Attention-related modulation in the superior colliculus encodes perceptual sensitivity, but not perceptual choice

Domain: chemistry
Published: 2026-02-28
Editorial outcome: major_revision

Abstract
Neurons in the superior colliculus (SC), like those in cortex, are modulated by shifts in attention but contribute differently from visual cortex neurons. It remains debated whether SC attention-related activity represents enhanced perceptual sensitivity, decision criterion shifts, or motor bias linked to saccade planning at neurons’ response fields. We dissociated these components by independently controlling behavioral sensitivity, perceptual decision criterion, and motor response criterion in a visual spatial attention task in two male monkeys. SC activity correlated strongly with behavioral sensitivity and motor criterion for selecting a saccade target within the response field, independent of saccade execution. In contrast, SC responses remained unchanged despite large shifts in decision criterion when motor bias was excluded. Notably, SC activity did not predict trial-by-trial choice accuracy. These results demonstrate that SC specifically supports components of attention related to heightened perceptual sensitivity and response selection, while being largely independent of internal perceptual decision criterion and trial outcome.

Introduction
Perceptual performance greatly improves with selective attention, and many distinct perceptual-, decision- and motor-related factors can independently alter attentional performance 1,2. Neuronal activity in numerous cortical and subcortical brain regions changes with shifts in attention 3-6. Previous studies examining attention-related modulations in the framework of signal detection theory 7 suggest that neuronal modulation in area V4 in visual cortex is associated with perceptual sensitivity (d’), but not with the decision criterion 8,9. The superior colliculus (SC), a midbrain subcortical structure, plays a crucial role in visual perceptual performance 5,10-12. It is believed that the SC contributes to visual attention through mechanisms that are distinct from those in the visual cortex 13, 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 signals 14. 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 behavior 15-17. 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 thresholds 11,12,16, 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 task 18 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 task 18 (Fig. 1a; Methods). The animal fixated on a central spot (0.2o 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 (0o) or non-match to the preceding sample Gabor (median thresholds [interquartile range], monkey S, 27o [25o-40o]; monkey P, 45o [38o-50o]) 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 to160 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).

Behavioral performance was quantified using the framework of signal detection theory 7 (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 (c) was measured using neuronal d’ (Methods). There was a significant spike modulation as measured by neuronal d’ for behavioral c 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 c (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 c 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, Figs. 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 (Figs. 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 decision 16,19. 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 Figure 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; d’ 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 d’ blocks (c trials, Fig. 2b).

Behavioral d’ increased significantly at the attended location compared to the unattended location on d’ 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, Figs. 2c and 2e), 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, Figs. 2c and 2e). On c 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, Figs. 2d and 2f) 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, Figs. 2d and 2f). This independent control of perceptual d’ and decision criterion (Figs. 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, Figs. 3a-b). In contrast, spike rates did not change during changes in decision criterion of similar magnitude (yellow and green, Figs. 3a-b). There was a significant spike modulation as measured by neuronal d’ during the sample stimuli presentation for behavioral d’, but not for decision c in visuo-motor neurons (neuronal d’, for behavioral d’ mean ± SEM = 1.29 ± 0.08; P < 10−17; for decision c 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 d’, but not for decision c (neuronal d’, or behavioral d’ mean ± SEM = 0.2 ± 0.06; P < 10−02; for decision c mean ± SEM = 0.023 ± 0.06; P = 0.4; n = 58/88, signed rank test; Figs. 3c, d & f; Supplementary Table S2). Spike rates of motor neurons were unaffected by behavioral d’ or decision c (neuronal d’, for behavioral d’ mean ± SEM = 0.13 ± 0.21, P = 0.45; for decision c mean ± SEM = –0.19 ± 0.16, P = 0.14; n = 30/52, signed rank test; Supplementary Fig. S4 & Supplementary Table S2).

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 (Figs. 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 d’ and c (Figs. 2g-h, Supplementary Fig. S4).

One possible reason for the absence of perceptual c-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 d’- and c- 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 Figure 2 (Supplementary Fig. S5). There was no significant spike modulation for c 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 c 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 Figure 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 (β = –0.1, p < 10–3; left, Fig. 4c). Additionally, neuronal d’ was positively correlated with the trial-averaged behavioral d’ within each session (β = 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).

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 d’ 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).

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, Figs. 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, Figs. 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, Figs. 5b-c) as well as correct detection (brown traces, Figs. 5b-c) were not significantly encoded during the trial. Because saccade targets were fixed within a block in the dataset shown in Figure 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 Figures 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.

Methods
Animals and surgery
Two adult male rhesus monkeys (Macaca mulatta, 9 and 13 kg) were each implanted with a titanium head post using aseptic surgical techniques 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 V4 9,32 and the locus coeruleus 18.

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; 0.30°-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; 32o for monkey S and 42 o 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) (Figs. 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 were 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 sides 18 (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 values 8,9. 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 attention 33.

During behavioral d’ and c 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 7,500 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 theory 7,32 as: 𝑑′ = Φ−1(𝐻)−Φ−1(𝐹) and 𝑐 = − 1/2 [Φ−1(𝐻)+Φ−1(𝐹)]; where –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 d’ and c were measured using neuronal sensitivity as: 𝑑′ = (𝜇1 −𝜇2)/√ 1/2 (1^2 +2^2); where  and  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 d’ and c, high or low) (Figs. 3c and 3e, 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) (Figs. 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; Figs. 1k-l). All trials within each session of the visual task described in Figure 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 d’ and c
We used linear classifiers based on support vector machine to quantify single-trial encoding of behavioral d’ and c in SC neurons (Figs. 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 (Figs. 4a-b) was estimated by a modified Mahalanobis distance 34. 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 = √(𝜇1 −𝜇2)^𝑇𝑆−1(𝜇1 −𝜇2) ; where S = (S1 + S2)/2; 𝜇 and S 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) during sample stimuli (50-250 ms from the onset) to the behavioral d’ at the neuron’s RF (𝑑′𝑏𝑒ℎ𝑎𝑣𝑖𝑜𝑟) and the proximity between the neuron’s RF and the attended stimulus (𝑀𝐷𝑅𝐹−𝑆𝑎𝑚𝑝𝑙𝑒): 𝑑′𝑛𝑒𝑢𝑟𝑜𝑛𝑎𝑙 ~ 𝛽0 +𝛽1 ∗𝑀𝐷𝑅𝐹−𝑆𝑎𝑚𝑝𝑙𝑒 +𝛽2 ∗𝑑′𝑏𝑒ℎ𝑎𝑣𝑖𝑜𝑟; where i is regression coefficient (i = 0, 1 and 2).

Within-session correlation: spike count–neuronal modulation
For the dataset presented in Figure 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 d’ manipulation trial blocks within each session (Figs. 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 decompositions 9,35 (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 Figure 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 Figure 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 Figure 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.

Data availability
All data are available in the main text, source data or the supplementary information.

Code availability
All behavioral and neuronal data analysis was done using Matlab (MathWorks Inc.). Behavioral task was controlled using custom-written software (https://github.com/MaunsellLab/Lablib-Public-05-February-2026).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is an excellent study that addresses a central and debated question in systems neuroscience: what is the specific contribution of the superior colliculus (SC) to visual spatial attention? The authors leverage an elegant behavioral paradigm to systematically dissociate perceptual sensitivity (d'), perceptual decision criterion (c), and motor response bias. Their central finding—that neuronal activity in the SC robustly encodes trial-by-trial fluctuations in perceptual sensitivity (d') but is invariant to changes in perceptual decision criterion (c) or the ultimate correctness of the choice—is a significant contribution to the field. The work is of high quality and the conclusions will potentially have a substantial impact on how we understand the role of subcortical structures in cognitive function. With that said, I have two major concerns and several minor ones that I feel are important to resolve in order to maximize the clarity of what is presented.\n\nMajor Comments\n1. The manuscript's core findings are very clearly articulated in the Results section, where the formal terms of signal detection theory (d' and c) are used with precision. However, in the Abstract and Discussion, this precision is sometimes lost when summarizing the findings. For example, the Discussion states \"SC neuronal activity was independent of perceptual decision, challenging the proposed role of SC in perceptual decision making\". The extensive evidence provided supports a more specific claim: that SC activity is independent of the perceptual decision criterion (c). For clarity, we suggest the authors carefully revise the Abstract and Discussion to ensure that the summary language precisely reflects the specific variables (d', c, and correct/error) they have so effectively dissociated.\n2. The finding that SC activity does not predict the correctness of a choice on a trial-by-trial basis is surprising and potentially very important. However, the dPCA analysis supporting this claim combined dissimilar trial types: \"correct\" trials included both Hits and Correct Rejections, while \"error\" trials included both Misses and False Alarms. Because a Hit and a Correct Rejection lead to opposite saccade plans, the underlying neural activity in a motor-related structure like the SC may be very different. Lumping these trials may create highly variable categories that are difficult to separate with a linear decoder, potentially masking a true neural correlate of correctness. To fully substantiate this key claim, we believe a more nuanced analysis is required. We suggest the authors either perform a 4-way classification (Hit vs. Miss vs. CR vs. FA) or, perhaps more simply, two separate binary classifications that hold the stimulus constant: (1) Hit vs. Miss trials, and (2) Correct Rejection vs. False Alarm trials.\n\nMinor Comments\n1. Inclusion of Single-Neuron Distributions: The manuscript primarily presents population-averaged data, which is clear and effective. However, to provide a more complete picture, it would be very helpful to also show distributions of the key single-neuron metrics. For example, adding histograms or scatter plots of Neuronal d' values for the \\Delta c and \\Delta d' conditions (akin to Supp. Fig. S4b) would allow the reader to appreciate the variability of these effects across the population and assess how uniform the modulation was for a given cell class.\n2. Reporting Variance Explained for dPCA: The dPCA analysis in Figure 5 is central to the paper's trial-by-trial claims. The Methods state that decoding was performed using the top three components. For methodological completeness, please report the cumulative percentage of variance explained by these top three components.\n3. Framing of the Latency Analysis (Lines 147-164): To improve the logical flow of this paragraph, it would be helpful to state the hypothesis being tested before presenting the analysis. Adding a sentence at the beginning, such as, “If response bias effects interact with saccade planning or execution, one might expect to find that variations in response latency result in systematic variation in neuronal activation for high and low bias conditions,” would nicely frame the subsequent results.\n4. Framing of the Within-Session Fluctuation Analysis (Lines 268-294): The analysis in Figure 4 is elegant. However, the initial framing around \"shorter timescales\" might suggest the focus is on the timescale of covariation itself. We suggest adding a sentence to clarify that the goal is to use the natural, within-session fluctuations in behavioral d' as a tool to probe the graded relationship between attentional intensity and neuronal modulation.\n5. Clarification of Reward Adjustment Heuristic (Lines 192-194): The authors state that the reward ratio was adjusted by small amounts to maintain a stable criterion. For full reproducibility of this elegant paradigm, please explicitly describe the heuristic used for these adjustments in the Methods section.\n6. Line 194: There is a small typo (\"...to a maintain decision criterion...\").\n7. Lines 263-264: The claim that \"information about behavioral d’ was represented by visuo-motor neurons during the presentation of saccade targets\" is strongly supported by Supplementary Figure S5e, but the citation is missing from the sentence. Please add it for clarity.\n8. Figure 1e: The re-use of red and yellow from panels 1c/d is potentially confusing, as the data in 1e are derived differences. We suggest using distinct colors in panel 1e.\n9. Figure 5: The time axis is labeled \"(s)\" but the values (e.g., 0, 200) appear to be in milliseconds. Please correct this to \"(ms)\" for consistency with other figures.", "reviewer_2": "The study by Ghosh and Maunsell, titled “Neuronal modulation of the superior colliculus associated with visual spatial attention represents perceptual sensitivity, independent of perceptual decision and motor biases,” provides significant insights into how neuronal activity in the superior colliculus (SC) correlates with distinct cognitive components, including perceptual sensitivity, perceptual decision criteria, reward, and motor response biases. The manuscript employs innovative experimental designs, effectively dissociating these cognitive elements. The authors elegantly demonstrate that SC activity is correlated with perceptual sensitivity but not with decision criteria within the neurons’ response fields. Furthermore, SC neuronal activity is enhanced under conditions of lower motor response criteria, particularly when there is a bias toward saccades directed toward the neuron’s response field. The manuscript is well-written and clearly structured, effectively communicating the main findings. This study significantly advances our understanding and clarifies the specific functional role of the superior colliculus in visual attention. \n\nI have only a few minor comments aimed at further improving the manuscript:\n1. The authors clearly demonstrate consistency in behavioral results across monkeys. However, it is unclear whether the main neuronal effects are consistent across individual monkeys. Clarifying this aspect would strengthen the current results.\n2. The manuscript occasionally might be challenging to follow for readers who are not familiar with the authors' previous work. Specifically, multiple definitions of d’, including perceptual d’, behavioral d’, and neuronal d’. It would be helpful if the authors could briefly define these terms clearly within the main text.\n3. It would be helpful if the authors provided additional details regarding the decoding analysis. Specifically, addressing how they managed potential imbalances in trial numbers, for example, between stimulus detection outcomes (correct vs. error trials).\n4. Minor typos:\n* Line 73: “withing” should be corrected to “within.”\n* Line 311: “Figs. 4b-c” should be corrected to “Figs. 5b-c.”\n* Line 313: “Fig. 4a” should be corrected to “Fig. 5a,” and “Figs. 4b-c” should be corrected to “Figs. 5b-c.”\n* Line 314: “Figs. 4b-c” should be corrected to “Figs. 5b-c.”\n* Citation references 19 and 25 currently refer to the same paper."}, "author_response": "Response to Reviewers, manuscript# NCOMMS-25-50592\nWe thank all the reviewers for their insightful and constructive questions and comments on our\nmanuscript. These have been very helpful in guiding our revisions, and have significantly\nstrengthened the manuscript.\nWe have addressed each of the key issues identified by the reviewers. In the following sections we\nprovide a detailed response to each point raised, and describe new analyses and texts that have\nbeen incorporated into the revised manuscript.\nREVIEWER COMMENTS\nReviewer #1:\nThis is an excellent study that addresses a central and debated question in systems neuroscience:\nwhat is the specific contribution of the superior colliculus (SC) to visual spatial attention? The\nauthors leverage an elegant behavioral paradigm to systematically dissociate perceptual\nsensitivity (d'), perceptual decision criterion (c), and motor response bias. Their central finding—\nthat neuronal activity in the SC robustly encodes trial-by-trial fluctuations in perceptual sensitivity\n(d') but is invariant to changes in perceptual decision criterion (c) or the ultimate correctness of\nthe choice—is a significant contribution to the field. The work is of high quality and the\nconclusions will potentially have a substantial impact on how we understand the role of\nsubcortical structures in cognitive function. With that said, I have two major concerns and several\nminor ones that I feel are important to resolve in order to maximize the clarity of what is presented.\nWe sincerely thank the Reviewer for the thoughtful and positive evaluation of our study. We\nare grateful for the recognition of the scientific significance of our findings and their\ncontribution to understanding the specific role of the superior colliculus in visual attention. We\nalso appreciate the reviewer’s constructive comments, which have helped us refine the\ninterpretation and presentation of our results. We have carefully addressed all major and minor\nconcerns, and we believe that the revised manuscript now more clearly highlights the\nconceptual and mechanistic advances of this work.\nMajor Comments\n1. The manuscript's core findings are very clearly articulated in the Results section, where the\nformal terms of signal detection theory (d' and c) are used with precision. However, in the\nAbstract and Discussion, this precision is sometimes lost when summarizing the findings. For\nexample, the Discussion states \"SC neuronal activity was independent of perceptual decision,\nchallenging the proposed role of SC in perceptual decision making\". The extensive evidence\nprovided supports a more specific claim: that SC activity is independent of the perceptual\ndecision criterion (c). For clarity, we suggest the authors carefully revise the Abstract and\nDiscussion to ensure that the summary language precisely reflects the specific variables (d', c,\nand correct/error) they have so effectively dissociated.\nour findings. We agree that the Abstract and Discussion should reflect the same formal\ndistinctions among signal-detection variables that are used in the Results. To address this, we\ncarefully revised the Abstract and Discussion to ensure that all summary statements use the\nformal terms of signal detection theory (d’, criterion, and correctness) precisely and\nconsistently. The following revised text now distinguishes perceptual sensitivity, decision\ncriterion, and motor bias explicitly throughout.\nAbstract\n“Neurons in the superior colliculus (SC), like those in the cerebral cortex, are strongly\nmodulated by shifts in attention, but make a contribution that is distinct from attention-related\nmodulations in the visual cortex. It has been a point of contention whether attention-related\nenhancement of SC activity represents a selective increase in perceptual sensitivity within\nneurons’ response fields or a change in decision criterion or motor bias linked to saccade\nplanning. We dissociated specific contributions of SC neuronal activity to these components\nby independently controlling the monkeys’ behavioral sensitivity, perceptual decision criterion\nand motor response criterion in a visual spatial attention task. SC activity was strongly\ncorrelated with behavioral sensitivity in the neuron’s response field, as well as with the motor\ncriterion to select a saccade target within the response field, independent of saccade execution.\nIn contrast, the responses of the same SC neurons remained unchanged in the face of\ncorrespondingly large changes in perceptual decision criterion when motor bias was carefully\nexcluded. Surprisingly, SC neuronal activity did not convey information about trial-by-trial\ncorrectness of behavioral choice. These results demonstrate that the SC contributes specifically\nto the component of attentional state associated with heightened perceptual sensitivity and\nresponse selection, while being largely independent of the internal perceptual decision criterion\nand trial outcome.”\nDiscussion\n“Our findings demonstrate that neuronal activity in the superior colliculus (SC) is strongly\nmodulated by perceptual sensitivity (d’) associated with visual spatial attention. Throughout\nthis study, we dissociated three components of attentional performance defined by signal\ndetection theory: perceptual d’, perceptual decision criterion, and motor response criterion,\nalong with trial-by-trial correctness (hit, miss, correct rejection, false alarm). The magnitude\nof this modulation depends on the spatial proximity of the locus of attention to the neuron’s\nresponse field, as well as the magnitude of perceptual d’ modulation. However, SC activity\ndoes not reflect whether the monkeys correctly detected a stimulus change at the single-trial\nlevel. Instead, the neuronal modulation corresponds to an elevated cognitive state associated\nwith improved perceptual sensitivity. SC activity was also enhanced with lower motor response\ncriterion, which occurred when there was a bias to saccade toward the neuron’s RF. In contrast,\nshifts in perceptual decision criterion at the neuron’s RF, which involved a bias toward\nselecting a target category rather than location, did not affect SC neuronal activity.\nLuo and Maunsell reported that neurons in the lateral prefrontal cortex (LPFC) represent both\nbehavioral d’ and criterion, while the visual area V4 selectively represents behavioral d’ in a\nsimilar visual detection task. However, the motor response criterion was not dissociated from\n2\nthe perceptual decision criterion. By behaviorally dissociating these behavioral components,\nwe reveal a functional dissociation between SC activity and distinct decision variables.\nSpecifically, SC neuronal firing rates selectively tracked motor criterion, but remained\nindependent from the perceptual decision criterion, indicating that the SC does not encode the\ninternal threshold governing categorical judgments of “match” versus “non-match”.\nFurthermore, SC modulation was uncorrelated with trial-by-trial correctness and instead\nreflected an elevated, spatially selective behavioral d’, indicating a sustained attentional state\nof heightened perceptual d’ rather than discrete perceptual decision outcomes, as observed in\nvisual cortex…. \nConclusion\nSC spiking robustly represents a cognitive state associated with improved perceptual\nsensitivity in visual spatial attention tasks, independently of its modulation by response bias,\nwhich has long been seen in tasks that involve saccade planning. However, when these spatial\ncomponents are controlled, non-spatial perceptual decisions and trial-by-trial perceptual\ndetection do not affect SC spiking. Collectively, these findings establish that the SC primarily\nencodes spatially selective perceptual sensitivity and motor preparatory bias, rather than the\ninternal decision threshold or trial outcome, underscoring its specialized role in linking\nattention to action.”\n2. The finding that SC activity does not predict the correctness of a choice on a trial-by-trial basis\nis surprising and potentially very important. However, the dPCA analysis supporting this claim\ncombined dissimilar trial types: \"correct\" trials included both Hits and Correct Rejections,\nwhile \"error\" trials included both Misses and False Alarms. Because a Hit and a Correct\nRejection lead to opposite saccade plans, the underlying neural activity in a motor-related\nstructure like the SC may be very different. Lumping these trials may create highly variable\ncategories that are difficult to separate with a linear decoder, potentially masking a true neural\ncorrelate of correctness. To fully substantiate this key claim, we believe a more nuanced\nanalysis is required. We suggest the authors either perform a 4-way classification (Hit vs. Miss\nvs. CR vs. FA) or, perhaps more simply, two separate binary classifications that hold the\nstimulus constant: (1) Hit vs. Miss trials, and (2) Correct Rejection vs. False Alarm trials.\nWe thank the reviewer for this insightful comment. We agree that, in the dataset shown in\nFigure 5a, Hit and Correct Rejection trials involve opposite saccade directions because\nsaccade targets were fixed within a block. Although our dPCA model included saccade\nlocation as an independent factor, thereby separating motor-related variance from other task\nvariables, we performed an additional control analysis to ensure that pooling across trial types\ndid not obscure correctness-related activity. Specifically, we repeated the decoding separately\nfor (i) hit versus false alarm trials and (ii) correct rejection versus miss trials, each pair sharing\nthe same saccade direction but differing in behavioral outcome (correct versus error). These\nanalyses again revealed no reliable trial-by-trial prediction of correctness from population\nactivity of SC visuo-motor neurons, confirming that the absence of correctness-related\ndecoding is not due to mixed motor plans but reflects a genuine lack of outcome-predictive\nsignals in the SC.\nsupplementary figure on the new analysis.\nResults\n“In contrast, perceptual decision criterion (red traces, Figs. 5b-c) as well as correct detection\n(brown traces, Figs. 5b-c) were not significantly encoded during the trial. Because saccade\ntargets were fixed within a block in the dataset shown in Figure 5a, we verified that this lack\nof correctness-related decoding was not confounded by opposite motor plans between trial\ntypes. A control analysis compared hit versus false alarm and correct rejection versus miss\ntrials, each pair sharing the same saccade direction but differing in behavioral outcome (see\nSupplementary Fig. S6). The results confirmed that SC population activity did not predict\ncorrectness even when motor direction was held constant. In the datasets shown in Figures 5b–\nc, saccade target locations were randomized on a trial-by-trial basis, such that motor direction\nand correctness were orthogonal by design, eliminating this potential confound.”\nSupplementary Information\nFigure S6. Single-trial decoding of motor response criterion, saccade direction and correct\ndetection associated with attentional performance from SC visuo-motor neurons shown in Figure\n1. (a) Time course of single-trial decoding accuracy (cross-validated leave-one-out trials) for motor\nresponse criterion (low vs high), executed saccade direction (in-RF versus opp-RF), and correct\ndetection (hit versus false alarm) based on demixed principal component analysis of the population\nPSTHs of SC visuo-motor neurons (n = 44/69), as shown in Figure 1 (Methods). Only the hit and false\nalarm trials were considered. The locations of the saccade targets were fixed and alternated across\nblocks, with one target placed within the neuron’s RF. Only neurons for which at least 10 trials were\nconducted for each decoding factor were included. Error bars, 95% confidence intervals from shuffled\ntrials. (b) Same as in (a) except for correct rejection and miss trials for the same set of SC neurons.\n1. Inclusion of Single-Neuron Distributions: The manuscript primarily presents population-\naveraged data, which is clear and effective. However, to provide a more complete picture, it\nwould be very helpful to also show distributions of the key single-neuron metrics. For example,\nadding histograms or scatter plots of Neuronal d' values for the \\Delta c and \\Delta d'\nconditions (akin to Supp. Fig. S4b) would allow the reader to appreciate the variability of these\neffects across the population and assess how uniform the modulation was for a given cell class\nWe thank the reviewer for this helpful suggestion. In the revised manuscript, we have added\nsingle neuron distributions to illustrate the variability of neuronal modulation across the\npopulation. The following revised Figure 3e–f, Supplementary Figures S4 & S5 now include\nscatter plots and histograms showing the distributions of neuronal d’ values for both the\nbehavioral Δd’ and Δc conditions. These additions provide a clearer depiction of the\nheterogeneity within each neuronal class.\nResults\ndecision criterion. (a) Trial-averaged PSTHs of an example visuo-motor SC neuron when the\nmonkey’s behavioral d’ and decision criterion at the neuron’s RF location were independently\ncontrolled relative to the stimulus at the opposite hemifield (Fig. 2). Spike rates are aligned to the onsets\nof sample stimuli, saccade targets, go-cue, and the saccade (top). Error bars, ±1 SEM. (b) PSTHs are\nsimilar to those in (a), except for the population of visuo-motor neurons when one of the visual sample\nstimuli was located within the neuron’s RF (n = 105/165). (c-d) Similar to (a-b), except for an example\nand population of visual neurons in the SC (n = 58/88). (e-f) Spike rate modulation of SC neurons with\nchanges in behavioral d’ (Dbeh d’) and decision criterion (Dc). Bottom left, Population distribution of\nneuronal d’ quantifying modulation as a function of Dbeh d’ and Dc for visuo-motor (e) and visual\nneurons (f). Top & right, marginal distributions of neuronal d’ for Dc (top) and Dbeh d’ (right).\nTriangles represent population means. (g-h) Decoding accuracies for behavioral d’ (top) and decision\ncriterion (bottom) from spike counts using a linear classifier based on support vector machine, averaged\nacross individual visuo-motor (g) and visual (h) neurons, as shown in (b) and (d). Dashed lines, 95%\nconfidence intervals based on shuffled trials. Error bars, ±1 SEM.\nSupplementary Information\nFigure S4. Neuronal modulation in SC motor neurons with changes in behavioral d’ and\nperceptual decision criterion, when one of the sample stimuli (randomized) was placed in the\nneuron’s RF. (a) Population PSTHs of SC motor neurons when monkeys’ spatial attention and\ndecision criterion were independently controlled, and one of the sample stimuli was placed within the\nneuron’s RF (n = 30/52). The spike rates are aligned to the onsets of sample stimuli, saccade targets,\ngo-cue and the saccade. Error bars, ± 1 SEM. (b) Neuronal modulation as measured by neuronal d’\nbased on spike-counts over 200 ms (50-250 ms from the onset of sample stimuli), associated with\n6\nchanges in behavioral d’ (Dbeh d’) and decision criterion (Dc). Bottom left, Population distribution of\nneuronal d’ quantifying modulation as a function of Dbeh d’ and Dc for visuo-motor during sample\nstimuli. Top & right, marginal distributions of neuronal d’ for Dc (top) and Dbeh d’ (right).\nTriangles represent population means. (c) Decoding accuracies for behavioral d’ (top) and criterion (bottom)\nbased on SVM linear classifiers, averaged across individual motor neurons. Dashed lines, 95%\nconfidence intervals based on shuffled trials. Error bars, ± 1 SEM.\nFigure S5. Neuronal modulation in SC with behavioral Dd’ and perceptual decision Dc, when the\none of the saccade targets (randomized) was placed in the neuron’s RF. (a) Population PSTHs of\nvisuo-motor SC neurons when monkeys’ spatial attention and decision criterion were independently\ncontrolled, and one of the saccade targets was placed at the neuron’s RF location (n = 60/165). The\nspike rates are aligned to the onsets of sample stimuli, saccade targets, go-cue and the saccade. Error\nbars, ± 1 SEM. (b-c) Neuronal modulation as measured by neuronal d’ based on spike-counts over 200\nms (50-250 ms from the onset of sample stimuli or saccade target), associated with changes in\nbehavioral d’ (Dbeh d’) and decision criterion (Dc). Bottom left, Population distribution of neuronal d’\nquantifying modulation as a function of Dbeh d’ and Dc for visuo-motor during sample stimuli (b) and\nsaccade-target presentation (c). Top & right, marginal distributions of neuronal d’ for Dc (top) and Dbeh\n7\nd’ (right). Triangles represent population means. (d-f) Similar to (a-c), for visual neurons. (g-h)\nDecoding accuracies for behavioral d’ (top) and criterion (bottom) based on SVM linear classifiers,\naveraged across individual visuo-motor (g) and visual (h) neurons. Dashed lines, 95% confidence\nintervals based on shuffled trials. Error bars, ± 1 SEM.\n2. Reporting Variance Explained for dPCA: The dPCA analysis in Figure 5 is central to the\npaper's trial-by-trial claims. The Methods state that decoding was performed using the top\nthree components. For methodological completeness, please report the cumulative percentage\nof variance explained by these top three components?\nWe thank the reviewer for this helpful suggestion. We have now reported the cumulative\nvariance explained by the top three dPCs for each decoding parameter (motor response\ncriterion, perceptual d’, perceptual decision criterion, saccade direction and correct detection)\nand trial-event epoch (sample onset, saccade-target onset, go and saccade onset). These values\nhave been summarized in the Results section and further detailed in Supplementary Table S5\nin the revised manuscript.\nResults\n“Across parameters and trial-event epochs (sample onset, saccade-target onset, go and saccade\nonset), the first three dPCs explained between 1.5 and 47.3% of total variance, with the largest\ncontributions from saccade direction (36.7-47.3%) followed by perceptual motor response\ncriterion (1.7-2.2%), and condition-independent components (41.3-62.6%) in the fixed-target\ncondition (Fig. 5a). In the randomized-saccade-target condition with one of the saccade-targets\nin the neuron’s RF (Fig. 5b), the top three dPCs accounted for 0.4-64.9% of the total variance,\ndominated by saccade direction (56.3-64.9%) followed by perceptual d’ (2.6-5.1%), and\ncondition-independent activity (38.2-56.6%). For the randomized-saccade-target condition\nwith the sample stimulus in the RF (Fig. 5c), the top three components explained 0.3–56.9%\nof the total variance, with the largest variance captured by perceptual d’ (6.3-18.7%) and\ncondition-independent components (22.7-56.9%). Across all datasets, perceptual decision\ncriterion and correctness accounted for small fractions of variance (typically < 3.5%;\nSupplementary Table S5).”\nSupplementary Information\n“Table S5. Cumulative percentage of variance explained by the first three demixed principal\ncomponents (dPCs) for each decoding parameter and trial-event epoch for visuo-motor neurons\nacross different task conditions (Fig. 5).\n% Variance explained\nTask condition: fixed saccade-targets, target in-RF (Fig. 5a)\nparameters trial-event epoch\nsample target go (fix saccade\nOff)\n8\nmotor response criterion 1.9 2 2.2 1.7\nsaccade direction 1.5 36.7 43.5 47.3\ncorrect detection 0.6 0.4 0.6 0.4\ncondition independent 41.3 62.6 51.8 58.9\nTask condition: randomized saccade-targets: target in-RF (Fig. 5b)\nbehavioral d’ 5.1 2.6 3.2 1.3\nperceptual decision 1.5 0.6 0.9 0.4\ncriterion\nsaccade direction 0.5 56.3 57.8 64.9\ncorrect detection 0.5 2.5 3.2 0.3\ncondition independent 56.6 38.2 28.6 53.9\nTask condition: randomized saccade-targets: sample in-RF (Fig. 5c)\nbehavioral d’ 18.7 6.3 6.4 18.7\nperceptual decision 1.6 2.8 3.5 3.3\ncriterion\nsaccade direction 0.3 6.3 7.8 15.7\ncorrect detection 0.6 0.9 0.6 1.1\ncondition independent 56.8 25.3 22.7 24.1\n”\n3. Framing of the Latency Analysis (Lines 147-164): To improve the logical flow of this\nparagraph, it would be helpful to state the hypothesis being tested before presenting the\nanalysis. Adding a sentence at the beginning, such as, “If response bias effects interact with\nsaccade planning or execution, one might expect to find that variations in response latency\nresult in systematic variation in neuronal activation for high and low bias conditions,” would\nnicely frame the subsequent results.\nWe thank the reviewer for this valuable suggestion to clarify the rationale of the latency\nanalysis. We have revised the beginning of the relevant paragraph to explicitly state the\nhypothesis being tested.\nResults\n“If response bias interacts with saccade planning or execution, variations in the animal’s\nresponse latency should be accompanied by systematic changes in neuronal activation between\nhigh and low bias conditions. To test this hypothesis, we examined whether the spike\nmodulation associated with motor response bias (also referred to as ‘motor intent’ or ‘motor\nplanning’) could be dissociated from activity related to the physical act of saccade execution.”\n4. Framing of the Within-Session Fluctuation Analysis (Lines 268-294): The analysis in Figure\n4 is elegant. However, the initial framing around \"shorter timescales\" might suggest the focus\nis on the timescale of covariation itself. We suggest adding a sentence to clarify that the goal\nis to use the natural, within-session fluctuations in behavioral d' as a tool to probe the graded\nrelationship between attentional intensity and neuronal modulation.\nsection to clarify that the goal of the analysis was not to investigate temporal timescales per se,\nbut to leverage natural within-session fluctuations in behavioral d’ to examine the graded\nrelationship between the strength of spatially selective attention and SC neuronal modulation.\nResults\n“To further examine how fluctuations in behavioral sensitivity relate to neuronal modulation,\nwe leveraged natural within-session variations in behavioral d’ as a tool to probe the graded\nrelationship between the strength of spatially selective attention and SC activity. To assess\nbehavioral performance on this finer behavioral scale, behavioral d’ was computed using a 25-\ntrial moving window separately for all four trial types (low versus high selective attention; in-\nRF versus opposite-RF location) during Dd’ manipulation trial blocks within each session.”\n5. Clarification of Reward Adjustment Heuristic (Lines 192-194): The authors state that the\nreward ratio was adjusted by small amounts to maintain a stable criterion. For full\nreproducibility of this elegant paradigm, please explicitly describe the heuristic used for these\nadjustments in the Methods section.\nWe thank the reviewer for this constructive suggestion. We have now added a detailed\ndescription of the reward-adjustment heuristic to the Methods section (“Independent control\nof behavioral d’ and criterion associated with visual spatial attention”).\nMethods\n“….During behavioral Dd’ and Dc trial blocks, the reward ratio for correct responses (hits and\nCRs) was adaptively adjusted in small increments based on recent performance to maintain a\nstable decision criterion near zero. Reward volumes were modified by approximately 5 to 20%\nevery 10 to 15 trials depending on the animal’s average criterion in the preceding window.\nWhen a consistent bias toward one choice (positive or negative criterion) was detected, the\nreward for the less frequent correct response was slightly increased, while that for the more\nfrequent correct response was reduced by the same proportion. Adjustments continued until\nthe mean criterion across two consecutive windows remained within ±0.1. This heuristic\nensured criterion stability while maintaining balanced motivation and total reward rate across\nconditions.”\n6. Line 194: There is a small typo (\"...to a maintain decision criterion...\").\nWe have corrected the typo to “…to maintain a decision criterion…”.\n7. Lines 263-264: The claim that \"information about behavioral d’ was represented by visuo-\nmotor neurons during the presentation of saccade targets\" is strongly supported by\nSupplementary Figure S5e, but the citation is missing from the sentence. Please add it for\nclarity.\nreference to the revised Supplementary Figure S5g in the corresponding sentence to clarify\nand directly support this statement.\nResults\n“However, information about behavioral d’ was represented by visuo-motor neurons during\nthe presentation of saccade targets (Supplementary Fig. S5g).”\n8. Figure 1e: The re-use of red and yellow from panels 1c/d is potentially confusing, as the data\nin 1e are derived differences. We suggest using distinct colors in panel 1e.\nWe thank the reviewer for this helpful suggestion. In the revised Figure 1e, we have replaced\nthe red and yellow colors with distinct, non-overlapping hues (magenta and violet) to clearly\ndistinguish the derived difference data from the raw data shown in panels Figure 1c & d.\n9. Figure 5: The time axis is labeled \"(s)\" but the values (e.g., 0, 200) appear to be in\nmilliseconds. Please correct this to \"(ms)\" for consistency with other figures.\nWe have corrected the labeling error in the time-axis of Figure 5, changing “(s)” to “(ms)” in\nthe revised manuscript.\nReviewer #2:\nThe study by Ghosh and Maunsell, titled “Neuronal modulation of the superior colliculus\nassociated with visual spatial attention represents perceptual sensitivity, independent of\nperceptual decision and motor biases,” provides significant insights into how neuronal activity in\nthe superior colliculus (SC) correlates with distinct cognitive components, including perceptual\nsensitivity, perceptual decision criteria, reward, and motor response biases. The manuscript\nemploys innovative experimental designs, effectively dissociating these cognitive elements. The\nauthors elegantly demonstrate that SC activity is correlated with perceptual sensitivity but not with\ndecision criteria within the neurons’ response fields. Furthermore, SC neuronal activity is\nenhanced under conditions of lower motor response criteria, particularly when there is a bias\ntoward saccades directed toward the neuron’s response field. The manuscript is well-written and\nclearly structured, effectively communicating the main findings. This study significantly advances\nour understanding and clarifies the specific functional role of the superior colliculus in visual\nattention.\nI have only a few minor comments aimed at further improving the manuscript:\nWe deeply appreciate the Reviewer’s generous and insightful evaluation of our manuscript.\nWe are particularly grateful for the recognition of the study’s conceptual clarity and the\neffectiveness of our experimental design in disentangling perceptual sensitivity, decision\ncriterion, and motor bias. The reviewer’s constructive feedback has been valuable in improving\n11\nthe precision and presentation of our results. We have carefully implemented all suggested\nrevisions, which have further strengthened the coherence and overall impact of the manuscript.\nMinor comments\n1. The authors clearly demonstrate consistency in behavioral results across monkeys. However,\nit is unclear whether the main neuronal effects are consistent across individual monkeys.\nClarifying this aspect would strengthen the current results.\nWe appreciate the reviewer for this suggestion. In the revised manuscript, we have included\nthe main neuronal effects (neuronal d’ values) for each animal (monkey P and monkey S)\nacross neuron classes (visuo-motor, visual and motor) and experimental configurations for\nchanges in behavioral d’ and criterion in the following Supplementary Tables S1–S4.\nSupplementary Information\n“Table S1. Neuronal d’ of the SC neurons (during sample stimuli) with changes in behavioral\ncriterion when saccade-targets were fixed across trials and alternated across blocks. One of the\nsample stimuli was in placed within the neuron’s RF location (Fig. 1).\nFor behavioral Dcriterion: during sample stimuli\nmonkey P match-saccade-target in-RF nonmatch-saccade-target in-\nRF\nno. of neuronal d’ p-value neuronal d’ p-value (signed\nneurons (mean ± SEM) (signed rank (mean ± SEM) rank test)\ntest)\nvis-motor 21 1.35 ± 0.2 < 10–4 0.74 ± 0.2 < 10–2\nvisual 6 0.81 ± 0.38 0.09 -0.24 ± 0.22 0.3\nmotor 6 1.6 ± 0.7 0.09 0.86 ± 0.7 0.3\nmonkey S\nvis-motor 23 0.82 ± 0.12 < 10–3 1.3 ± 0.2 < 10–3\nvisual 3 -0.7 ± 1.3 NA 1.01 ± 0.9 NA\nmotor 10 0.41 ± 0.31 0.27 0.55 ± 0.19 0.03\nTable S2. Neuronal d’ of the SC neurons (during sample stimuli) with changes in behavioral\nd’ and criterion when saccade-targets were randomized on trial-by-trial basis, and one of the\nsample stimuli was placed within the neuron’s RF location (Fig. 2 & 3).\nRandomized sac-targets trial-by-trial; sample in-RF: during sample stimuli\nmonkey P for behavioral Dd’ for behavioral Dcriterion\nno. of neuronal d’ p-value neuronal d’ p-value (signed\nneurons (mean ± SEM) (signed rank (mean ± SEM) rank test)\ntest)\nvis-motor 65 1.14 ± 0.1 < 10–10 0.06 ± 0.06 0.25\nvisual 41 0.16 ± 0.07 0.14 0.04 ± 0.05 0.35\nmotor 18 0.1 ± 0.29 0.62 0.14 ± 0.19 0.71\n12\nmonkey S\nvis-motor 40 1.15 ± 0.13 < 10–7 -0.08 ± 0.11 0.48\nvisual 17 0.31 ± 0.13 0.03 -0.03 ± 0.165 0.9\nmotor 12 0.19 ± 0.29 0.47 -0.24 ± 0.10 0.08\nTable S3. Neuronal d’ of the SC neurons (during sample stimuli) with changes in behavioral\nd’ and criterion when saccade-targets were randomized on trial-by-trial basis, and one of the\nsaccade-targets was placed within the neuron’s RF location (Fig.2 & Supplementary Fig.\nS5).\nTrial-by-trial randomized sac-targets; sac-target in-RF: during sample stimuli\nmonkey P for behavioral Dd’ for behavioral Dcriterion\nno. of neuronal d’ p-value neuronal d’ p-value (signed\nneurons (mean ± SEM) (signed rank (mean ± SEM) rank test)\ntest)\nvis-motor 25 0.21 ± 0.11 0.04 0.12 ± 0.08 0.1\nvisual 22 0.13 ± 0.09 0.11 0.07 ± 0.19 0.71\nmotor 7 -0.38 ± 0.31 0.37 -0.57 ± 0.29 0.11\nmonkey S\nvis-motor 35 0.02 ± 0.14 0.7 -0.07 ± 0.1 0.78\nvisual 8 0.57 ± 0.21 0.04 -0.15 ± 0.17 0.46\nmotor 15 0.33 ± 0.14 0.04 -0.03 ± 0.2 0.93\nTable S4. Neuronal d’ of the SC neurons (during saccade-target presentation) with changes\nin behavioral d’ and criterion when saccade-targets were randomized on trial-by-trial basis,\nand one of the saccade-targets was placed within the neuron’s RF location (Fig 2 &\nSupplementary Fig. S5).\nTrial-by-trial randomized sac-targets; sac-target in-RF: during saccade-target\nmonkey P for behavioral Dd’ for behavioral Dcriterion\nno. of neuronal d’ p-value (signed neuronal d’ p-value (signed\nneurons (mean ± SEM) rank test) (mean ± SEM) rank test)\nvis-motor 25 -0.09 ± 0.13 0.9 -0.38 ± 0.23 0.09\nvisual 22 -0.01 ± 0.1 0.83 -0.19 ± 0.14 0.08\nmotor 7 0.52 ± 1.0 0.47 0.41 ± 0.32 0.46\nmonkey S\nvis-motor 35 -0.06 ± 0.14 0.11 -0.13 ± 0.21 0.9\nvisual 8 0.63 ± 0.35 0.04 0.31 ± 0.17 0.31\nmotor 15 -0.45 ± 0.46 0.17 -0.14 ± 0.36 0.9\n”\n2. The manuscript occasionally might be challenging to follow for readers who are not familiar\nwith the authors' previous work. Specifically, multiple definitions of d’, including perceptual\n13\nd’, behavioral d’, and neuronal d’. It would be helpful if the authors could briefly define these\nterms clearly within the main text.\nWe thank the reviewer for this helpful suggestion. We have included the following revision in\nthe Results section to clearly define all forms of d’s used in the study: perceptual d’, behavioral\nd’, and neuronal d’ along with the decision criterion and correctness measures.\nResults\n“Behavioral performance was quantified using the framework of signal detection theory\n(Methods). In this framework, perceptual d’ denotes the theoretical sensitivity to stimulus\ndifferences (match versus non-match). This sensitivity was measured behaviorally as\nbehavioral d’, computed empirically from the animal’s hit and false-alarm rates, reflecting the\nsubject’s perceptual discriminability. Behavioral d’ therefore operationalizes perceptual d’ as\nexpressed in the subject’s performance. The decision criterion (c) represents the internal bias\nfor reporting a perceived stimulus difference independent of stimulus evidence. We\nindependently examined two forms of criterion: motor and perceptual. The motor response\ncriterion refers to the animal’s bias or intent to make a saccade toward one potential target\nlocation over the other, reflecting response-level or motor planning bias. The perceptual\ndecision criterion defines the internal threshold or bias to judge whether a test stimulus is a\nmatch or non-match, independent of spatial configuration of saccade targets. “Correctness”\nrefers to trial-by-trial behavioral outcomes–correct (hit and correct rejection) versus erroneous\n(miss and false alarm) detections. Neuronal d’ quantifies discriminability in neuronal firing\nrates, indicating how well neural activity differentiates between conditions–for example,\nselecting a saccade target inside versus outside the neuron’s RF.”\n3. It would be helpful if the authors provided additional details regarding the decoding analysis.\nSpecifically, addressing how they managed potential imbalances in trial numbers, for example,\nbetween stimulus detection outcomes (correct vs. error trials).\nWe thank the reviewer for pointing out the potential impact of unequal trial numbers across\nconditions on the decoding analysis. In our demixed principal component analysis (dPCA), we\nexplicitly accounted for this by implementing the rebalancing procedure described by Kobak\net al. (2016). We have now clarified this procedure in the revised Methods section.\nMethods\n“Mean-subtracted and trial-averaged spike trains of each neuron were separated into\nmarginalized averages corresponding to task variables and a residual noise term to ensure that\neach marginalization captured variance specific to one variable. The neuronal data were then\nreconstructed using a set of encoder and decoder weight matrices that linearly projected the\nhigh-dimensional neural responses onto a small number of latent axes (demixed components)\nand back into the original neuronal space. The decomposition was optimized by minimizing a\nloss function defined as the difference between the original marginalized data and its low-\ndimensional reconstruction using a least-square method. This approach iteratively adjusted the\nencoder–decoder pairs to best reproduce the condition-averaged population activity while\nmaintaining independence across task-related components.\ncorrect and error trials), we implemented a re-balancing procedure described by Kobak et al.\nNeural responses were first averaged within each condition, and the noise-covariance matrix\nwas re-balanced by averaging it across conditions. This ensures that each condition is weighted\nequally in the decomposition and prevents trial-count differences from influencing the\nresulting components.\nBecause neurons in our dataset were recorded across different sessions, cross-neuron trial-by-\ntrial covariances cannot be estimated reliably. Therefore, following Kobak et al., we used a\ndiagonal noise-covariance matrix, containing only per-neuron variances.”\n4. Minor typos:\n* Line 73: “withing” should be corrected to “within.”\n* Line 311: “Figs. 4b-c” should be corrected to “Figs. 5b-c.”\n* Line 313: “Fig. 4a” should be corrected to “Fig. 5a,” and “Figs. 4b-c” should be corrected\nto “Figs. 5b-c.”\n* Line 314: “Figs. 4b-c” should be corrected to “Figs. 5b-c.”\n* Citation references 19 and 25 currently refer to the same paper.\nWe thank the reviewer for carefully noting these typographical and reference errors. We have\naccordingly corrected all of them in the revised manuscript.\nWe thank the reviewers for their supportive and thoughtful feedback on our revised manuscript.\nWe are pleased that the major concerns have been resolved, and we appreciate the remaining\nsuggestions, which have helped us further refine the clarity and precision of the text. Below,\nwe\noutline the minor changes made in response.\nREVIEWER COMMENTS\nReviewer #1:\nI am happy to see this manuscript again! I thank the authors for their exceptionally thorough and\nthoughtful response to my initial review. They have fully addressed all major and minor concerns,\nand in doing so, have substantially strengthened the manuscript. The authors successfully\ndissociate SC activity from non-spatial, abstract decision variables and trial-by-trial correctness,\nwhile confirming its role in encoding spatial priority and motor selection. I have no further\nscientific concerns and am delighted to recommend acceptance. Below I note some inevitable\ntypographical errors that can be addressed at the proof stage. Signed, James P. Herman.\nThank you for your thoughtful and encouraging feedback. We're pleased to hear that the\nrevisions fully addressed your concerns and helped strengthen the manuscript. We appreciate\nyour recommendation for acceptance and will ensure that the noted typographical issues are\ncorrected at the proof stage.\nMinor Comments\n1. Main Text, Page 11 (Results): The new text reads, \"...followed by perceptual motor response\ncriterion (1.7-2.2%).\". This appears to be a minor conflation of terms and should likely just\nread \"motor response criterion\" to match Supplementary Table S57.\n2. Main Text, Page 12 (Results, Line 348): The text reads, \"...increased sharply d' before saccade\nexecution...\". The \"d'\" appears to be a stray fragment and should be removed.\n3. Main Text, Page 20 (Methods, Lines 685-686): The phrase \"...did not obscure correctness-\nrelated signals owing to the saccade targets were fixed...\" is grammatically incorrect. It should\nbe corrected to \"because the saccade targets were fixed\" or \"owing to the saccade targets\nbeing fixed\".\n4. Main Text, Page 20 (Methods, Line 687): The text reads, \"An additional decoding analysis\nwas done... (Supplementary Fig. XX).\". This placeholder should be updated to (Supplementary\nFig. S6).\n5. Supplement, Page 1 (Table S1 Title): The text reads, \"...was in placed within...\". This should\nbe corrected to \"was placed within...\".\n6. Supplement, Page 2 (Table S4 Header): There appears to be a text-formatting error in the\ntable's main header.\n7. Supplement, Page 6 (Fig. S4 Legend): Part (b) of the legend describes the data as being from\n\"visuo-motor\" neurons, but the figure itself is for the motor neuron population.\n8. Supplement, Page 9 (Fig. S7 Legend): Part (a) of the legend contains the typo \"...presented\nwithing the neuron's RF...\". This should be \"within.\nthe listed items in the main text and supplementary materials, including terminology\nclarifications, grammatical fixes, figure references, and formatting adjustments. These changes\nhave been incorporated into the final revised version.\nReviewer #2:\nWe appreciate the authors' thoughtful and thorough revisions. The additional analyses and\nclarifications have substantially improved the manuscript, and the authors have addressed the\nmajority of our earlier concerns. Below are a few remaining minor suggestions that we believe\nwill further improve clarity and interpretation.\nWe appreciate the reviewer’s thoughtful feedback and are glad the revisions satisfactorily\naddressed the concerns. We carefully considered the remaining suggestions and have made the\ncorresponding changes to further improve the clarity and interpretation of the manuscript.\nComments\n1. The subtitle “Spike modulation of SC visuo-motor neurons associated with changes in\nresponse criterion” appears mismatched with the content of the subsequent paragraph, which\nfocuses more broadly on neuronal modulation and does not specifically center on response\ncriterion. Revising this subtitle to better reflect the content would improve the section’s\ncoherence.\nWe have revised this subtitle to “Behavioral isolation of response criterion from perceptual\nsensitivity” for better coherence.\n2. In Figure 3, panel d is labeled “population vis-motor,” but based on the surrounding text and\nthe example neuron above, it should read “population visual.”\nWe have corrected the typographical error in Figure 3d in the revised manuscript.\n3. Re-consistency across monkeys (comments): We appreciate the detailed supplementary tables\nsummarizing neuronal effects for each animal. This addition greatly improves transparency.\nThe main effects appear largely consistent across monkeys.\nWe appreciate your positive feedback on the added cross-monkey summary tables.\n4. A minor conceptual concern remains regarding the condition in which \"neuronal d’ is\nmeasured during sample presentation under changes in behavioral d’\". In these blocks, the\nhigh behavioral d’ condition also corresponds to the high-reward side, meaning that the\n“high-d’ sample” is also the high-reward stimulus. The authors show that neuronal d’\ncorrelates with behavioral d’, suggesting that part of the modulation reflects behavioral\nsensitivity. However, in some analyses (e.g., Fig. 3g), decoding performance in the high-d’\ncondition could plausibly reflect contributions from the reward manipulation as well. Ideally,\ndistinguishing attention from reward would require conditions in which both sides receive high\nreward for both Hits and CRs, thereby creating high reward but lower behavioral d’. Given\nthe complexity of the current paradigm, such a manipulation may not be experimentally\nfeasible. Nevertheless, it would strengthen the manuscript if the authors could briefly discuss\nthe potential influence of reward, given the fact that SC activity can be modulated by reward\n(e.g., Baruchin, 2023).\nWe have added a brief text revision in the ‘Discussion’ noting that SC modulation may reflect\nattention shaped by reward-driven spatial selection and suggest future work to disentangle\nmotivational influences.\n“As SC neurons are sensitive to expected reward (Baruchin, Alleman and Schröder, J.\nNeurosci., 2023) the observed neuronal modulation may reflect a spatially selective state\nheightened attention driven by external motivation, since attentional state was manipulated by\nadjusting reward size. Future work is needed to further isolate SC contribution to spatial\nselection using motivational factors beyond reward, such as task difficulty (Ghosh and\nMaunsell, Sci. Adv., 2022)”.\n3"}]

Decision letter