Introduction

Perceptual performance greatly improves with selective attention, and many distinct perceptual-, decision- and motor-related factors can independently alter attentional performance1,2. Neuronal activity in numerous cortical and subcortical brain regions changes with shifts in attention3,4,5,6. Previous studies examining attention-related modulations in the framework of signal detection theory7 suggest that neuronal modulation in area V4 in visual cortex is associated with perceptual sensitivity (d’), but not with the decision criterion8,9. The superior colliculus (SC), a midbrain subcortical structure, plays a crucial role in visual perceptual performance5,10,11,12. It is believed that the SC contributes to visual attention through mechanisms that are distinct from those in the visual cortex13, but the precise mechanisms underlying specific components of perceptual behavior mediated by SC neuronal responses have been the subject of debate.

Different neuronal groups within the SC have distinct response properties and varying degrees of spike modulation by sensory, cognitive, and motor signals14. Visuo-motor neurons in the intermediate and deep layers of the SC are more responsive to changes in various cognitive states than the visual neurons located in the superficial layer or the motor neurons in deep layers. Previous studies suggest that the visuo-motor neurons are central to the SC’s role in perceptual detection during visually guided behavior15,16,17. These neurons are strongly modulated when animals enhance their perceptual d’ at the neuron’s response field (RF)5,15. While it has been proposed that the SC also contributes to attentional performance via changes in decision criterion or thresholds11,12,16, the specific contributions of different SC neuron subtypes to the diverse perceptual and behavioral aspects of attentional performance remain unclear.

To address this, we recorded spikes from multiple neurons in the SC of rhesus monkeys while they performed a novel visual orientation-change detection task18 that cleanly dissociated perceptual d’, decision criterion, and motor response criterion. The results revealed that the firing rate of SC neurons increased with attention-related increases in perceptual d’ at their RF location, while remaining unaffected by changes in the perceptual decision criterion. The task design also enabled a clear dissociation of these perceptual components from motor response bias linked to saccade planning. This attentional modulation was more pronounced for visuo-motor neurons than for purely visual neurons, and was virtually absent in motor neurons. In contrast, changes in perceptual decision criterion had no impact on the spiking of any SC neurons. The results offer a comprehensive account of how distinct sensory and cognitive components relevant to behavioral performance are represented in the SC and relate to representations of motor plans. This behavioral task holds particular significance in isolating specific behavioral components associated with attention states in brain areas that respond to a range of different signals.

Results

Behavioral isolation of response criterion from perceptual sensitivity

In our task, the motor response criterion corresponds to bias to saccade toward one location or the other – a property frequently described in the SC. We independently controlled the motor response criterion between low and high levels while maintaining a uniform perceptual d’ in two rhesus monkeys using a visual orientation change detection task18 (Fig. 1a; Methods). The animal fixated on a central spot (0.2° diameter) at the start of each trial, and maintained a gaze on this spot until it went off. After a variable duration of fixation (400–700 ms), two Gabor sample stimuli appeared for 200 ms, one in each hemifield. Following a brief delay (200–300 ms), a single Gabor test stimulus appeared for 200 ms in one of the two locations with a 50% probability of having the same or a different orientation than the sample stimulus that appeared in that location. The monkey had to report whether the test Gabor orientation was a match (0°) or non-match to the preceding sample Gabor (median thresholds [interquartile range], monkey S, 27° [25°–40°]; monkey P, 45° [38°–50°]) by making a saccade to the appropriate saccade target after the fixation spot went off (go cue) to receive a juice reward for correct detection. Match and non-match saccade targets (different colors and shapes) appeared 100 to 160 ms after the test stimulus was turned off in opposite locations orthogonal to the sample stimuli. The locations of match and non-match saccade targets were fixed within a trial block and were interchanged over interleaved trial blocks. The block-wise predictability of the saccade target locations made it possible to measure and control animals’ motor response criterion (motor intention).

Fig. 1: Spike modulation of SC neurons associated with response criterion.
Fig. 1: Spike modulation of SC neurons associated with response criterion.The alternative text for this image may have been generated using AI.
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a Visual orientation change detection task (Methods). Monkeys fixated (400–700 ms) while attending to one of the two sample Gabor stimuli (200 ms) in opposite hemifields. After a brief delay (200–300 ms), a test stimulus (200 ms) appeared at one location. Monkeys reported orientation changes by making a saccade to the correct target (distinguished by color and shape) for juice reward once the fixation spot disappeared (go-cue). Saccade target positions were fixed within a trial-block. b Behavioral response criterion (c) was controlled between low and high across interleaved trial-blocks, while sensitivity (d’) was held constant by adjusting reward size (Methods). Response c across sessions (monkey P, 4 sessions; monkey S, 5 sessions) for low and high c conditions, when the match saccade target  was at the neuron’s RF (c) or opposite hemifield (d). Gray lines, individual sessions; triangles, session averages. Error bars, 95% confidence intervals. e Average changes in c and d’ across the same 9 sessions. While d’ remained stable, c varied between low and high. Error bars, 95% confidence intervals. f Left, delayed memory saccade task for classifying SC neurons (Methods). Top, visual and saccade-related responses of an example visual-motor neuron. Bottom, PSTHs aligned to visual target and saccade onsets at preferred and non-preferred RFs. Error bars, ± 1 SEM. g PSTHs of the same example neuron in (f), grouped by saccade location and response bias. Spike rates aligned to sample, saccade target, go-cue and saccade onset. Error bars, ± 1 SEM. h Same as (g) for population of visuo-motor neurons (n = 44). Mean ( ± 1 SEM) neuronal d’ for visuo-motor (i; n = 44) and motor (j; n = 16) neurons selecting a saccade target in the RF at different bias levels. k Mean ( ± 1 SEM) saccade latencies across 9 sessions, grouped by bias and saccade target selection. Latencies from the go-cue were split into three quantiles. l Population-averaged neuronal discrimination latencies for selecting RF versus opposite targets, grouped by bias and saccade latency (Methods). Top, visuo-motor (n = 44); bottom, motor neurons (n = 16). Error bars, ± 1 SEM.

Behavioral performance was quantified using the framework of signal detection theory7 (Methods). In this framework, perceptual d’ denotes the theoretical sensitivity to stimulus differences (match versus non-match). This sensitivity was measured behaviorally as behavioral d’, computed empirically from the animal’s hit and false-alarm rates, reflecting the subject’s perceptual discriminability. Behavioral d’ therefore operationalizes perceptual d’ as expressed in the subject’s performance. The decision criterion (c) represents the internal bias for reporting a perceived stimulus difference independent of stimulus evidence. We independently examined two forms of criterion: motor and perceptual. The motor response criterion refers to the animal’s bias or intent to make a saccade toward one potential target location over the other, reflecting response-level or motor planning bias. The perceptual decision criterion defines the internal threshold or bias to judge whether a test stimulus is a match or non-match, independent of spatial configuration of saccade targets. “Correctness” refers to trial-by-trial behavioral outcomes–correct (hit and correct rejection) versus erroneous (miss and false alarm) detections. Neuronal d’ quantifies discriminability in neuronal firing rates, indicating how well neural activity differentiates between conditions–for example, selecting a saccade target inside versus outside the neuron’s RF.

To control the response criterion, monkeys were instructed to distribute their spatial attention equally to the two locations while shifting their bias toward the two locations in interleaved small blocks of trials (monkey P, 120–140 trials, monkey S, 120–160 trials) (Fig. 1b). The criterion at each location was varied independently of behavioral d’ by adjusting the reward size ratio for hits and correct rejections (CR) at that location while keeping average reward sizes the same at the two locations.

Monkeys selectively shifted their behavioral criterion between low and high values when the match saccade target was in the RF (F(1, 16) = 14.96, p < 10–7, repeated measures ANOVA, Fig. 1c), and, in separate blocks, when the non-match saccade target was in the RF (F(1, 16) = 15.10, p < 10–7, Fig. 1d), without detectable changes in behavioral d’ (match saccade target in-RF, F(1, 16) = 0.02, p = 0.84; non-match saccade target in-RF, F(1, 16) = 0.08, p = 0.58). The criterion changes accounted for the behavioral improvement of stimulus change-detection, hit rate (mean ± SEM, for low and high criterion respectively 34.9 ± 4.4% and 86.7 ± 1.7%; p = 0.0039, signed rank test). This independent control of behavioral criterion and perceptual sensitivity (Fig. 1e) was crucial for isolating and investigating the neuronal modulations of SC neurons associated with response bias in attentional performance.

Spike modulation of SC neurons associated with changes in motor response criterion

We recorded spiking activities from populations of SC neurons while varying the monkeys’ response criterion and holding behavioral d’ fixed during the visual attention-demanding task (monkey S, n = 36; monkey P, n = 33). SC neurons were classified as visuo-motor, visual, or motor based on the selectivity of visual and saccadic responses during a delayed memory visual task (visuo-motor, n = 44; visual, n = 9; motor, n = 16 from both animals; Fig. 1f & Supplementary Fig. S1; Methods).

Visuo-motor neurons spiked more to the saccade target stimuli during trial blocks when the monkey’s response bias at the RF was high (Supplementary Fig. S1). This occurred whenever saccades to the RF were associated with more reward (either low behavioral criterion with the non-match saccade target in the RF or high behavioral criterion with the match saccade target in the RF). Neuronal spike modulation associated with changes in behavioral criterion (Δc) was measured using neuronal d’ (Methods). There was a significant spike modulation as measured by neuronal d’ for behavioral Δc in visuo-motor neurons (neuronal d’, for nonmatch saccade target in-RF, mean ± SEM = 1.03 ± 0.15; P < 10−6; for match saccade target in-RF, mean ± SEM = 1.07 ± 0.12; P < 10−7, signed rank test; Supplementary Table S1). There was no neuronal modulation in SC visual neurons for behavioral Δc (neuronal d’, for nonmatch saccade target in-RF, mean ± SEM = 0.17 ± 0.36; P = 0.98; for match saccade target in-RF, mean ± SEM = 0.28 ± 0.52; P = 0.2, signed rank test; Supplementary Table S1). Response modulation of SC motor neurons with behavioral Δc were weak, but significant (for nonmatch saccade target in-RF, mean ± SEM = 0.67 ± 0.27 P = 0.03; for match saccade target in-RF, mean ± SEM = 0.88 ± 0.34; P = 0.03, signed rank test; Supplementary Table S1).

If response bias interacts with saccade planning or execution, variations in the animal’s response latency should be accompanied by systematic changes in neuronal activation between high and low bias conditions. To test this hypothesis, we examined whether the spike modulation associated with motor response bias (also referred to as ‘motor intent’ or ‘motor planning’) could be dissociated from activity related to the physical act of saccade execution. Trials were classified according to the monkeys’ saccade location (in-RF or opposite-RF) and the level of response bias (high versus low response bias) in selecting a saccade location. Spike rates of visuo-motor neurons following the onset of saccade targets increased with a higher level of the monkeys’ intent to select a saccade target within the RF compared to the opposite location (green versus yellow traces, Fig. 1g, h). Neuronal d’ increased significantly after the onset of saccade targets with higher response bias (Fig. 1i).

In contrast, SC motor and visual neurons showed no modulation in response to changes in response bias (Fig. 1j & Supplementary Fig. S2). We further examined whether response bias-related neuronal modulation reflects the latency of saccade initiation. All trials were grouped into fast, intermediate, and slow quantiles based on the saccade latency relative to the go-cue separately for each trial type. (Fig. 1k). The neuronal latency of saccade target selection for individual visuo-motor and motor neurons was defined as the earliest time, relative to the go-cue, when decoding accuracy (in-RF vs. opposite-RF) was significantly greater than the shuffled trials (p < 0.05 over at least 80 ms). This was assessed for each set of response bias and saccade latencies. (Fig. 1l; Methods). The neuronal latency of saccade target selection in visuo-motor neurons was significantly shorter for high response bias trials compared to low response bias trials (F(1, 43) = 48.00, p < 10–8, repeated measures ANOVA), and was unaffected by saccade latency (F(2, 86) = 0.89, p = 0.41). In contrast, the neuronal saccade target selection latency in motor neurons was independent of the strength of response bias (F(1, 15) = 0.72, p = 0.41), but covaried with saccade latency (F(2, 30) = 6.22, p < 0.01). Together, an increased level of response bias toward a potential saccade location within the neurons’ RF enhances the responses of visuo-motor neurons in the SC. This modulation occurs independently of the preparation or execution of the saccade. In contrast, SC motor neurons specifically represent the preparation or execution of the saccade itself rather than the level of motor response bias.

Independent control of perceptual sensitivity and perceptual decision criterion

Previous studies have suggested that spiking of visuo-motor and visual neurons in the SC closely varies with perceptual attentional performance and decision16,19. Thus, we examined how the activity of individual SC neurons relates to perceptual d’ and decision criterion (independently) in relation to response bias. Monkeys’ behavioral d’ and decision criterion were independently controlled using the same visual orientation change detection task as in Fig. 1 (Fig. 2a; Methods). However, the locations of the match and non-match saccade targets were randomly interchanged across the trials. This dissociated animal’s spatially selective motor response bias from perceptual d’ and perceptual decision criterion, as there was no prior information about the saccade targets until after the test stimulus was turned off. Animals were instructed to switch their spatial attention by adjusting reward sizes for correct detections between the two locations in small blocks of trials (monkey S, 120–160 trials, monkey P, 120–140 trials; Δd’ trials, Fig. 2b). While a relatively large average reward for correct responses (hits and CRs) at one location motivated animals to selectively shift their behavioral d’, the reward size ratio for hits and CRs was adjusted by small amounts across trials to maintain a decision criterion close to zero (see Methods for detailed reward-adjustment procedure). In separate blocks of trials, perceptual decision criterion was controlled between low and high values at a location independent of behavioral d’ by adjusting the reward size for hits and CRs in small blocks of trials that were randomly interleaved with Δd’ blocks (Δc trials, Fig. 2b).

Fig. 2: Independent control of behavioral sensitivity (d’) and perceptual criterion.
Fig. 2: Independent control of behavioral sensitivity (d’) and perceptual criterion.The alternative text for this image may have been generated using AI.
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a Visual orientation change detection task. The task was similar to that shown in Fig. 1, except that the positions of the saccade targets were randomized on each trial. b Monkeys’ spatial attention and decision criterion were independently controlled between the two stimuli locations in interleaved blocks of trials by adjusting the reward size for correct detections. c,e Monkeys’ behavioral d’ across sessions (monkey P, 27 sessions; monkey S, 20 sessions) for Δd’ trial blocks. Behavioral d’ is better (left) on trials when the test stimulus appeared at the attended location (valid trials) compared to the unattended location (invalid trials) without any changes in criterion (right). Gray lines, individual sessions. Filled squares, session average. Error bars, 95% confidence intervals. d,f Similar to Fig. 2c and 2e, except for Δc trial blocks in same experimental sessions (monkey P, 27 sessions; monkey S, 20 sessions). Behavioral d’ remained uniform (left), while criterion (right) changed between low and high values. g,h Average changes in behavioral d’ and criterion at one of the two locations contralateral to the recorded SC across sessions (monkey P, right visual field, 27 sessions; monkey S, left visual field, 20 sessions) on Δd’ and Δc trial blocks. Gray lines, individual session. Error bars, 95% confidence intervals.

Behavioral d’ increased significantly at the attended location compared to the unattended location on Δd’ trial blocks (monkey P, 27 sessions, F(1, 52) = 17.38, p < 10–9; monkey S, 20 sessions, F(1, 38) = 24.48, p < 10–4, repeated measures ANOVA; left, Fig. 2c, e), without significant changes in decision criterion (monkey S, F(1, 38) = 0.95, p = 0.33, monkey P, F(1, 52) = 1.44, p = 0.23; right, Fig. 2c, e). On Δc trial blocks within the same experimental sessions, animals selectively shifted their decision criterion (monkey P, F(1, 52) = 397.02, p < 10–18; monkey S, F(1, 38) = 186.87, p < 10–15; right, Fig. 2d, f) without significant changes in behavioral d’ (monkey P, F(1, 52) = 1.47, p = 0.23; monkey S, F(1, 38) = 0.05, p = 0.83; left, Fig. 2d, f). This independent control of perceptual d’ and decision criterion (Fig. 2g, h) was crucial for investigating the relative contributions of distinct perceptual and behavioral components of attentional performance by SC neurons.

Spike modulation of SC neurons associated with changes in perceptual sensitivity and decision criterion

We simultaneously recorded spiking activities from populations of visuo-motor (n = 165), visual (n = 88) and motor neurons (n = 52) in the SC while the monkeys’ behavioral d’ and perceptual decision criterion were controlled during the visual attention task (monkey S, n = 127; monkey P, n = 178; Supplementary Fig. S3). Visuo-motor neurons responded more strongly to the sample stimuli during trial blocks when the monkey’s behavioral d’ at the RF was high (blue and orange, Fig. 3a, b). In contrast, spike rates did not change during changes in decision criterion of similar magnitude (yellow and green, Fig. 3a, b). There was a significant spike modulation as measured by neuronal d’ during the sample stimuli presentation for behavioral Δd’, but not for decision Δc in visuo-motor neurons (neuronal d’, for behavioral Δd’ mean ± SEM = 1.29 ± 0.08; P < 10−17; for decision Δc mean ± SEM = 0.005 ± 0.06; P = 0.71; n = 105/165, signed rank test; Fig. 3e; Supplementary Table S2). A much weaker but significant neuronal modulation was seen in SC visual neurons for behavioral Δd’, but not for decision Δc (neuronal d’, or behavioral Δd’ mean ± SEM = 0.2 ± 0.06; P < 10−2; for decision Δc mean ± SEM = 0.023 ± 0.06; P = 0.4; n = 58/88, signed rank test; Fig. 3c, d, f; Supplementary Table S2). Spike rates of motor neurons were unaffected by behavioral Δd’ or decision Δc (neuronal d’, for behavioral Δd’ mean ± SEM = 0.13 ± 0.21, P = 0.45; for decision Δc mean ± SEM = –0.19 ± 0.16, P = 0.14; n = 30/52, signed rank test; Supplementary Fig. S4 & Supplementary Table S2).

Fig. 3: Neuronal modulation of SC neurons with changes in behavioral d’ and perceptual decision criterion.
Fig. 3: Neuronal modulation of SC neurons with changes in behavioral d’ and perceptual decision criterion.The alternative text for this image may have been generated using AI.
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a Trial-averaged PSTHs of an example visuo-motor SC neuron when the monkey’s behavioral d’ and decision criterion at the neuron’s RF location were independently controlled relative to the stimulus at the opposite hemifield (Fig. 2). Spike rates are aligned to the onsets of sample stimuli, saccade targets, go-cue, and the saccade (top). Error bars, ± 1 SEM. b PSTHs are similar to those in (a), except for the population of visuo-motor neurons when one of the visual sample stimuli was located within the neuron’s RF (n = 105/165). c, d Similar to (a, b), except for an example and population of visual neurons in the SC (n = 58/88). e,f Spike rate modulation of SC neurons with changes in behavioral d’ (Δbeh d’) and decision criterion (Δc). Bottom left, Population distribution of neuronal d’ quantifying modulation as a function of Δbeh d’ and Δc for visuo-motor (e) and visual neurons (f). Top & right, marginal distributions of neuronal d’ for Δc (top) and Δbeh d’ (right). Triangles represent population means. g, h Decoding accuracies for behavioral d’ (top) and decision criterion (bottom) from spike counts using a linear classifier based on support vector machine, averaged across individual visuo-motor (g) and visual (h) neurons, as shown in (b) and (d). Dashed lines, 95% confidence intervals based on shuffled trials. Shaded error bars, ± 1 SEM.

To further examine how the activity of individual SC neurons relates to changes in perceptual d’ and decision criterion, we examined decoding accuracy (10-fold cross validation) using a linear classifier based on a support vector machine (Fig. 3g, h). Spike counts of visuo-motor neurons more reliably encoded information about behavioral d’, but not decision criterion, during the sample stimuli, compared to visual and motor neurons, despite the equivalent magnitudes of the behavioral Δd’ and Δc (Fig. 2g, h, Supplementary Fig. S4).

One possible reason for the absence of perceptual Δc-related neuronal modulation in SC neurons during the sample stimuli is that the saccade targets were positioned far beyond the neuron’s response field. Because the criterion is closely related to selecting a response choice, criterion-related neuronal processing might have been associated with the choice targets rather than the attended sensory stimuli in the trials in which criterion was manipulated. To test this possibility, in the same experimental sessions we measured behavioral Δd’- and Δc- related modulation of SC neurons whose response fields overlapped with one of the saccade targets while controlling behavioral d’ and c independently, as shown in Fig. 2 (Supplementary Fig. S5). There was no significant spike modulation for Δc in any of the neuron groups during the sample stimulus (mean ± SEM neuronal d’, visuo-motor, 0.005 ± 0.07; P = 0.38; visual, 0.012 ± 0.14; P = 0.4; motor, –0.20 ± 0.17; P = 0.43; signed rank test; Supplementary Table S3). Moreover, behavioral Δc did not affect the spike response at the onset of saccade targets (mean ± SEM neuronal d’, visuo-motor, –0.23 ± 0.15; P = 0.17; visual, –0.06 ± 0.12; P = 0.43; motor, 0.03 ± 0.27; P = 0.44; signed rank test; Supplementary Table S4). Spike counts of these neurons also did not represent information about decision criterion during the sample stimuli or saccade target presentations, as measured by decoding accuracy in cross-validated trials (10-fold) (Supplementary Fig. S5). However, information about behavioral d’ was represented by visuo-motor neurons during the presentation of saccade targets (Supplementary Fig. S5g). Therefore, the strong spike modulation of SC visuo-motor neurons was specifically linked to a change in perceptual d’ rather than perceptual decision criterion.

Neuronal modulation in SC visuo-motor neurons follows variations in behavioral sensitivity and depends on spatial alignment with attended location

The increase in spike rate of SC visuo-motor neurons with higher behavioral d’ is a neuronal correlate of trial-averaged behavioral performance as spatial attention shifts between stimulus locations across blocks of trials. However, attentional states can fluctuate on much shorter timescales. Therefore, we next examined at a granular level how neuronal modulation covaries with both the graded levels of behavioral d’ within individual sessions and the spatial alignment between a neuron’s RF and the attended location.

We measured the proximity of SC visuo-motor neurons’ RFs to the attended Gabor sample stimulus using Mahalanobis distance in the experimental sessions described in Fig. 2 (n = 129/165, Fig. 4a, b). The dependence of neuronal modulation on the spatial distance between the neuron’s RF and the attended stimulus, as well as on behavioral d’ within each session at the single-neuron level, was estimated using a linear regression model (Fig. 4c). Neurons with RFs closer to the attended stimulus were more modulated (β1 = –0.1, p < 10–3; left, Fig. 4c). Additionally, neuronal d’ was positively correlated with the trial-averaged behavioral d’ within each session (β2 = 0.45, p < 10–3; right, Fig. 4c). At the population level, the spatial proximity of neurons to the attended location explained a greater proportion of the variance in neuronal d’ compared to behavioral d’ (13.5% versus 7.4%; Fig. 4d).

Fig. 4: Neuronal modulation of SC visuo-motor neurons related to spatial attention depends on the level of behavioral sensitivity and alignment of the neuron’s spatial response field with the attended stimulus location.
Fig. 4: Neuronal modulation of SC visuo-motor neurons related to spatial attention depends on the level of behavioral sensitivity and alignment of the neuron’s spatial response field with the attended stimulus location.The alternative text for this image may have been generated using AI.
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a A schematic illustrating the alignment of a neuron’s spatial RF and Gabor sample stimuli as measured by Mahalanobis distance. b Cumulative distributions of Mahalanobis distances (MD) between visuo-motor neurons’ RF (neurons, n = 129) and Gabor stimuli in two opposite hemifields, and between the two Gabor stimuli (47 sessions). c Linear regression fit for neuronal d’ (n = 129 neurons) as a function of the trial-averaged behavioral d’ within each session (Right; p = 0.0008) and the Mahalanobis distance between the RF and the Gabor stimulus in the same hemifield (Left, RF-GaborinRF; p = 0.0008). Dashed lines, 95% CI. d Variances explained by the RF-GaborinRF distance (MD) and behavioral d’ in the regression fit in (c). e Trials within each session were sorted according to behavioral d’ into four equal quantiles, and then session-averaged data is plotted for each quantile and monkey (monkey P, 27 sessions; monkey S, 20 sessions). f Trial-averaged neuronal d’ for visuo-motor neurons (n = 165) across four trial quantiles with increasing behavioral d’, compared using a repeated measures ANOVA (F(3, 492) = 9.04, p = 7.8 × 10–6). Error bars, ± 1 SEM.

To further examine how fluctuations in behavioral sensitivity relate to neuronal modulation, we leveraged natural within-session variations in behavioral d’ as a tool to probe the graded relationship between the strength of spatially selective attention and SC activity. To assess behavioral performance on this finer behavioral scale, behavioral d’ was computed using a 25-trial moving window separately for all four trial types (low versus high selective attention; in-RF versus opposite-RF location) during Δd’ manipulation trial blocks within each session. These behavioral d’ distributions were sorted into four equal quantiles to get a within-session gradient of behavioral performance (Fig. 4e). Neuronal d’ scaled with behavioral d’, with stronger neuronal modulation observed in high-performing trials (F(3, 492) = 9.04, p < 10–5, repeated measures ANOVA; Fig. 4f). These results suggest that SC visuo-motor neurons integrate spatial and behavioral factors, with attentional modulation being stronger when the neuron’s RF aligns with behaviorally relevant stimulus and attention is more intense.

Single-trial decoding of distinct cognitive and behavioral factors associated with attentional performance from SC visuo-motor neurons

Previous studies, and the current results, suggest that different sensory, cognitive and behavioral factors are multiplexed in the single-trial spike trains of SC visuo-motor neurons. Thus, we decomposed single-trial population firing rates of SC visuo-motor neurons into demixed principal components (dPCs) to quantify relative encoding of motor response criterion (low versus high intent to select a saccade-target location; Fig. 1), perceptual decision criterion (low versus high bias to select a saccade target independent of location; Fig. 2), perceptual d’ (in-RF versus opposite-RF; Fig. 2), saccade location (in-RF versus opposite-RF; Figs. 1 and 2) and correct detection (correct versus error; Figs. 1 and 2) (Fig. 5; Methods).

Fig. 5: Single-trial decoding of distinct perceptual, cognitive, and behavioral factors associated with attentional performance from SC visuo-motor neurons.
Fig. 5: Single-trial decoding of distinct perceptual, cognitive, and behavioral factors associated with attentional performance from SC visuo-motor neurons.The alternative text for this image may have been generated using AI.
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a Time course of single-trial decoding accuracy (cross-validated leave-one-out trials) for motor response criterion (response bias), executed saccade location, and correct detection based on demixed principal components of the population PSTHs of SC visuo-motor neurons (n = 44/69), as shown in Fig. 1 (Methods). The locations of the saccade targets were fixed, with one target placed within the RF of the neuron. Only neurons for which at least 10 trials were conducted for each decoding factor were included. Error bars, 95% confidence intervals from shuffled trials. b Similar to (a), except for sessions in Fig. 2 where one of the saccade targets was placed within the neuron’s RF and the saccade targets were randomized trial-by-trial (visuo-motor, n = 60/165). Additional decoding factors included perceptual d’ and perceptual decision criterion. c Similar to (b), except for the sessions when one of the sample stimuli was placed within the neuron’s RF (visuo-motor, n = 104/165).

Across parameters and trial-event epochs (sample onset, saccade-target onset, go and saccade onset), the first three dPCs explained between 1.5 and 47.3% of total variance, with the largest contributions from saccade direction (36.7–47.3%) followed by motor response criterion (1.7–2.2%), and condition-independent components (41.3–62.6%) in the fixed-target condition (Fig. 5a). In the randomized-saccade-target condition with one of the saccade-targets in the neuron’s RF (Fig. 5b), the top three dPCs accounted for 0.4–64.9% of the total variance, dominated by saccade direction (56.3–64.9%) followed by perceptual d’ (2.6–5.1%), and condition-independent activity (38.2–56.6%). For the randomized-saccade-target condition with the sample stimulus in the RF (Fig. 5c), the top three components explained 0.3–56.9% of the total variance, with the largest variance captured by perceptual d’ (6.3–18.7%) and condition-independent components (22.7–56.9%). Across all datasets, perceptual decision criterion and correctness accounted for small fractions of variance (typically <3.5%; Supplementary Table S5).

When saccade targets were within the neuron’s RF, the decoding accuracy for saccade location increased sharply before saccade execution (cyan traces, Fig. 5a, b) and emerged earlier when saccade target locations were fixed (cyan traces, Fig. 5a). Perceptual d’ was also strongly encoded during the sample period when the attended stimulus, rather than the saccade target, was presented at the neuron’s RF (blue traces, Fig. 5b, c). Information regarding the motor response criterion was represented independently of the saccade execution when the saccade target locations were fixed (magenta traces, Fig. 5a).

In contrast, perceptual decision criterion (red traces, Fig. 5b, c) as well as correct detection (brown traces, Fig. 5b, c) were not significantly encoded during the trial. Because saccade targets were fixed within a block in the dataset shown in Fig. 5a, we verified that this lack of correctness-related decoding was not confounded by opposite motor plans between trial types. A control analysis compared hit versus false alarm and correct rejection versus miss trials, each pair sharing the same saccade direction but differing in behavioral outcome (see Supplementary Fig. S6). The results confirmed that SC population activity did not predict correctness even when motor direction was held constant. In the datasets shown in Fig. 5b, c, saccade target locations were randomized on a trial-by-trial basis, such that motor direction and correctness were orthogonal by design, eliminating this potential confound.

Together, these results suggest that SC visuo-motor neurons multiplex perceptual, response selection and motor execution signals according to instantaneous task demands but do not carry trial-by-trial information predictive of behavioral correctness.

Discussion

Our findings demonstrate that neuronal activity in the superior colliculus (SC) is strongly modulated by perceptual sensitivity (d’) associated with visual spatial attention. Throughout this study, we dissociated three components of attentional performance defined by signal detection theory: perceptual d’, perceptual decision criterion, and motor response criterion, along with trial-by-trial correctness (hit, miss, correct rejection, false alarm). The magnitude of this modulation depends on the spatial proximity of the locus of attention to the neuron’s response field, as well as the magnitude of perceptual d’ modulation. However, SC activity does not reflect whether the monkeys correctly detected a stimulus change at the single-trial level. Instead, the neuronal modulation corresponds to an elevated cognitive state associated with improved perceptual sensitivity. SC activity was also enhanced with lower motor response criterion, which occurred when there was a bias to saccade toward the neuron’s RF. In contrast, shifts in perceptual decision criterion at the neuron’s RF, which involved a bias toward selecting a target category rather than location, did not affect SC neuronal activity.

Luo and Maunsell8,20 reported that neurons in the lateral prefrontal cortex (LPFC) represent both behavioral d’ and criterion, while the visual area V4 selectively represents behavioral d’ in a similar visual detection task. However, the motor response criterion was not dissociated from the perceptual decision criterion. By behaviorally dissociating these behavioral components, we reveal a functional dissociation between SC activity and distinct decision variables. Specifically, SC neuronal firing rates selectively tracked motor criterion, but remained independent from the perceptual decision criterion, indicating that the SC does not encode the internal threshold governing categorical judgments of “match” versus “non-match”. Furthermore, SC modulation was uncorrelated with trial-by-trial correctness and instead reflected an elevated, spatially selective behavioral d’, indicating a sustained attentional state of heightened perceptual d’ rather than discrete perceptual decision outcomes, as observed in visual cortex8,9. As SC neurons are sensitive to expected reward21, the observed neuronal modulation may reflect a spatially selective state heightened attention driven by external motivation, since attentional state was manipulated by adjusting reward size. Future work is needed to further isolate SC contribution to spatial selection using motivational factors beyond reward, such as task difficulty9.

Does the oculomotor activity in the SC support a common cognitive function of spatial ‘selection’?

Results from various experimental tasks investigating the functions of the SC suggest that its neuronal activity mediates many different cognitive functions, including spatial orientation, target selection, covert attention, and saccadic eye movements. Consistent with our findings, previous research shows that SC visuo-motor neurons are modulated with visual target selection in their response field independently of saccade execution17. Deficits in spatial target selection, as observed in visual search tasks22, may underlie ipsilateral choice biases or delayed decisions when the SC is unilaterally inactivated during two-alternative forced-choice tasks11,23.

SC activity is also crucial for behavioral performance in covert visual attention tasks that rely on perceptual sensitivity. SC inactivation – either pharmacological or optogenetic – impairs perceptual performance10,13,24. In light of these previous findings, our results showing modulation of SC neurons with perceptual d’ or response criterion support the role of the SC in a common ‘spatial selection’ mechanism that either enhances the perception of stimulus details or the speed or accuracy of actions in a task-dependent manner. Selective attention is often broadly defined as the common mechanism for selective prioritization2,25 of a stimulus for perceptual benefit, working memory, or motor action. However, because perceptual decision criterion (Δc) did not modulate SC activity, our findings suggest that the SC’s oculomotor circuitry does not support the ‘selection’ of non-spatial content, highlighting a fundamental distinction between spatial and non-spatial decision processes in the SC.

Non-spatial cognitive signal in the SC beyond oculomotor control

Consistent with earlier findings, we found that spike modulation in SC visual neurons associated with spatially selective visual attention is substantially weaker than that reported for visuo-motor neurons15. While recent studies have proposed that SC visual neurons may also support non-spatial cognitive functions such as object categorization, which is thought to be closely linked to abstract decision criterion19, our findings suggest a more limited role in this regard. However, the relative strength of neuronal encoding for object category versus perceptual d’ was not examined. By using an encoding analysis similar to that used in previous studies19, we identified only a small fraction of SC visual neurons that reliably represented the perceptual (non-spatial) decision criterion (3%), compared to perceptual d’ (12%) (Supplementary Fig. S7). The population-level representations of the perceptual decision criterion in visual neurons were notably weaker than those of perceptual d’, both in terms of the proportion of responsive neurons and the magnitude of their modulation (Supplementary Fig. S7).

Brain areas reciprocally connected to the SC, such as the visual cortex, intraparietal cortex (LIP), and frontal eye field (FEF), are known to represent different aspects of cognition and decision-making26,27,28. It is hypothesized that different microcircuitry of SC neuronal subpopulations based on their connectivity patterns with other brain networks may mediate task-dependent distinct neuronal computations beyond oculomotor control14,24,29. Future experiments with independent controls of cognitive factors, combined with specific manipulations of neuronal or circuit activity within these areas, may provide insights into the comparative causal contributions of the SC to distinct cognitive and behavioral functions.

Information readout by brain structures downstream to the SC, whether to perceive in detail or to act upon

The SC is a node within a network of many brain structures that mediate distributed computations related to visual attention, decision formation and motor action. The question arises regarding how the neurons downstream of the SC decode enhanced spiking if the same neuron responds to perceptual sensitivity, response selection and motor planning. Previous studies show that downstream neurons in the SC-FEF pathway via mediodorsal thalamus differentially process complex sensory and motor signals, with thalamus filtering out delay activity and supporting the FEF in predominantly retaining perisaccadic activity30. Simultaneously recorded large ensembles of SC neurons reveal that population coding places sensory and motor-related representations into distinct patterns, enabling downstream areas to decode them, despite individual neurons responding to multiple cognitive and motor processes31. Pairwise correlation, an information encoding strategy independent of spike rates, is sensitive to distinct neural processes that guide saccades and varies within and between SC neuron subclasses29. This may also contribute to distinguishing multiplexed signals by regulating information transfer based on task context.

SC spiking robustly represents a cognitive state associated with improved perceptual sensitivity in visual spatial attention tasks, independently of its modulation by response bias, which has long been seen in tasks that involve saccade planning. However, when these spatial components are controlled, non-spatial perceptual decisions and trial-by-trial perceptual detection do not affect SC spiking. Collectively, these findings establish that the SC primarily encodes spatially selective perceptual sensitivity and motor preparatory bias, rather than the internal decision threshold or trial outcome, underscoring its specialized role in linking attention to action.

Methods

Animals and surgery

Two adult male rhesus monkeys (Macaca mulatta, 9 and 13 kg) were each implanted with a titanium headpost before behavioral training began. All experimental procedures were approved by the Institutional Animal Care and Use Committee of the University of Chicago and followed the US National Institutes of Health guidelines.

Before behavioral training began, an aseptic surgery was performed under gas anesthesia to implant a head-restraining post. Anesthesia was induced by an intramuscular (IM) injection of a single dose of Ketamine (2–3 mg/kg) and Dexmedetomidine (15–60 µg/kg), followed by endotracheal intubation to maintain a clear airway. Anesthesia was maintained by continuous inhalation of Isoflurane (0.5–5%). The level of anesthesia was monitored by limb retraction reflex, respiration and heart rate and rhythm, end-tidal CO2, O2 saturation, noninvasive blood pressure and rectal temperature. Throughout the surgical procedure the animal was administered intravenous lactated Ringer’s solution at a rate of 5–15 ml/kg/hr. Body temperature was maintained at 37–38 °C. Once the procedure was completed, the animal was given Atipamezole (150–600 µg/kg IM) to reverse the effects of Dexmedetomidine.

After the completion of training (3 to 5 months), we surgically implanted a stainless-steel recording chamber over a 19 mm craniotomy in an aseptic surgery under anesthesia targeting the SC on one side (right, monkey S; left, monkey P) to access the SC, guided by MRIs obtained before the initial surgery. The cylinders were centered on the skull at 3.5 mm A, 10.0 mm L, and tilted in the coronal plane to advance toward the midline (monkey P, 9°; monkey S, 11°). The same two monkeys were used in previous studies that described different findings on neuronal responses in area V49,32 and the locus coeruleus18.

Visual change-detection task

Monkeys sat in a primate chair facing a calibrated CRT display (1024 × 768 pixels, 100 Hz frame rate) at 57 cm viewing distance inside a darkened room. Binocular eye position and pupil area were recorded at 500 Hz using an infrared camera (EyeLink 1000, SR Research). Trials started once the animal fixated within 1.5° of a central white spot (0.2° square) presented on a mid-level gray background (Fig. 1a)18. The animal had to maintain fixation until its saccade response at the end of the trial. After a randomly selected fixation period of 400 to 700 ms, two achromatic Gabor sample stimuli appeared for 200 ms, one in each visual hemifield. After a random variable delay of 200 to 300 ms, a Gabor test stimulus appeared for 200 ms at one of the two stimulus locations, selected randomly with equal probability. Shortly after the test stimulus turned off (100 to 150 ms), two saccade targets of different color and shape (non-match target, green square; match target, magenta circle; 0.3°−0.4°) appeared in opposite directions from the fixation spot along an imaginary line orthogonal to the axis of the sample stimuli. A go-signal (fixation spot turning off) occurred 150 to 200 ms after the saccade target appeared and indicated the animal should make a saccade to the appropriate saccade target depending on the change in the test Gabor orientation relative to the sample. The orientation of the test stimulus changed from the sample stimulus on random half of trials (non-match trial; 32° for monkey S and 42° monkey P). On the rest of the trials, the orientation of the test stimulus remained unchanged (match trial). Orientation of sample Gabor stimulus at each location was randomized across trials from 0° to 175° (5° intervals). Orientations of left and right sample stimuli were independent and never identical. Gabor stimuli were varied each day and remained unchanged throughout each session (monkey P, left Gabor, azimuth, −9.0° to −1.0°, elevation, −8.0° to 7.0°; sigma, 0.75° to 2.7°, spatial frequency, 0.15 to 0.5 cycles per degree, right Gabor, azimuth, 1° to 13°, elevation, −9.1° to 9.6°, sigma, 0.65° to 3.0° spatial frequency, 0.14 to 2.2 cycles per degree; monkey S, left Gabor, azimuth, −15° to −2.3°, elevation, −10° to 7.5°, sigma, 1° to 1.8°, spatial frequency, 0.3 cycles per degree, right Gabor, azimuth, 2.3° to 8.0°, elevation, −7.5° to 7°, sigma, 1° to 1.3°, spatial frequency, 0.3 cycles per degree). The eccentricities of the saccade targets remained unchanged throughout each session. (monkey P, 3.6° to 5.7°; monkey S, 3.3° to 9°).

Independent control of behavioral d’ and criterion associated with visual spatial attention

Monkeys’ behavioral response criterion (c) (Fig. 1a-b) in one of the sample stimulus locations was controlled between low and high values across interleaved trial blocks, while behavioral sensitivity (d’) between the two stimulus locations remained uniform by adjusting reward size for correct detections. The locations of match and non-match saccade targets remained fixed throughout a trial block (120–160 trials), and were cued by a few instruction trials (10–15) that preceded the trial block start and were not included in the analysis. The probability of test trials for the two sides was equal. The ratio of the reward size for hit trials over correct-rejection trials (hit:CR) associated with one of the sample stimuli was 2–3 to achieve a low response criterion (bias to select the non-match saccade target). Conversely, a hit:CR reward ratio of 0.3–0.5 led to a high response criterion (bias against selecting the non-match saccade target). Both the reward ratio for hit:CR in the opposite sample stimulus location, as well as the average reward size (hit and CR) between the two stimulus locations, were kept near 1 throughout the session. This maintained a uniform criterion at the opposite location and uniform behavioral d’ between the two locations (Fig. 1b).

Perceptual decision criterion was independently controlled between low and high values (four trial conditions) in interleaved blocks of trials (120–160 trials, Fig. 2a). The criterion was controlled in the same manner as described in the previous section, except that the match and non-match saccade targets randomly switched their positions across trials. This dissociated the spatially selective response preference, such that the criterion was a perceptual decision criterion that was independent of spatial ‘selection’ for saccade or selective perceptual d’.

Behavioral d’ was controlled between the two locations using both different reward size as well as different probability of test trials for the two sides18 (Fig. 2a). Average reward size ratio (hit and CR) for the valid location (attended) over the invalid location was 3.0–3.5. The ratio of valid and invalid test stimulus probabilities for the locations was 2–3. Both the test stimulus probability and reward size contributed to reliably control the behavioral d’ at the two stimulus locations. The hit:CR reward ratio at the two locations was 1. Varying reward size was particularly effective in keeping the perceptual decision criterion close to zero. In previous studies, we have used reward size differences with and without a test stimulus probability difference to control behavioral d’ and criterion values8,9. Expecting a high reward size or a high expectation of a test stimulus might access a common valency (product of the probability of a test stimulus and its reward size) associated with a stimulus location that drives the motivation to shift attention33.

During behavioral Δd’ and Δc trial blocks, the reward ratio for correct responses (hits and CRs) was adaptively adjusted in small increments based on recent performance to maintain a stable decision criterion near zero. Reward volumes were modified by approximately 5 to 20% every 10 to 15 trials depending on the animal’s average criterion in the preceding window. When a consistent bias toward one choice (positive or negative criterion) was detected, the reward for the less frequent correct response was slightly increased, while that for the more frequent correct response was reduced by the same proportion. Adjustments continued until the mean criterion across two consecutive windows remained within ±0.1. This heuristic ensured criterion stability while maintaining balanced motivation and total reward rate across conditions.

Memory guided saccade task

In each session, we mapped visual and saccade response fields by having the monkeys do a memory-guided saccade task before the visual attention task (Fig. 1f). After fixating for 400 to 600 ms, a circular saccade target (0.35° diameter) appeared for 250 ms at one of the six equally spaced peripheral locations. A common target eccentricity was selected based on recorded neurons’ visual response fields (2.5°–10°). Following a delay of 500–800 ms, the fixation spot disappeared, and the monkey executed a saccade to the remembered location of the visual target (within 4°–7°). At least 20 correct trials were collected at each stimulus location in each session.

Neurophysiological recordings

Neuronal signals from an extracellular multielectrode linear array (16 channel V-probe and 32 channel U-probe; Plexon Inc.) were amplified, bandpass filtered (250 to 7500 Hz), and sampled at 30 kHz using a data acquisition system (Cerebus, Blackrock Microsystems) (Figs. 1 and 3). We simultaneously recorded from multiple single units and small multiunits over 56 sessions (25 sessions for monkey S; 31 sessions for monkey P).

Data analysis

Behavioral performance

All completed trials were included in our analysis. Behavioral d’ and perceptual criterion (c) at a spatial location were measured from hit rates within nonmatch trials and false alarm (FA) rates within match trials using 1-dimensional signal detection theory7,32 as: \({d}^{{\prime} }={\Phi }^{-1}\left(H\right)-{\Phi }^{-1}(F)\) and \(c=-\frac{1}{2}\left[{\Phi }^{-1}\left(H\right)+{\Phi }^{-1}(F)\right]\); where Φ–1 is inverse normal cumulative distribution function; H and F are respectively the rates of hits and false alarms.

Neuronal response

Spikes from each electrode were sorted offline (Offline Sorter, Plexon Inc.) by manually well-defining cluster boundaries using principal components analysis and waveform features. Well-isolated clusters were classified as single units from multiunits based on the isolation quality of unit clusters. The degree to which unit clusters were separated in two-dimensional (2D) spaces of waveform features (first three principal components: peak, valley, and energy) was measured by multivariate analysis of variance (MANOVA) F statistic using Plexon Offline Sorter (Plexon Inc.). Unit clusters with MANOVA P < 0.05 were taken to occupy a statistically distinct and well separated location in 2D space and considered to be single units. Spike counts in 2 ms bins were smoothed using half-Gaussian kernel (standard deviation 15 ms, rightward tail). Spike trains were aligned to the onsets of the stimulus (visual stimulus and saccade target) or task events (fixation, go cue, saccade) across trials to generate peristimulus time histograms (PSTHs) for spike rates. Population spike rates were calculated by averaging individual unit PSTHs after normalizing them to their peak spike rate.

Classification of SC neuronal responses

Neurons were categorized based on their average evoked spike counts to visual targets (50 to 300 ms after onset) and saccades (−100 to 50 ms from the saccade’s onset), during the memory-guided saccade task (Fig. 1f, Supplementary Figs. S1 and S3). An evoked spike rate was considered significant if it was significantly greater than (p < 0.05, signed rank sum test) the response during the fixation period (-250 to 0 ms from visual target onset). Neurons classified as visually selective (‘visual’) if they had a significant difference in their peak visual response (preferred response field) from the response to the visual target at the opposite location (180°, non-preferred response field; p < 0.05, signed rank sum test) and they had no saccade response. Similarly, neurons were classified as saccade selective (‘motor’) if their peak saccade-related response (preferred response field) was greater compared to the saccade response to the opposite location (180°, non-preferred response field; p < 0.05, signed rank sum test) and they had no visual response. Neurons with both visual and saccade selectivity were categorized as ‘visuo-motor’ neurons.

Neuronal d’

Neuronal spike rate modulations associated with behavioral Δd’ and Δc were measured using neuronal sensitivity as: \({d\hbox{'}}_{{neuron}}=({\mu }_{1}-{\mu }_{2})/\sqrt{\frac{1}{2}\left({{\sigma }}_{1}^{\,2}+{{\sigma }}_{2}^{\,2}\right)}\); where μi and σi are the average and standard deviation of spike counts within 50 to 250 ms from the onset of sample stimuli or saccade targets (i, trial conditions, for Δd’ and Δc, high or low) (Figs. 3c, e, Supplementary Figs. S4 and S5). PSTHs for neuronal d’ were calculated from spike count trains that had been smoothed using a Gaussian window with a sigma of 50 ms, binned at 20 ms intervals (10 ms overlap) (Fig. 1i, j).

Neuronal latency in saccade target discrimination

The earliest time at which neuronal response could reliably discriminate the location of monkey’s saccade (in-RF versus opposite-RF) was the neuronal latency for saccade target discrimination of a single unit (visuo-motor or motor; Fig. 1k–l). All trials within each session of the visual task described in Fig. 1 were grouped into four quartiles based on the saccade latency relative to the go-cue. These quartiles were separately determined for saccades directed towards the in-RF or opposite-RF location. Single trial spike counts were smoothed using a Gaussian window with a sigma of 50 ms, binned at 20 ms intervals (10 ms overlap), and aligned relative to the go-cue. Subsequently, the area under the receiver operating characteristic (AUROC) curve was estimated for saccades directed towards the in-RF versus the opposite-RF for each neuron and each set of trial quartiles. The earliest time relative to the go-cue when the AUROC was significantly higher compared to the AUROC derived from shuffled trials (95% confidence interval, 100 repetitions) was determined as the neuronal latency for discriminating a saccade target to be in-RF versus opposite-RF.

Linear decoder for behavioral Δd' and Δc

We used linear classifiers based on support vector machine to quantify single-trial encoding of behavioral Δd’ and Δc in SC neurons (Fig. 3f, g, Supplementary Figs. S4 and S5). Single trial spike counts were binned at 50 ms intervals (30 ms overlap) and aligned to visual stimuli or task-related events. These counts were then sorted into two groups based on low or high values of behavioral d’ or criterion at the neuron’s RF. Classifiers were trained on the training dataset (leave-one-out, 10-fold, 1000 repetitions) and decoding accuracy to behavioral d’ or criterion on single trials was estimated on the cross-validation trials. Similar decoding accuracy was estimated on shuffled trials to obtain 95% confidence intervals (100 repetitions).

Proximity of neuron’s response field (RF) to attended sample stimulus

Proximity between each neuron’s RF and sample stimulus (Fig. 4a-b) was estimated by a modified Mahalanobis distance34. It measures the statistical distance between two multivariate normal distributions similar to the Mahalanobis distance, but takes into account the covariance of both distributions: \({MD}=\sqrt{{\left({\mu }_{1}-{\mu }_{2}\right)}^{T}{S}^{-1}({\mu }_{1}-{\mu }_{2})}\); where S = (S1 + S2)/2; μi and Si are respectively the mean and covariance of distribution i (1 and 2); ‘T’ and ‘–1’ are transpose and inverse respectively. For each neuron, the spatial RF was measured and fit using a bivariate Gaussian. This measure of the RF-stimulus proximity accounts for both the alignment of the stimulus with the neuron’s RF and the correspondence between stimulus and RF size.

Linear regression: neuronal d’ versus behavioral d’ and the distance between the RF and the Gabor at the RF location

A linear regression model (Fig. 4c) was used to fit neuronal d’ (\({d}_{{neuronal}}^{{\prime} }\)) during sample stimuli (50–250 ms from the onset) to the behavioral d’ at the neuron’s RF (\({d}_{{behavior}}^{{\prime} }\)) and the proximity between the neuron’s RF and the attended stimulus (\({{MD}}_{{RF}-{Sample}}\)): \({d}_{{neuronal}}^{{\prime} }\, \sim \,{\beta }_{0}+{\beta }_{1}*{{MD}}_{{RF}-{Sample}}+{\beta }_{0}*{d}_{{behavior}}^{{\prime} }\); where βi is regression coefficient (i = 0, 1 and 2).

Within-session correlation: spike count–neuronal modulation

For the dataset presented in Fig. 2, behavioral d’ was calculated over a sliding window of 25 trials (with a 5-trial overlap) for each of the four trial types (low versus high behavioral d’; in-RF versus opposite-RF stimulus location, eight trial types total) during the behavioral Δd’ manipulation trial blocks within each session (Fig. 4e, f). These behavioral d’ values for each trial type were then categorized into four quartiles in each experimental session (Fig. 4e). Neuronal d’ was calculated based on the spike counts during the sample stimuli (50–250 ms from the sample onset) for each quartile (Fig. 4f).

Population decoding using demixed principal components analysis

Population activity of visuo-motor neurons in the SC was decomposed into distinct components, each carrying information about a single task-related or cognitive variable, using demixed principal component decompositions9,35 (Fig. 5). Mean-subtracted and trial-averaged spike trains of each neuron were separated into marginalized averages corresponding to task variables and a residual noise term to ensure that each marginalization captured variance specific to one variable. The neuronal data were then reconstructed using a set of encoder and decoder weight matrices that linearly projected the high-dimensional neural responses onto a small number of latent axes (demixed components) and back into the original neuronal space. The decomposition was optimized by minimizing a loss function defined as the difference between the original marginalized data and its low-dimensional reconstruction using a least-square method. This approach iteratively adjusted the encoder–decoder pairs to best reproduce the condition-averaged population activity while maintaining independence across task-related components. To avoid biases arising from unequal trial numbers across conditions (for example, between correct and error trials), we implemented a re-balancing procedure described by Kobak et al.35. Neural responses were first averaged within each condition, and the noise-covariance matrix was re-balanced by averaging it across conditions. This ensures that each condition is weighted equally in the decomposition and prevents trial-count differences from influencing the resulting components. Because neurons in our dataset were recorded across different sessions, cross-neuron trial-by-trial covariances cannot be estimated reliably. Therefore, following Kobak et al., we used a diagonal noise-covariance matrix, containing only per-neuron variances.

For the dataset in Fig. 1, trials were categorized by motor response criterion (low versus high saccade bias in-RF), saccade direction (in-RF versus opposite-RF) and stimulus detection (correct [hit, CR] versus error [miss, FA]), resulting in six trial configurations (Fig. 5a). For the dataset in Fig. 2, trials were classified by behavioral d’ (low versus high in-RF), perceptual decision criterion (low versus high saccade bias), saccade direction (in-RF versus opposite-RF), and stimulus detection (correct [hit, CR] versus error [miss, FA]), yielding eight configurations (Fig. 5b, c). All SC visuo-motor units with at least 10 trials for each condition from both monkeys were included in this analysis. Single-trial spike rates were filtered using a half Gaussian kernel (sigma = 30 ms) and then subsampled at 100 Hz. We analyzed spike rates over 500 ms (50 time points, starting 100 ms before sample onset, 50 ms before saccade target onset, 200 ms before go-cue, 400 ms before saccade onset). Decomposition into demixed components was performed on the training datasets using a leave-one-out approach and 200 repetitions. Subsequently, decoding accuracy was calculated on the remaining cross-validated test trials using the top three components. Confidence intervals (95%) were calculated on shuffled datasets.

An additional decoding analysis was done for the dataset in Fig. 5a to verify that pooling across trial types with opposite saccade directions did not obscure correctness-related signals owing to the saccade targets being fixed within a block (Supplementary Fig. 6). This dPCA analysis was restricted to trials sharing the same saccade plan by separately comparing hit versus false alarm trials (saccades to non-match-target) and correct rejection versus miss trials (saccades to match-target). Both comparisons held motor direction constant while differing in behavioral outcome. The analysis was otherwise identical to the main dPCA-based decoding procedure, using the same cross-validation and component selection criterion.

Statistical analysis

Unless otherwise specified multifactor repeated measures ANOVA for comparing normally distributed datasets. Normality was checked using a Kruskal-Wallis test.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.