Prefrontal attentional saccades explore space rhythmically

Recent studies suggest that attention samples space rhythmically through oscillatory interactions in the frontoparietal network. However, the precise mechanism through which the prefrontal cortex, at the source of attention control signals, organizes this rhythmic exploration of space remains unknown. We show that, when decoded at a high spatial (0.1°) and temporal resolution (50ms), the prefrontal covert attentional spotlight, aka the mind’s eye, continuously explores space at an alpha 7-12 Hz rhythm. When sensory events are presented at a specific optimal phase (resp. anti-phase) with respect to this rhythm, sensory encoding and behavioral report are accurate (resp. poor). We propose that this rhythmic prefrontal attentional spotlight dynamics corresponds to a continuous overt exploration of space via alpha-clocked attentional saccades. These attentional saccades are highly flexible, their pattern of space exploration depending both on within-trial and across-task contingencies. These results are discussed in the context of exploration and exploitation strategies and prefrontal top-down attentional control. Highlights The decoded prefrontal attentional spotlight samples visual space in rhythmic cycles This rhythmic attentional exploration predicts neuronal sensory processing accuracy This rhythmic attentional exploration predicts overt behavioral accuracy These rhythmic cycles define alpha-clocked attentional saccades Space exploration by attentional saccades is highly flexible and under top-down control


Introduction 1
The brain has limited processing capacities and cannot efficiently process the continuous flow of 2 incoming sensory information. Selective attention allows the brain to overcome this limitation by filtering 3 sensory information on the basis of its intrinsic salience (a child crossing the road in front of your car) or 4 its extrinsic value (your old favorite coffee mug which you know is somewhere on your crowded desk). 5 Visual selective attention speeds up reaction times 1,2 , enhances perceptual sensitivity and spatial 6 resolution 3,4 and distorts spatial representation up to several degrees away from the attended location 5 . 7 Visual selective attention modulates both neuronal baselines 6,7 and the strength of visual responses 8 , 8 decreases neuronal response latencies 9 , modifies the spatial selectivity profiles of the neurons 10,11 and 9 decreases shared inter-neuronal noise variability 12 . 10 Based on the early work of William James (1890), the spotlight theory of attention assumes that 11 attention is focused at one location of space at a time 1,13 . In this framework, the spotlight is moderately 12 flexible. It is shifted from one location to another, independently from eye position, under the voluntary 13 control of the subject, and its size is adjusted to the region of interest very much like a zoom lens. 14 Converging evidence demonstrate that the prefrontal cortex (PFC) is at the origin of the attentional control 15 signals underlying the behavioral attentional spotlight 7,[14][15][16][17] . Supporting this idea, we recently 16 demonstrated that this attentional spotlight can be reconstructed and tracked from PFC neuronal 17 population activity with a very high spatial and temporal resolution 18,19 . However, recent experimental 18 work provides a completely different perspective onto selective attention, suggesting that spatial 19 attention samples the visual scene rhythmically [20][21][22][23][24][25][26] . These studies report that target detection 20 performance at an attended location fluctuates rhythmically very much like overt sampling processes, such 21 as eye exploration in primates [27][28][29] or whisking in rodents 30,31 . The neural processes at the origin of this 22 rhythmic sampling of space by attention are still poorly understood. Recent works propose that neural 23 oscillations in the fronto-parietal network organize alternating attentional states that in turn modulate 24 perceptual sensitivity 22,32 . 25 In the present study, we provide evidence reconciling these two seemingly contradictory views of 26 spatial attention. Specifically, we demonstrate that the decoded PFC 2D (x,y) attentional spotlight explores 27 space continuously, through a sequence of attentional saccades that are generated at a specific alpha 7-28 12 Hz frequency. Crucially, we show that these oscillations of the attentional locus determine both 29 neuronal sensory processing, defining how much information is available in the PFC about incoming 30 sensory stimuli, and perception, determining whether these incoming sensory stimuli are prone to elicit 31 an overt behavioral response or not. Using Markov chain probabilistic modelling, we further show that 32 space exploration by alpha-clocked attentional saccades depends on both trial and task specific spatial 33 contingencies, implementing an alternation between exploration and exploitation cycles. 34 35

36
In order to access FEF attentional content in time, monkeys performed a manual response cued target-37 detection task ( fig. 1A) while we recorded the MUA bilaterally from their FEF neuronal ensembles, using two 24-38 contacts recording probes ( fig. 1C). Distractors were presented during the cue-to-target interval and target luminosity 39 was adjusted so as to make the task difficult to perform without orienting attention ( fig. 1B). Previous studies 40 demonstrate that PFC based decoding procedures allow to access in which quadrant [33][34][35] or at which (x,y) location 41 attention is placed 18 . In these studies, neuronal signals were averaged over time intervals ranging from 150 ms -400 42 ms 18,35 . Larger averaging window sizes produce higher decoding accuracies (suppl. fig. 1  Here, we seek to characterize spatial attention dynamics in time. As a result, the continuous decoding of 56 attention is performed onto neuronal responses averaged over 50 ms successive (1 ms time steps, suppl. fig. 1) time 57 windows. At this temporal resolution, clear variations in the PFC attention-related information are observed. Indeed, 58 when a classifier is trained to decode attention at a given time from cue onset, and tested onto novel activities 59 recorded during the cue to target interval (cross-temporal decoding analysis, fig. 2A). Fluctuations in instantaneous 60 classification accuracies can be noted, at a distance from cue processing. These fluctuations are reliably associated 61 with a distinct peak in the power spectrum relative to chance, in the 7 -12 Hz range. This is illustrated for an exemplar bins shifted by 5% of their width. The lag that generated the highest discrimination between maximum and minimum 125 decoding accuracy in the cycle was used to define optimal phase-shift between sensory processing and attention 126 signal oscillations (18) (fig. 4B). An average difference in peak and trough decoding accuracies of 10% can be noted 127 when decoding accuracies are cumulated, across all sessions, at optimal phase-shift between sensory processing and 128 signal oscillations ( fig. 4B). This difference is highly systematic as illustrated is figure 4C for each session and each 129 monkey independently. The average target decoding accuracy at peak for monkey M1 (resp. monkey M2) was of 54% 130 +/-4 (resp. 58%+/-2). At trough, these values dropped to 44% +/-3 (resp. 47%+/-1.

153
Again, as for target processing, the lag that generated the highest discrimination between maximum and minimum 154 hit rates in the oscillatory cycle was used to define optimal phase-shifts between target detection and signal 155 oscillations ( fig. 4D, inset). An average difference in peak and trough decoding accuracies of 10% can be noted when 156 decoding accuracies are cumulated at optimal phase-shift between target detection and signal oscillations ( fig. 4D).

157
Again, this difference is highly systematic as illustrated in fig. 4E for each session and each monkey independently.

204
In a second step, we quantified how responses to distractors (false alarm rate) depended on distractor 205 presentation time relative to the PFC attention information oscillation cycle. An average difference in peak and 206 trough false alarm rate of more than 10% can be noted when false alarms are computed at optimal phase-shift 207 between distractor detection and signal oscillations ( fig. 7D). This difference is highly systematic across sessions and 208 monkeys ( fig. 7E). The average distractor detection at peak for monkey M1 (resp. monkey M2) was of 45% +/-1.5 12 (resp. 42%+/-2). At trough, these values dropped to 36% +/-2 (resp. 29%+/-2.5). As seen for hit rates, phase lag 210 between signal and optimal distractor detection was quite variable ( fig. 7D,  Attentional "saccades"

233
The above described analyses were performed on a quantification of the accuracy with which attention 234 could be localized in one of the four visual quadrants, based on the observed PFC population neuronal response. In 235 a previous study 18 , we demonstrated that the continuous (x,y) readout of a linear classifier assigning neuronal 236 activities to a spatial location of attention is a relevant proxy for a real-time access to the attentional spotlight 237 represented in the PFC. Importantly, this continuous (x,y) readout of the PFC attentional spotlight is predictive of 238 behavior, both in terms of hit and false alarm rates. In the following, we apply the same approach to extract (x,y) 239 attentional spotlight trajectories in time before and after cue presentation, to the major difference that the readout 240 is obtained at higher temporal resolution, from neuronal responses averaged over 50 ms rather than on 150 ms as 241 presented in the Astrand et al. 18

310
This is exemplified in fig. 10D, which represents the decoded attentional spotlight trajectory during the cue to target 311 interval in a representative trial of a two position task.

312
Finally, we provide evidence that the PFC attentional spotlight explores space at an alpha that remains stable 313 within trials and across tasks. In addition, we show that how this decoded spotlight explores space depends on both 314 within-trial and across-task task contingencies. Overall, we show that the attentional spotlight, decoded from PFC FEF activities at high temporal 329 resolution, explores space rhythmically. This rhythmic exploration takes place in the 6-12 Hz (alpha) 330 frequency range, independently of the ongoing task. Importantly, these oscillations of the attentional 331 locus determine both neuronal sensory processing, defining how much information is available in the PFC 332 about incoming sensory stimuli, and perception, determining whether these incoming sensory stimuli are 333 prone to elicit an overt behavioral response or not. From the spatial perspective, this exploration of space 334 corresponds to attentional saccades. These attentional saccades explore space biased by both within-trial 335 and across-task contingencies, implementing an alternation between exploration and exploitation cycles. 336 337

The prefrontal attentional spotlight explores space rhythmically 338
Converging behavioral evidence indicates that attention and perception are not anchored at a 339 specific location in space, but rather exhibit a temporal alpha rhythmicity 25 . This rhythmic sampling of 340 space is phase-reset and entrained by external events of interest. It can also be observed spontaneously 341 38 , and is proposed to organize the tracking of task-relevant spatial locations by attention in time 342 20,21,23,25,26,37,39,40 . It has been proposed that, when prior information is available, such a rhythmic sampling 343 of information is more efficient than a continuous sampling of space 41 . These observations have led to 344 reconsider the model of a continuously active attention spotlight in favor of a rhythmic sampling of 345 attention at relevant spatial locations, including during sustained attention states 21,25 . 346 Our present findings reconcile these two models, describing a dynamic PFC attentional spotlight 347 that continuously explores space at a specific rhythm. This rhythmic exploration shares major 348 characteristics with previous behavioral reports on attentional rhythms: (1) these oscillations are ongoing 349 and can be identified independently of the intervening task events, (2) they are reset by relevant external 350 events such as spatial cues and (3) they occur in a well-defined functional alpha frequency range. However, 351 even if attentional exploration targets task relevant locations, as reflected by the rhythmic enhancement 352 of neuronal sensory processing and behavioral performance at the cued target location, exploration is not 353 restricted to these locations. Rather, space exploration by the attention spotlight extends to un-cued a 354 priori task irrelevant spatial locations, as reflected by the rhythmic enhancement of neuronal sensory 355 processing and behavioral overt report at un-cued unpredictable distractor locations. 356 The phase between the attentional spotlight ongoing oscillations and a given stimulus 357 presentation accounts from 10% (in the case of the target) to 30% (in the case of distractors) of the 358 accuracy with which PFC neuronal populations encode the location of this stimulus. In other terms these 359 oscillations -i.e. where the attention spotlight falls in space-critically impact the sensory processing of 360 incoming stimuli. Tracing down this effect all throughout the visual system would be extremely relevant. 361 Neuronal responses to low-salience task-relevant stimuli has been shown to arise earlier in the PFC than 362 in the parietal cortex (Ibos et al. 2013). As a result, one predicts that this dependence of sensory processing 363 onto attention spotlight oscillations will be found at all stages of the visual system. However, phase 364 relationships between local neuronal and stimulus presentation is expected to vary, reflecting a top-down 365 cascade of influences, in agreement with the role of the FEF in attentional control 7,[15][16][17]42,43 . 366 These oscillations also determine overt behavioral perceptual outcome, accounting from 10% (in 367 the case of false alarm production) to 30% (in the case of correct target identifications) of stimulus 368 detection. This is globally higher than the range of reported oscillatory changes in behavioral hit rates 369 21,22,24 , highlighting the high predictive power of these neuronal population oscillations. 370 Overall, this suggests the existence of perceptual cycles 25 that organize as a rhythmic alternation 371 between exploitation and exploration states of space sampling by attention (Fibelkorn and Kastner, 2019). 372 373

Exploring versus exploiting space by attention 374
Two models have been proposed to account for the spatial deployment of attention [44][45][46][47][48] a parallel 375 processing model, driven by bottom-up information, dominating when visual search is easy; and a serial 376 processing model, driven by top-down mechanisms, dominating in difficult visual search 37 . In the context 377 of this latter model, it has been hypothesized that the brain controls an attentional spotlight that scans 378 space for relevant sensory information. In a previous study 18 , we assessed, based on the (x,y) decoding of 379 the neuronal population activity of the FEF, the tracking of this attentional spotlight in time 18 . Here, we 380 show that this PFC attentional spotlight explores space serially both at relevant (cued) and irrelevant (un-381 cued) locations, alternating between the exploitation and the exploration of the visual scene 25 . The activity 382 of the parietal 10 and PFC 49 cortical regions has been shown to change drastically between exploitation 383 and exploration behavior. In particular, exploration is associated with faster though less accurate 384 oculomotor behavior 10 and a disruption of PFC control signals 49 . This is proposed to facilitate the 385 processing of unexpected external events 10 , the expression of novel behavior and learning through trial 386 and error 49 . 387 Our observations strongly indicate that exploration and exploitation dynamically alternate within 388 trials. This alternation of exploration and exploitation of space by the attentional spotlight thus appears 389 to optimize subject's access to incoming information from the environment by a continuous exploration 390 strategy, very much like is described for overt exploration behaviors such as saccadic eye movements, 391 whisking or sniffing 24,50,51 . This covert exploration of the environment by attention however takes place at 392 a slightly higher frequency than the typical theta exploration frequency described for overt exploration. 393 This is probably due to energetic and inertial considerations in controlling the remote effector during overt 394 exploration (e.g. eye, whisker or nose muscles). Interestingly, the rhythm at which this PFC 395 exploration/exploitation alternation takes place coincides with the rhythm at which attention behaviorally 396 explores the different part of a given object 21 . Overall, this leads us to postulate the existence of 397 attentional saccades that can either be directed towards specific items for exploitation purposes, or 398 deployed onto the entire visual field for exploration purposes. 399 400

Continuous attentional sampling and attentional saccades 401
Covert exploration of space by attention is more energy efficient than overt exploration by the 402 eyes and the former serves to inform and guide the latter. In an initial "premotor theory of attention", 403 these two processes, namely attentional selection and saccadic eye movements, have been suggested to 404 rely on identical cortical mechanisms. This theory hypothesizes that attentional displacements or saccades 405 of the mind, mirror saccades of the eyes except for the recruitment of the extra-ocular muscles 52 . Since 406 then, several studies have contributed to a functional dissociation between these two processes, and 407 rhythmic attentional sampling has been shown to be independent from microsaccade generation 22,24,53 . 408 Our observations support a continuous exploration of space by the PFC attentional spotlight organized 409 thanks to a rhythmic re-orientation of the attentional spotlight taking place at an alpha rhythm. This 410 framework leads to an interesting set of experimental predictions. For instance, attentional capture and 411 distractibility by an intervening distracting item is expected to coincide with an ongoing attentional re-412 orienting towards this item 18 . Likewise, inhibition of return [54][55][56][57] , is expected to reflect as an under-413 exploration of previously visited locations with respect to unexplored locations. This covert saccade-like 414 exploration is proposed to be an intrinsic property of attention, taking place irrespectively of the ongoing 415 behavior and building onto a rhythmic alpha clock. Its spatial pattern, that is to say the portion of space that is being explored by these attentional saccades, as well as the frequency at which task-relevant items 417 are explored are however expected to be under top-down control. 418 419

Top-down control 420
Numerous studies indicate that the PFC and specifically the FEF play a crucial role in attention 421 orientation and attention control 7,[15][16][17]34,42,43 . As a result, one expects that the exploration of space by the 422 PFC attention spotlight be strongly biased by top-down voluntary control. Confirming this prediction, we 423 show that task goals significantly affect attentional space exploration strategy. Specifically, we observe 424 that, the locations where the PFC attentional spotlight explores space are modulated both 1) within trials, 425 by the expected position of the target after cue presentation, and 2) across tasks, by the general 426 expectations about sensory events. In other words, relevant task items are more explored than irrelevant 427 locations, where relevance concatenates information relative to the ongoing trial and task design. This is 428 in agreement with prior behavioral observations reporting that the attentional sampling rate observed at 429 the behavioral level decreases as the number of task relevant items increases 23,58 . Overall, this indicates 430 that the rhythmic exploration of space by attention, is an intrinsic, default-mode state of attention, that 431 can be spatially modulated by task context and internal expectations. A strong prediction is that this 432 rhythmicity in attentional spatial processing will directly impact attention selection processes in lower 433 level cortical areas, through long-range feedback processes 53 , possibly mediated by NMDA receptors 59 . 434 435

Conclusion 436
Overall, our work describes for the first time the spatial and temporal properties of the population 437 PFC attention spotlight. It demonstrates a continuous exploration of space, that is mediated by attentional 438 saccades that unfold at an alpha 7-12 Hz rhythm and that accounts for both neuronal sensory processing 439 reliability and overt behavioral variability. Importantly, it bridges the gap between behavioral evidence of 440 attentional rhythmic space sampling and local field attention related oscillatory mechanisms 22,25,32 , 441 revealing the neuronal population dynamics associated with rhythmic attentional sampling. 442

Behavioral task and Experimental setup
The task is a 100% validity endogenous cued target detection task ( fig 1A). The animals were placed in front of a PC monitor (1920×1200 pixels and a refresh rate of 60 HZ), at a distance of 57 cm, with their heads fixed. The stimuli presentation and behavioral responses were controlled using Presentation In order to make sure that the monkeys did use the cue instruction, on half of the trials, distractors were presented during the cue to target interval. Two types of distractors could be presented: (i) uncued landmark distractor trials (33% of trials with distractor); these corresponded to a change in luminosity, identical to the awaited target luminosity change, and could take place equiprobably at any of the uncued LMs; (ii) workspace distractor trials (67% of trials with distractor); these corresponded to a small square presented randomly in the workspace defined by the four landmarks. The contrast of the square with respect to the background was the same as the contrast of the target against the LM; when presented at the same radial eccentricity as the LMs, the workspace distractor had the same size as the landmarks; for smaller eccentricities, the size of the workspace distractor was adjusted for cortical magnification such that it activated an equivalent cortical surface at all eccentricities. The monkeys had to ignore all of these distractors. Responding to any of them interrupted the trial. If the response occurred in the same response window as for correct detection trials (150 -750 ms), the trial was counted as a false alarm (FA) trial. Failing to respond to the target (Miss) similarly aborted the ongoing trial. Overall, data was collected for 19 sessions (M1 10 Sessions, M2 9 Sessions). The behavioral performance of each animal is presented in figure 1B, for hit, miss and false alarm trials. A two-position variant of the above described task was also presented to the monkey. In this task, while the four landmarks were present all throughout the task as previously, only two diagonally opposite positions amongst the four were cued all throughout the session. The pair of cued stimuli changed from one session to the next. 16 such sessions were recorded (8 sessions for M1, 8 sessions for M2). All else was as described for the main four position task.

Electrophysiological recording
Bilateral simultaneous recordings in the two frontal eye fields (FEF) were carried out using two 24 contacts Plexon U-probes ( fig. 1B). The contacts had an interspacing distance of 250 μm. Neural data was acquired with the Plexon Omniplex® neuronal data acquisition system. The data was amplified 400 times and digitized at 40,000 Hz. A threshold defining the multi-unit activity (MUA) was applied independently for each recording contact and each session before the actual task-related recordings started.
Neuronal decoding procedure MUA recorded during the task were aligned on the cue presentation time and sorted according to the monkey's behavioral response (Correct trials, misses trial, false alarm trials). As in Astrand et al. 18,34 , a regularized linear decoder was used to associate, on correct trials, the neuronal activity estimated on a given interval in the cue to target interval and the cued location. The decoder was trained on a random set of 70% of the correct trials at a specific time in the cue to target interval, then tested on the 30% remaining at all time after cue presentation. During training, the input to the classifier was a 48 elements by N-trial matrix corresponding to the average neuronal response on each recording channel for the time interval of interest for each of the N training trials. The imposed output of the classifier was the (x,y) coordinates of the cued landmark for each of these N training trials. During testing, the output of the classifier was estimated for a 48 element vector corresponding to the average neuronal response on each recording channel for the time interval of interest on a testing trial, new to the classifier. This output can be read as a continuous (x,y) estimate of attention location 18 or as a class output, corresponding to one of the four possible visual quadrants 18,33,34 . When seeking for a continuous (x,y) readout of attention location, we performed the training using the neuronal activities of Hits averaged over 50 ms immediately before target presentation, then we tested the decoder on neuronal activities averaged over 50 ms all throughout the cue to target interval. When taking a classification perspective, we performed crosstemporal decoding analyses (suppl. figure 1A-B), where successive classifiers were formed based on successive overlapping (every 10ms) time windows during the cue to target interval and tested on independent trials and successive overlapping time windows during the cue to target interval. Mean decoding performance was calculated along the testing axis as the number of correct classifications divided by the total number of classifications. This procedure was repeated 10 times and the grand average over the 10 repeats are used for further analyses. Supplementary figure 1C-H represents this crosstemporal decoding analysis performed onto a training and a testing time interval running from cue presentation to 1200 ms post-cue, when the classifiers are based on neuronal activity sampled over 300, 150, 100, 75, 50 or 25ms. As expected, overall classification performance drops with neuronal sampling window size 60 . Importantly to the present paper, temporal variations in available content arise at lower sampling window sizes ( fig. 2, suppl. Fig. 1F-H). The core analyses of the present paper were performed using a neuronal sampling window size of 50ms.

Oscillations in behavioral performance
Hits and Misses from M1 and M2 were compiled in time (aligned to cue presentation), and merged together across the 19 recording sessions. Behavioral performance, defined as the proportion of (hits/(hits +misses)) was then computed at every millisecond over. The spectral analysis of this time series was performed on detrended data using a Morlet Wavelet transform as in Fiebelkorn et al. 22 , over the attentional period ranging from 500 ms post cue presentation to 2100ms. Standard error in the power spectrum corresponds to spectral variability during this time interval. Global power spectrum 1/f component was removed from the dataset using a *f normalization (figure 5).

Signal frequency and phase analyses
In the present paper, frequency and phase analyses were performed onto time series (inset in fig. 2A

Characterizing impact of population oscillations onto individual channel spiking activity
For each trial, channel and session, spike trains were smoothed on a 50 ms sliding window over a -700 ms pre-cue to 2000 ms post-cue time series. On the one hand, a Super MUA signal was computed by averaging the spiking activity of the 48 recording channels of each session and each trial. On the other hand, the initial individual channel continuous spiking activity was transformed to identify high-spiking (defined by a spiking rate above 65% of the maximum spiking regime of the individual channel, labelled as 1) and lowspiking (labelled as 0) epochs. The probability of individual channel firing as a function of the oscillatory cycles of the session's Super MUA was then computed as follows. For each channel, for frequencies from 5 Hz to 15 Hz, the spiking probability was computed for the up (+/-π/2 around oscillation peak) and down (+/-π/2 around oscillation trough) oscillatory phases of the frequencies of interest over the entire time window. For each frequency, the analysis time window was adjusted to 1.5 oscillatory cycle length and computations were performed over a minimum of 50 time bins. All further analyses on this metric were performed onto an attentional epoch running from 500 ms post-cue to 2100 ms post-cue.

Peak and trough classification
In order to track whether the frequencies identified on the decoded attentional information causally reflected onto behavior, the following analysis was performed. For each session i, characteristic attention information oscillatory frequency F(i) and Phase P(i) determined using the above described wavelet transform analysis. The decoded classification attention information signal was modeled as a sinusoidal wave determined by the function MSi(t)=sin(2. π.F(i).t-P(i)). Using this modeled signal (MSi), and based on target time from cue presentation, trials were assigned to one of 10 possible phase intervals ranging from [-π +π] phase offset from the modeled sinusoidal wave For each of these subsets of trials, decoding accuracy of target location (resp. distractor location) and percentage of hit trials (resp. FA trials) was extracted ( fig. 3BC and 4BC). As sensory processing or behavioral outcome could be phase lagged with respect to signal oscillations, target time was progressively shifted using 5 ms steps, so that the phase interval associated with peak sensory processing or behavioral outcome coincided with phase 0. This procedure was applied independently for each of the 18 recording sessions and the outcome of this analysis was then averaged over all sessions, so as to account for variations of F(i) and Phase P(i) from one session to the next. For a precise estimation of phase difference between oscillations in attention information classification decoding and oscillations in sensory processing or behavioral outcome, a circular mean of the corresponding wavelet transform continuous phase difference between the two signals at frequency F(i) was extracted.

Markov chain modeling of spatial attentional exploration strategies
Markov probabilistic chain models were used to characterize the spatial attention exploration strategy of each monkey from cue to target presentation. For each trial, (x,y) time series corresponding to the decoded spatial location of attention during the cue to target interval was collapsed onto the four possible screen quadrants, thus representing how attention moved from one quadrant to the other in time. Based on these discrete time series across all trials of a given session. A Markov chain model was used to estimate the probability that attention stayed in a given quadrant as well as the probabilities that it moved from the current quadrant to one of the three others. This model was performed using the Hmmestimate Matlab function of the Statistics and Machine Learning Toolbox. To compensate for possible idiosyncratic exploration biases of each monkey, the post-cue transition probabilities were normalized with respect to pre-cue spatial attention exploration transition probabilities. Transition probabilities were then normalized for each session and averaged over all sessions and both monkeys. This Markov chain modeling of spatial attentional exploration strategy was independently performed for both tasks: the four cuedlocation and the two-cued location tasks.