the WTA index promptly decreased in both populations. The modulation rate (linear regression slope during time bin 1) for both contralateral and ipsilateral units were similar and not significantly different from one another (ipsilateral: –1.4 ± 0.5 s⁻¹; contralateral: –2.0 ± 0.4 s⁻¹; p = 0.12^y, bootstrap t test). After this initial rapid decay, normalization stabilized (Fig. 7B, time bin 2), and we found that linear regression slopes were not different from zero for either the ipsilateral (p = 0.42^z, bootstrap t test) or contralateral population (p = 0.86^aa, bootstrap t test) during this period. However, the normalization level at which ipsilateral responses stabilized was significantly lower than the level at which contralateral responses stabilized (both relative to the WTA line; p < 1 × 10⁻⁴,^ab bootstrap t test comparing means during time bin 2). This is likely a direct consequence of the initial response increase being stronger in contralateral relative to ipsilateral units and the decrease being of similar magnitude in both subpopulations.

To make the temporal dynamics of the responses more intuitive, we applied a state space analysis (Murray et al., 2017; Ebitz et al., 2018) to the population of ipsilateral and contralateral neurons. We averaged the SDFs of neurons (scaled to the mean response to their preferred stimuli) in each subpopulation for the four attentional conditions. This effectively reduced the dimensionality of the dataset from n = 232 to 2 dimensions, with each dimension representing the activity of cells with opposing spatial tuning (contralateral or ipsilateral). The two horizontal axes in Figure 8A represent these two dimensions, the vertical axis represents time, and trials of different attentional conditions are color coded.

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Figure 8.

Temporal dynamics of attention. A, State space trajectories. Average activity across contralateral neurons (x-axis) is plotted against average activity across ipsilateral neurons (y-axis) for each point in time (z-axis) and averaged within each trial condition. Colored lines are average activity during the four possible attention trial conditions, and the black line is the average activity during the Fixation trial condition in which no cue was presented. B, Euclidean distance through time of each average attention trial condition trajectory (colored) from the fixation trajectory in A. Dashed black line is the average of the four conditions. A linear regression slope was computed for the dashed line during the latter portion of the delay epoch (gray time bin). C, Time-evolving Euclidean distance of each attention trial condition’s delay epoch activity (i.e., activity after distracter onset) from its respective mean activity during the cue epoch. Dashed line is the average of the four conditions. D, Pairwise Euclidean distance between each attention trial trajectory in A. Dashed line is the average of all the pairwise comparisons. Comparisons were made between conditions where the animal attended to the top left (tl), top right (tr), bottom left (bl), or bottom right (br) quadrants of the screen. A linear regression slope was computed during the latter portion of the delay epoch (gray time bin).

In this plot, by folding the trajectories around the “distracter onset” plane (corresponding to the time at which distracters appeared during the attentional conditions), one can compare how much the trajectories during the cue epoch and during the attentional delay epoch resemble each other. Identical cue and attentional delay trajectories for a given cue would indicate that attention operates to bring the population state toward an ideal WTA regime that fully filters out the neural activity evoked by distracters. On the other hand, if the trajectories in the attention conditions approximate the trajectory for the attention-free fixation condition, the network would be in a full normalization regime and attention would have no effect.

Note that during the cue period, no stimulus was displayed in fixation trials, and the animals were simply holding their gaze on the fixation point. Distances from the different cue/attentional conditions to the fixation condition depart from zero after cue onset and reached their maximum during the first 200–300 ms of the cue period (Fig. 8B). On distracter onset, neural trajectories converged toward the fixation condition trajectory at ∼470–480 ms. However, as attention was sustained on the target, trajectories diverge from fixation and the average separation between the attention conditions and fixation trajectories increased again over time. We computed a linear regression slope of the average distance as a function of time over the delay epoch (dotted black line, slope computed over gray shaded region) and found it to be significantly positive (bootstrap t test, 1000 samples, p < 0.001^ac). This result indicates that population activity increasingly diverges from the fixation condition as attention is sustained on the target.

To determine how much the effect of attention migrates toward an ideal WTA regime, we compared each neural trajectory during the delay epoch (after distracter onset) to its respective mean trajectory during the cue epoch (Fig. 8C). This shows how population activity when attending toward a stimulus surrounded by distracters compares to its activity when the stimulus was presented in isolation (i.e., how closely does delay activity resemble a perfect WTA). Distracter onset (time = 0; Fig. 8C) caused neural trajectories to diverge quickly away from the WTA regime, with average ipsilateral trial trajectories (mean of blue and green lines 50–250 ms after distractor onset) displaced farther than average contralateral trajectories (mean of red and yellow lines 50–250 ms after distractor onset; bootstrap t test, p < 0.001^ad). Following distracter onset, trial trajectories on average evolved toward, but did not fully reach a WTA regime (Fig. 8C, black dashed line). Trajectories of trial conditions in which attention was allocated toward the contralateral hemifield (i.e., average of red and yellow lines 285–585 ms after distractor onset) advanced closer to a pure WTA regime than trajectories of conditions in which attention was allocated to the ipsilateral hemifield (average of blue and green lines 285–585 ms after distractor onset; bootstrap t test, 1000 samples, p < 0.001^ae). Importantly, neither of the trajectories fully reached a WTA regime but seemed to asymptote and stabilize during the sustained attention period.

To determine how neural trajectories corresponding to a given trial condition differ from other conditions over time, we also measured the pairwise Euclidean distances between each trial condition (Fig. 8D). We found that trajectories were highly similar during the baseline period, and maximally differ after cue presentation during the cue period. Following distracter onset, the trajectories converged to a similar state, and diverged again during the delay epoch when attention was sustained (i.e., the average separation between each trial condition’s neural trajectory increased again after they collapsed). Specifically, the linear regression slope of the average pairwise distance as a function of time during sustained attention was significantly positive (dotted black line, slope computed over gray shaded region; bootstrap t test, 1000 samples, p < 0.001^af). This shows that as attention is sustained, neural trajectories become more divergent from each other.

Population coding of sustained attention

Given the non-trivial translation from single neuron coding to population coding, it is unclear whether the effects we reported in averaged populations extend to the full neuronal ensemble activity. Furthermore, given the observed temporal modulation of firing rates and normalization, it is unclear whether the population code during the cue period generalizes to the code during the attention period. Linear classifiers have proven effective for applications such as comparing the information content in neuronal ensembles during different trial periods and determining the similarity between different coding regimes (Moreno-Bote et al., 2014; Leavitt et al., 2017). Thus, we used linear classifiers to assess how similar the population code is when the subject is attending to a target in the presence of distracters compared to when the target is presented alone. We can consider the activity profile and the code used during the cue period as corresponding to a perfect WTA regime. The more the code generalizes between the attentional and cue periods, the more similar sustained attention is to an ideal WTA computation, and consequently the distracters are filtered.

We used a linear classifier to decode the locus of spatial attention; we trained our model on average firing rates integrated over a 300-ms window during the cue epoch (same window as in previous analyses; see Materials and Methods), and tested on average firing rates during a 300-ms window of the attention (delay) epoch. Using all 232 single neurons, the classifier achieved decoding accuracy of 87 ± 2% (Fig. 9A, pink line, test epoch firing rates computed in gray time bin). This shows that the population response with attention toward a target among distracters is similar to that of when the object was presented alone, suggesting an approximate WTA regime at the population level. We quantified the dynamics of this state similarity using the same classifier trained on the firing rates during the 300-ms cue epoch time bin and evaluated the time-evolving state similarity by testing the classifier on sliding windows of firing rates during the delay epoch (Fig. 9A, blue curve). We used a 25-ms boxcar window stepped by 25 ms to compute firing rates from the spike rasters. Decoding accuracy was nearly 100% immediately following distracter onset, likely because the neuronal population still contained residual cue-evoked activity and the distracter information had not yet reached PFC. At 80–90 ms after distracter onset, accuracy drastically fell toward chance level (∼25%; gray line is an estimate of chance level accuracy using shuffled permutation test). However, the decoding accuracy recovered and increased toward ∼60% shortly thereafter, and continued to steadily increase with sustained attention (linear regression slope of 0.02 ± 0.01% ms⁻¹; mean ± SD; Fig. 9B, blue arrow, regression computed using gray shaded region). Therefore, with sustained attention the pattern of neuronal ensemble coding of the attended stimulus evolved over time, and resembles the WTA observed when the cue was presented alone.

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Figure 9.

WTA decoding with sustained attention. A, Linear classifier using a pseudopopulation of 232 single unit firing rates trained on the latter 300 ms of the cue epoch, then tested on: (1) firing rates computed in a 300-ms time window (pink shaded error bar, using firing rates integrated over gray time bin shown along x-axis), and (2) dynamic, trailing moving windows during the delay epoch (window = boxcar with width 25 ms; step size = 25 ms). Solid lines are mean classification accuracy, and shaded error is 1 SD of entire bootstrapped sample. Classification accuracy slowly increased after recovery from transient activity after distracter onset (linear regression computed on dynamic classification accuracy during time bin denoted by gray shaded region) with a slope of 0.02 ± 0.01 ms⁻¹ (mean ± SD; blue arrow). B, Example confusion matrix derived from the final time point of the blue curve in A. Trials in which animals attended toward the ipsilateral hemifield were misclassified more than trials where they were to attend toward the contralateral hemifield (50 ± 3% vs 80 ± 3% correct).

We show a representative confusion matrix derived from test-set predictions made by a decoder at the final time bin of the sliding decoding window Figure 9B. Interestingly, the classifiers made a greater number of errors for trials in which attention was allocated toward the ipsilateral field than when attention was directed toward the contralateral field (50 ± 1% vs 80 ± 1%; bootstrap t test p < 10⁻³).^ag Importantly, our findings from Figure 9A,B were robust to controlling for the uneven population sizes of ipsilateral and contralateral neurons (data not shown); for this reason, we opt for including all recorded ipsilateral and contralateral neurons in this analysis as we believe this to be more representative of the underlying LPFC neuronal population. Thus, when attending toward a stimulus in the presence of distracters, the population read-out of information relevant to the contralateral hemifield is more effective than that of the ipsilateral hemifield. This is likely a resulting effect of the varying differences in magnitude of attentional modulation between the ipsilateral-tuned and contralateral-tuned populations (Fig. 6). Here, one may consider that if the same result would be obtained when recording from the same area in the opposite hemisphere, a downstream reader that read out information from both hemispheres would make few errors in this task.

Decoding the allocation of attention

One may ask what the accuracy of the classifier would be if it were trained on population activity evoked by the entire stimulus display during the attention period? To answer this, we examined the decodable information during the delay epoch in the different subpopulations of neurons and in the entire population (Fig. 10). We trained linear classifiers using firing rates from ipsilateral-tuned units, contralateral-tuned units, and the full population, trained and tested within short-duration windows over the duration of the delay epoch (stepped by 25 ms; see Materials and Methods). First, we note that the classification accuracy exceeded 95% on average, despite using very small integration time windows of 25 ms (Fig. 10A, black curve). Secondly, classification accuracies for to each oppositely-tuned population (contralateral: orange; ipsilateral: blue) both decreased following distracter onset, with the magnitude of decrease being greater in the ipsilateral-tuned population than contralateral-tuned population.

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Figure 10.

Ensemble decoding of locus of covert attention during delay epoch. A, Linear classifier trained and tested on 25-ms trailing windows stepped by 25 ms during the delay epoch of the task. Bootstrapped average classification accuracies using ensembles comprising exclusively the ipsilateral-tuned population (blue) or contralateral-tuned population (orange), or an ensemble comprising both populations (black). Shaded error bars are 1 SD of the entire bootstrap sample. B–D, Confusion matrices for the ipsilateral-tuned, contralateral-tuned and full population classifiers derived from the final time points of the curves in A.

Note that the decoding accuracy decreased to a level that was still well above chance, suggesting that even when distracters caused the firing rates to evolve toward those evoked by the four stimuli during fixation (Fig. 8), the population code still signals the target location. A possible explanation for this result is that the classifier may use information from a subpopulation of neurons (e.g., contralateral neurons) that are less affected by the appearance of the distracter (orange curve). This suggests that resilience to distracter interference may be a feature of this subpopulation of contralateral neurons. Here one may consider that classifiers using single neurons as features do not use central tendency statistics such as mean differences across the population (as does the state space analyses illustrated in Fig. 8) but can use information from only a subset of neurons and perform well above chance. Indeed, we found that both populations converged toward the same level of classification accuracy, despite there being more contralateral neurons relative to ipsilateral neurons, and despite attentional effects being on average larger in contralateral neurons.

Several conclusions can be derived from these results. First, that a linear classifier would approach ideal performance when using the population code based on the activity profile evoked by both targets and distracters compared to when using a code based on activity evoked by the target alone (Fig. 9). This can be further illustrated by the confusion matrices shown in Figure 10B–D. The matrix for the full population shows a yellow diagonal illustrating the classifier made almost no errors, while the other matrices diagonal show shades of orange (see color scale). Second, that each subpopulation alone reached a lower performance than the entire population considered together. Finally, that the activity of a relatively small population of area 8a neurons (n = 232) is sufficient to encode the allocation of attention to one of four target locations in the presence of distracters using a rate code that integrates information during time intervals as short as 25 ms.