Sparse spatial scaffolding for visual working memory

A central challenge for working memory is to retain information in a format in which representations remain separated and can be selectively prioritised for behaviour. While it is established that space serves as a foundational “scaffold” for mnemonic individuation, the format and flexibility of spatial scaffolding for working memory remain elusive. We hypothesised that information in working memory can be re-coded from its native spatial format at encoding to organise and retain mnemonic visual contents sparsely. To test this, we presented visual memory items at different directions and distances from fixation, such that distance was either useful or redundant as a spatial scaffolding feature. We leveraged spatial biases in fixational gaze behaviour during mnemonic selection as an implicit read-out of the spatial scaffold used for working memory. This revealed the use of fundamentally distinct spatial scaffolds depending on the spatial-layout of memory: incorporating distance when direction is insufficient as a scaffold for mnemonic individuation but “abstracting away” over distance when direction alone serves the job of mnemonic individuation. This unveils the principle of “sparse spatial scaffolding” for working memory, whereby the brain resorts to the minimal spatial scaffold needed for the individuation of internal representations.


Introduction
A central challenge for working memory is to code for information in a format in which individual representations remain separated and can be selectively prioritised for guiding behaviour [1][2][3][4][5][6] .Within the study of visual working memory, ample studies have made clear how space serves as a foundational "scaffold" for the separation and selection of individual working-memory representations [7][8][9][10][11][12][13][14][15][16] .Yet, how precisely space is used for working memory remains elusive and has been the subject of ample recent investigation.
Several recent studies have made clear how, once visual information has been encoded into working memory, the use of spatial location as a scaffold for memory individuation and selection is not necessarily veridical, but can be flexibly updated.For example, spatial organisation in visual working memory can be transformed [17][18][19][20][21][22][23] , compressed 24 , and engage additional spatial frames of reference 19,25,26 .This flexible nature of working memory -in which information can be re-coded from its native format at encoding (see also 23,[27][28][29][30][31][32][33] ) -provides the opportunity to tune the spatial scaffolding for working memory to the task in an adaptive and efficient manner.Accordingly, working memory may organise and retain mnemonic visual contents sparsely: utilising more sparse (abstracted) spatial scaffolds as long as they suffice for mnemonic individuation and selection, and engaging richer (more veridical) spatial scaffolds only when necessary.
To test this hypothesis of sparse spatial scaffolding for visual working memory, we developed a task in which we never tested the location of specific memory items, but in which space served as a scaffold for item separation and selection.Critically, we presented visual memory items at different directions and distances from fixation, such that item distance was either useful as a spatial scaffold for mnemonic individuation (because direction alone was insufficient), or redundant as a spatial scaffolding feature (because direction alone was sufficient for mnemonic individuation).
Building on our complementary recent findings and approaches 19,25,34,35 , we leveraged spatial biases in fixational gaze behaviour during mnemonic selection as a read-out of spatial coding for visual working memory.This enabled us to probe spatial scaffolding for working memory implicitly, without ever asking participants about memorised locations.This revealed the principle of "sparse spatial scaffolding" for working memory.Specifically, we unveil fundamentally different spatial codes depending on the spatiallayout of memory: exclusively utilising memorised item direction -and "abstracting away over distance" -when direction is sufficient as a spatial scaffold for mnemonic individuation, and additionally utilising distance only when direction is insufficient as a scaffold.

Results
Human par]cipants performed working-memory tasks in which we cued (via a central colour retro-cue) the selec]on of one of four spa]ally separated visual items for an orienta]on comparison to the ensuing test s]mulus (Fig. 1a).We presented items either near (3 degrees) or far (6 degrees) from the central fixa]on dot and used spa]al biases in fixa]onal gaze behaviour during mnemonic selec]on as an implicit read-out of the spa]al scaffolding used for visual working memory (an approach that we applied successfully in several recent complementary studies: 19,25,[34][35][36] ).
In what follows, we first establish that our spa]al marker can track the use of both 'direc]on' and 'distance', when direc]on and distance are both useful as a spa]al scaffold for individua]ng the four visual memory items -even when direc]on and distance were never asked about.We then show across two addi]onal experiments that par]cipants resort to a sparse spa]al scaffold that abstracts away over distance, when direc]on alone is sufficient for individua]ng the four memory items.
The key outcome variable in our study was gaze during mnemonic selec]on.Before turning to our gaze data, we first confirmed that par]cipants were able to perform this task well above chance in all three versions that we ran (Supplementary Fig. 1).Fixa]onal gaze behaviour during mnemonic selec]on tracks the use of both direc]on and distance as spa]al scaffolding features for visual working memory Figure 1b shows gaze ]me courses aker retro-cues that prompted the selec]on of memory items that had been encoded lek or right from fixa]on, at either the near (Fig. 1b, lek) or far (Fig. 1b, right) posi]on.Consistent with prior studies from the lab, we observed clear spa]al biases in gaze in the direc]on of the original loca]on of the cued memory item.Importantly, this occurred even though (1)  there was nothing to look at to the lek and right aker the retro-cue, (2) our colour retro-cue and ensuing test s]mulus were presented centrally, and (3) we never asked par]cipants about the original loca]on of memory items .
To study whether distance was incorporated in the spa]al scaffold used for working memory -in addi]on to direc]on -we collapsed lek and right trials into a single measure of 'towardness' (as in 34- 37 ) and overlayed towardness between trials with cues to near and far items.As shown in Figure 1c, we found that gaze aker the retro-cue became significantly biased in the direc]on of the cued memory item, both when the cued item was near (cluster P < 0.001) or far (cluster P < 0.001).In addi]on, the spa]al bias in gaze was clearly modulated by the memory item's distance at encoding, with a larger bias when cued to select the further item (cluster P < 0.001; black horizontal line in Fig. 1c).
The observed gaze biases originated from biases in fixa]onal gaze behaviour (as in [36][37][38][39] ) -and not looking back at the original loca]on of the memorised item (as in [40][41][42][43][44] ) at 3 or 6 degrees, respec]vely.This can be appreciated by the heat maps (two-dimensional density plots) of the difference in gaze posi]on following cues to select the lek vs. right items, as depicted in Figure 1d (see Supplementary Fig. 2 for the heatmaps of gaze density following lek and right cues separately).
These spa]al biases in fixa]onal gaze behaviour during mnemonic selec]on confirm the use of space as a scaffold for mnemonic individua]on, even if item loca]ons are never asked about.These data further show that our gaze marker of this spa]al scaffold is able, in principle, to track the use of both direc]on (lek/right) and distance (near/far).Following a delay, a colour change of the central fixa,on dot (retro-cue) prompted par,cipants to select the colour-matching item from working memory to compare its orienta,on to a black bar in the upcoming test display.Memory items were presented to the leG or right and near (3°) or far (6°) from fixa,on at encoding, but par,cipants were never asked about memorised item loca,on.b) Time course of average gaze posi,on following central retro-cues that prompted the selec,on of the memory item that had been presented to the leG or right at encoding, separately for when the memory item was near (leG panel) or far (right panel) at encoding.c) Time courses of spa,al biases in gaze toward the cued memory item when this item was near (light) or far (dark) at encoding.Fixa]onal gaze behaviour reveals a sparse spa]al scaffold that abstracts over distance when direc]on alone is sufficient for mnemonic individua]on In Experiment 1, there were always two memory items in each direc]on (two lek and two right).Accordingly, direc]on (lek/right) alone was insufficient as a spa]al scaffold for individua]ng the four items, rendering distance useful as an addi]onal scaffolding feature.Following this logic, we refer to this condi]on as "direc]on-insufficient à distance-useful" (Fig. 2a, lek).
In Experiment 2, we included an addi]onal condi]on in which each memory item was placed along a separate direc]on from fixa]on (up, down, lek, and right), while again manipula]ng item distance.Cri]cally, in this condi]on direc]on became sufficient (in principle) as a spa]al scaffold for individua]ng the four memory items, poten]ally rendering distance redundant as an addi]onal scaffolding feature.Accordingly, we refer to this condi]on as "direc]on-sufficient à distance-redundant" (Fig. 2a, right).
When considering the condi]on in which distance was useful as an addi]onal scaffolding feature because direc]on alone was insufficient (Fig. 2b), we replicated our findings from Experiment 1.We again found that gaze aker the retro-cue became significantly biased in the direc]on of the cued memory item, both when the cued item was near (cluster P < 0.001) or far (cluster P < 0.001), and found that the spa]al gaze bias was again clearly modulated by the memory item's distance at encoding (Fig. 2b), with a larger bias when cued to select the further item (cluster P < 0.001).
Our key insight comes from the same spa]al gaze bias in the condi]on in which all four memory items each had a unique direc]on (lek, right, top, bo^om).Here, we s]ll observed clear gaze biases in the direc]on of the cued memory item (Fig. 2c), both when the cued item was near (cluster P < 0.001) or far (cluster P < 0.001).Cri]cally, however, in this condi]on, we no longer found a modula]on by distance (Fig. 2c).Importantly, this was observed even though we had presented the items at the exact same distances (3 and 6 degrees) as in the alterna]ve condi]on.This lack of modula]on by distance exclusively in this condi]on is consistent with the no]on that, in this condi]on, direc]on was sufficient as a scaffold, affording the brain to "abstract away" over distance.
To further quan]fy this key finding, we collapsed these gaze biases over the pre-defined window of 400-1000 ms aker cue onset -a window chosen a-priori based on 36 .This aggregate gaze-bias measure is depicted in Figure 2d.Analysis of variance confirmed a sta]s]cally significant interac]on between the factors "whether the cued item was near or far" and "whether direc]on was insufficient (distance useful) or sufficient (distance redundant)" (F(1, 24) = 9.13, p = 0.006, par]al η 2 = 0.276).Post-hoc analysis confirmed that when direc]on was insufficient as a spa]al scaffold for individua]ng all four memory items, par]cipants had a larger gaze bias when selec]ng the far compared to the near memory item (t(24) = -2.872,p Bonferroni = 0.05, Cohen's d = −0.574).However, when direc]on was sufficient for individua]ng the four items (because each memory item appeared in a dis]nct direc]on from fixa]on at encoding), par]cipants showed highly similar gaze bias regardless of whether we cued the near or the far memory item (t(24) = -0.401,p Bonferroni = 1, Cohen's d = 0.08).This suggests the use of a "sparser" spa]al scaffold in this condi]on, in which item distance was redundant as an addi]onal scaffolding feature.
Gaze heat maps, here split for trials with horizontal and ver]cal configura]ons, again revealed the fixa]onal nature of these gaze biases (Fig. 2e-f).
Figure 2. Fixa,onal gaze behaviour reveals a sparse spa,al scaffold that abstracts over distance when direc,on alone is sufficient for mnemonic individua,on.a) Representa,ve encoding displays used in Experiment 2. In Experiment 2 we addi,onally manipulated the usefulness of distance as a scaffolding feature for mnemonic individua,on.The "direc,on-insufficient à distance-useful" condi,on (leG) mirrored Experiment 1 where direc,on alone was insufficient for mnemonic individua,ng, rendering distance useful as an addi,onal scaffolding feature.In the alterna,ve "direc,on-sufficient à distance-redundant" condi,on (right), the four items each had a unique direc,on, rendering direc,on sufficient for item individua,on and distance redundant as an addi,onal scaffolding feature.Dashed circles indicate the later cued item in the different condi,ons (dashed circles were never shown in the experiment).b-c) Time courses of spa,al biases in gaze toward the cued memory item when this item was near (light) or far (dark) at encoding, when direc,on is insufficient and distance useful as a spa,al scaffold (panel b) or when direc,on was sufficient and distance redundant as an addi,onal spa,al scaffolding feature (panel c).d) Gaze bias averaged across the a-priori defined window from 400 to 1000 ms aGer the cue (based on 36 ).e-f) Heatmaps of two-dimensional gaze posi,on following leG vs. right cues (top row) or top vs. bo\om cues (bo\om row) across our four condi,ons.Shading in panels b-c and error bars in panel d indicate ±1 SEM calculated across par,cipants (n = 25).
Our findings are driven by spa]al scaffolding demands, not the mere presence of near and far items In Experiment 2, we manipulated whether direc]on was sufficient (distance redundant) or insufficient (distance useful) as a spa]al scaffold for individua]ng the four memory items by presen]ng items either in unique direc]ons from fixa]on, or by presen]ng mul]ple items in the same direc]on from fixa]on.However, in the former condi]on, the four items were always all near or all far, while in the la^er condi]on displays always contained two near and two far items.Accordingly, it remains possible that our findings of a dis]nct spa]al scaffold between the two condi]ons reflects the mere presence of both near and far items in one condi]on, and only near or far items in the other condi]on.
To rule out this possibility, we designed Experiment 3 where we repeated our key manipula]on, but this ]me ensured that displays always contained two near and two far items in both condi]ons (Fig. 3a).
The direc]on-insufficient (distance-useful) condi]on mirrored Experiment 2 (Fig. 3a, lek), while the direc]on-sufficient (distance-redundant) condi]on now always had two items placed at the 'near' posi]ons on one axis and another two items placed at the 'far' posi]ons on the orthogonal axis (Fig. 3a, right).Accordingly, both condi]ons now contained items at both distances, while direc]on was s]ll sufficient (and distance redundant) as a spa]al scaffold in one condi]on but not in the other.
Gaze data in Experiment 3 replicated those from Experiment 2: again, showing a larger fixa]onal gaze bias when selec]ng the further item, but only in the condi]on where direc]on was insufficient -and hence distance useful -for individua]ng the four memory items (Fig. 3b; cluster P < 0.001) and not in the direc]on-sufficient condi]on in which distance was redundant (Fig. 3c; no far-vs-near cluster).These findings were again corroborated by a significant interac]on (Fig. 3d; F(1, 24) = 7.54, p = 0.011, par]al η2 = 0.239), with post-hoc analysis confirming larger fixa]onal gaze bias when selec]ng the further item when direc]on was insufficient (distance useful) for item individua]on (t(24) = -3.518,p

Discussion
We unveil how the human brain engages fundamentally dis]nct spa]al codes for retaining visual representa]ons in working memory, depending on the u]lity of spa]al features as a scaffold for memory.Leveraging spa]al biases in fixa]onal gaze behaviour during mnemonic selec]on as an implicit read-out of spa]al scaffolding for visual working memory (as in 19,25,34,35 ), our present data unveil the principle of "sparse spa]al scaffolding" for visual working memory, whereby the brain uses the minimal spa]al features necessary for the separa]on and selec]on of individual contents in visual working memory.
6][47][48][49] ), we asked how we use space for memorising.We never asked par]cipants to report memorised item direc]on nor distance.Instead, space served as an organising medium (scaffold) serving the separa]on and selec]on of individual memory contents.While ample studies have made clear that space is a useful scaffold for working memory [7][8][9][10][11][12][13][14]50 , how space is used has remained elusive. Inpired by several findings [27][28][29] , we hypothesised that the brain may abstract away from the veridical spa]al lay-lout at encoding to a more efficient or "sparse" spa]al scaffold -as long as it serves the job of mnemonic individua]on.We found evidence for this.In our set-up, this was achieved by abstrac]ng away over distance when direc]on was sufficient for mnemonic individua]on, but incorpora]ng distance as an addi]onal scaffolding feature when direc]on was insufficient (when mul]ple items existed along the same direc]on).Ul]mately, the strength of our inference hinges on the suitability of our spa]al marker for studying spa]al scaffolding for working memory. Our fndings build directly on several prior studies where we successfully leveraged spa]al biases in fixa]onal gaze behaviour to study spa]al scaffolding for working memory -without ever asking par]cipants about memorised item loca]on 15,19,25,[34][35][36] .Here, we for the first ]me use this implicit marker to study the use of distance.In all three experiments, we confirm that this marker -while fixa]onal in nature -is sensi]ve to memorised item distance, in principle.This suggests that the lack of a "distance code" when distance is a redundant scaffolding feature -our key finding -is not due to a lack of sensi]vity of our marker, but rather reflects a sparser spa]al scaffold in which distance has been abstracted away.
2][53] ).While remaining fixa]onal in nature, our data reveal how this gaze bias is sensi]ve to "high-level" cogni]ve coding by tracking the flexible u]lisa]on of dis]nct spa]al scaffolds for working memory -that can either incorporate or abstract away over distance.This adds to growing apprecia]on of higher-level cogni]ve processing within deep-brain structures, such as the superior colliculus [54][55][56] that has been implicated in spa]al biases in fixa]onal gaze behaviour that we report here 57 .By studying spa]al coding for working memory following a cue that directed internal selec]ve a^en]on to a specific memory item, our findings complement prior studies on selec]ve a^en]on that also varied item distance 38,[58][59][60][61][62][63][64][65] , even if these typically studied externally directed a^en]on.Interes]ngly, at least several studies reported a rela]ve invariance of spa]al modula]ons in neural ac]vity (e.g., [58][59][60] or fixa]onal gaze behaviour 38 to the a^ended target's distance, while yet other studies did report distancedependent modula]ons (e.g., [61][62][63][64] ).We unveil a key variable that may underpin whether or not this is found: the u]lity of distance for the task at hand (see also 65 ).
Though our star]ng point was different, our experimental manipula]ons resemble those in complementary research on the role of eccentricity and crowding in vision (e.g., [66][67][68][69][70][71][72][73][74] ) and visual working memory (e.g., [75][76][77] ).This literature has typically focused on other ques]ons, such as how visual resolu]on changes when moving from central to peripheral vision.Our task was not designed to tap into such differences.We used clearly visible s]muli and placed them 3 degrees apart.Also, when considering performance, we did not observe lower accuracy for the far item in any of the three experiments (Supplementary Fig. 1).Instead, we here focused on whether and how distance was used as a scaffold for visual working memory when distance is a useful or a redundant scaffolding feature (in addi]on to direc]on).While our direc]on-insufficient (distance-useful) condi]on may invoke more crowding, we note that our key findings do not consist of a general increase or decrease of the fixa]onal gaze bias in this condi]on (but rather an interac]on with distance).Furthermore, the main insight from our study -that distance is abstracted away when it is a redundant scaffolding feature -originated from our condi]on with minimal crowding, when all items were presented in a dis]nct direc]on.
Having unveiled the principle of sparse spa]al scaffolding for visual working memory, our data open relevant avenues for future research.Our data leave unaddressed how the spa]al "pruning" of visual working memory develops between encoding and our moment of exposing the spa]al scaffold aker the cue, and how such spa]al pruning occurs across the mul]tude of brain areas involved in working memory 78 .Our findings hint most directly at the spa]al scaffold used by oculomotor circuitry in the brain, of which our gaze marker is a peripheral fingerprint 57 .Developing ways to con]nuously track the transforma]ons in the spa]al scaffold for working memory across ]me and across the brain remain challenging but also exci]ng avenues awai]ng future research.

Methods
Ethics.Experimental procedures were reviewed and approved by the local Ethics Commi^ee of the Vrije Universiteit Amsterdam.Each par]cipant provided wri^en consent before par]cipa]on and was reimbursed €10/hour.Par]cipants.We conducted three experiments with independent par]cipant recruitment.Twenty-five healthy human volunteers par]cipated in each experiment (Experiment 1: age range: 18-31; 6 male and 19 female; 23 right-handed and 2 lek-handed; Experiment 2: age range: 18-27; 3 male, 21 female, and 1 non-binary; 24 right-handed and 1 lek-handed; Experiment 3: 20-30; 7 male and 18 female; 22 righthanded and 3 lek-handed).Sample size of 25 per experiment was set a-priori based on previous publica]ons from our lab that relied on the same outcome measure 25,36,37 .In Experiment 3, to achieve the intended sample size, two par]cipants were replaced due to the poor quality of the eye-tracking data.No par]cipants required replacement in Experiments 1 and 2. All par]cipants had normal or corrected-to-normal vision.S]muli and procedure.We designed a visual working-memory task in which we never tested the location of specific memory items, but in which space served as a scaffold for item separation and selection.In the critical versions of our tasks, we presented visual memory items at different directions (left/right/top/bottom) and distances (3 or 6 degrees) from fixation, and manipulated the spatial layout such that item distance was either useful as a spatial scaffolding feature (because direction alone was insufficient) or redundant (because direction alone was sufficient).Below, we first explain the basic task, before returning to our two key manipula]ons.
In all three experiments, par]cipants engaged in a visual working-memory task that required the selec]on of a visual item from working memory for an upcoming orienta]on comparison (Fig. 1a).Though we manipulated spa]al features of the display, note how we never asked par]cipants about memorised item direc]on, nor about memorised distance.To perform our task, memories of colourorienta]on bindings were sufficient, in principle.Spa]al loca]on merely served as a scaffold for separa]ng and selec]ng specific memory items.
Each trial began with a start fixa]on (200 ms) followed by a brief (250 ms) encoding display where four bars with different colours and orienta]ons appeared on either two or four direc]ons of the fixa]on dot.Aker a 750 ms working-memory reten]on interval, the fixa]on dot changed colour for 1000 ms serving as a retro-cue.This retro-cue cued with 100% validity which memory item (i.e. the colourmatching item) would have to be compared to the upcoming test s]mulus.The retro-cue was followed by another reten]on delay of 500 ms before the test display appeared.During the test display, a black bar appeared at the center of the screen.The test bar was always rotated between 10 to 20 degrees clockwise or counter-clockwise from the cued bar in memory.Par]cipants reported whether the cued memory item should be turned clockwise or counter-clockwise to match the black bar in the test display.Par]cipants received feedback immediately aker response by a number ("0" for wrong, or "1" for correct) appearing for 250 ms slightly above the fixa]on dot.Aker the feedback, inter-trial intervals were randomly drawn between 500 and 1000 ms.
Our key experiments (Experiments 2 and 3) had two key manipula]ons (Fig. 2a; Fig. 3a).We manipulated: (1) whether cued memory items were presented near (3°) or far (6°) from fixa]on, and (2) whether all items were presented in a unique direc]on (lek/right/bo^om/top) or whether certain direc]ons were shared between mul]ple items in the array (two lek and two right items, or two top and two bo^om items).Cri]cally, in the first condi]on (Fig. 2a, labelled "direc]on-insufficient à distance-useful"), there were always two items compe]ng along each direc]on of an axis (e.g., two up and two down, or two lek and two right), rendering direc]on alone insufficient as a spa]al scaffold for individua]ng the four items, and rendering distance useful as an addi]onal scaffold.In contrast, in the alterna]ve condi]on (Fig. 2a, labelled "direc]on-sufficient à distance-redundant"), all items were associated with a unique direc]on, such that direc]on was sufficient as a spa]al scaffold for individua]ng the four memory items, rendering distance redundant.. Experiment 1 (Fig. 1a) only included the condi]on with four items on a line (direc]on-insufficient à distance-useful) and served to validate the sensi]vity of our spa]al marker to track the use of both 'direc]on' and 'distance' when both features were useful as a scaffold.In Experiments 2 and 3, we added the direc]on-sufficient (distance-redundant) condi]on in which all items were presented in a different direc]on from fixa]on (see Fig. 2a and Fig. 3a).In Experiment 2 (Fig. 2a), in this direc]on-sufficient (distance-redundant) condi]on, the display in a given trial always contained four items that were either all near (3 degrees) or all far (6 degrees).In contrast, in Experiment 3 (Fig. 3a) displays in this condi]on always contained two near items (one axis) and two far items (on the orthogonal axis), to equate the total number of near and far items in each display between the two condi]ons in which direc]on was either sufficient (and distance redundant) or insufficient (and distance useful) as a spa]al scaffold for item individua]on.Please note that in Experiment 1, we only included the horizontal configura]on (as depicted in Fig. 1a), while in Experiments 2 and 3, we included both ver]cal and horizontal configura]ons in the direc]on-insufficient (distance-useful) condi]on (as depicted in Fig. 2a; Fig. 3a), such that we equally oken cued a lek/right/top/bo^om item in both the direc]on-insufficient (distanceuseful) and direc]on-sufficient (distance-redundant) condi]ons.
In the encoding display, bars were randomly assigned two or four dis]nct colours from the colour pool: green (RGB: 133, 194, 18), purple (RGB: 197, 21, 234), orange (RGB: 234, 74, 21), and blue (RGB: 21, 165, 234]).Bars were also drawn at dis]nct orienta]ons ranging from 0° to 180° with a minimum difference of 20° between each other.During the test display, the bar were always dark grey (RGB: 64, 64, 64) and were always oriented clockwise or counter-clockwise from the cued memory target, with a change in orienta]on randomly drawn between 10 to 20 degrees.The bar is 2 visual degrees in length and 0.4 visual degrees in width and the fixa]on point has a radius of 0.07 visual degrees.
Experiment 1 consisted of 4 sessions that each contained 10 blocks of 16 trials, resul]ng in a total of 640 trials.In Experiments 2 and 3, we added the direc]on-sufficient (distance-redundant) condi]on and therefore increased the number of trials.Experiments 2 and 3 each consisted of 5 sessions, which each contained 5 blocks of 32 trials, resul]ng in a total of 800 trials.Condi]ons were randomly mixed within each block.
Before the start of each experiment, par]cipants prac]ced the task for approximately five minutes.Experiment 1 required approximately 80 minutes while Experiments 2 and 3 each required approximately 100 minutes per par]cipant to complete.Par]cipants were instructed to keep fixa]on throughout the task, but trials were not aborted when larger eye movements occurred.The encoding display was too brief to allow gaze fixa]ons to all memory items, and during the main cue-period of interest there was nothing to look at on the screen apart from the central fixa]on dot.
Eye tracking.We used an EyeLink 1000 (SR Research, with 1000 Hz sampling rate) to track gaze from a single eye (right eye in all par]cipants except 1 for which the lek eye provided a be^er signal).The eyetracker camara was posi]oned on the table approximately 5 cm in front of the monitor and approximately 65 cm in front of the eyes.
Gaze data were read into Matlab using the Fieldtrip toolbox 79 .In line with previously established protocols 36,37,80 , we first iden]fied blinks and replaced iden]fied blink clusters (extending 100 ms before and aker detected blinks) with Not-a-Number (NaN) to effec]vely mi]gate any ar]facts from the blinks.Then, data were epoched from -1000 to +2000 ms rela]ve to the onset of the retro-cue.
We focused our analysis on spa]al biases in gaze posi]on over ]me in response to the central colour retro-cue that prompted the selec]on of one out of the four items in working memory.Because the cue was non-spa]al and the test s]mulus would occur centrally, any spa]al bias in gaze during this period must reflect selec]on within the spa]al lay-out of visual working memory.
To inves]gate direc]onal biasing of gaze during mnemonic selec]on, we first baseline corrected the eye data by subtrac]ng the mean data in the [-200 to 0 ms] baseline window.Then, we examined eye data on the x-axis when the cued item was on the lek or the right side, on the y-axis when the cued item was above or below fixa]on.Following our prior studies 25,36,37 , we condensed the relevant data from the lek/right and top/bo^om trials into a single gaze ]me course of "towardness" that captured the bias of gaze towards the memorized loca]on of the cued memory item.We could then compare this measure of towardness across our experimental condi]ons.
To zoom in on biases in fixa]onal gaze behaviour, we removed occasional trials with large gaze devia]ons from fixa]on (as was also done in 35,37,81 ) within the period of interest from 0-1000 ms rela]ve to cue onset.Specifically, we removed trials in which gaze values were larger than 2 degrees away from fixa]on, which corresponded to the inner radius of the near item posi]ons.This ensured that all reported effects cannot be driven by looking at the original loca]on of the cued memory items, but instead are fixa]onal in nature.Gaze remained close to fixa]on in the majority of trials, hence rela]vely li^le trials were removed following this procedure: (usable trials: Experiment 1: 95 ± 1.4%, Experiment 2: 93 ± 1.7%, Experiment 3: 91 ± 2.6%).
In addi]on, the fixa]onal nature of the gaze bias was also visualized through 2-dimensional (2D) heat maps of gaze density (as in 25,36,37 ).For this, we collated gaze-posi]on values across ]me and trials (without averaging) using the data from the 400 to 1000 ms window aker the retro-cue (a ]me window set a-priori based on 36 ).We then counted the number of gaze samples within 0.1° x 0.1° bins, ranging from -6° to 6° and sampling the full 2D space in steps of 0.05°× 0.05°.To obtain a density map, we divided 2D gaze-posi]on counts by the total number of gaze-posi]on samples.For visualiza]on purpose, density maps were smoothed using a 2D Gaussian kernel with an SD of 0.25° × 0.25° (using the built-in func]on "imgaussfilt" in MATLAB).To provide and comprehensive and undistorted view of gaze density in our task, trials with large gaze devia]ons were not removed from the data entering these gaze-density visualisa]ons.
To represent the heat map associated with the direc]onal gaze biases of interest, we first obtained the maps separately following cues to lek, right, top, and bo^om items and subtracted maps between condi]ons in which cues were associated with items in the opposite direc]on: lek versus right and top versus bo^om.We did this separately for each of our core experimental condi]ons.Sta]s]cal analysis.To evaluate and compare gaze towardness ]me courses, we employed a clusterbased permuta]on approach 82 , which is well-suited for evalua]ng mul]ple neighbouring ]me points while avoiding mul]ple comparisons.In this approach, we generated a permuta]on distribu]on by randomly permu]ng trial-average ]me courses at the par]cipant level 10,000 ]mes and iden]fying the largest clusters aker each permuta]on.P-values were computed as the propor]on of permuta]ons where the largest post-permuta]on cluster exceeded the size of the observed cluster(s) in the original (non-permuted) data.Using Fieldtrip, we performed this permuta]on analysis with default cluster se•ngs: grouping similarly signed significant data points from a univariate t-test at a two-sided 0.05 alpha level, and defining cluster size as the sum of all t-values within the cluster.
Because our central ques]on regarded spa]al scaffolding for working memory, we focused on the spa]al gaze bias as our primary outcome variable because this is a direct spa]al index.For completeness, we also considered our behavioural performance data as a func]on of our condi]ons.
We note however that performance data in the current study mainly served to ensure that par]cipants were able to complete the task across our condi]ons.We had no specific hypotheses about these data.Behavioral-performance data (accuracy and reac]on ]mes) were sta]s]cally evaluated using a two-way repeated-measures ANOVA with the factors whether the cued item was near or far and whether direc]on was sufficient (and distance-redundant) or direc]on was insufficient (and distance-useful) as a scaffold for separa]ng the four items in working memory.ANOVA results were supplemented with post-hoc t-tests.As measures of effect size, we used par]al eta squared for ANOVA and Cohen's d for follow-up t-tests.P-values of follow-up t-tests were Bonferroni corrected for mul]ple comparisons.

Figure 1 .
Figure 1.Fixa,onal gaze behaviour during mnemonic selec,on tracks the use of both direc,on and distance as spa,al scaffolding features for visual working memory.a) Task schema,c.Par,cipants memorised four bars with different colours and orienta,ons.Following a delay, a colour change of the central fixa,on dot (retro-cue) prompted par,cipants to select the colour-matching item from working memory to compare its orienta,on to a black bar in the upcoming test display.Memory items were presented to the leG or right and near (3°) or far (6°) from fixa,on at encoding, but par,cipants were never asked about memorised item loca,on.b) Time course of average gaze posi,on following central retro-cues that prompted the selec,on of the memory item that had been presented to the leG or right at encoding, separately for when the memory item was near (leG panel) or far (right panel) at encoding.c) Time courses of spa,al biases in gaze toward the cued memory item when this item was near (light) or far (dark) at encoding.d) Heatmaps of two-dimensional gaze posi,on following leG vs. right cues.Shading in panels b-c indicate ±1 SEM calculated across par,cipants (n = 25).
Figure 1.Fixa,onal gaze behaviour during mnemonic selec,on tracks the use of both direc,on and distance as spa,al scaffolding features for visual working memory.a) Task schema,c.Par,cipants memorised four bars with different colours and orienta,ons.Following a delay, a colour change of the central fixa,on dot (retro-cue) prompted par,cipants to select the colour-matching item from working memory to compare its orienta,on to a black bar in the upcoming test display.Memory items were presented to the leG or right and near (3°) or far (6°) from fixa,on at encoding, but par,cipants were never asked about memorised item loca,on.b) Time course of average gaze posi,on following central retro-cues that prompted the selec,on of the memory item that had been presented to the leG or right at encoding, separately for when the memory item was near (leG panel) or far (right panel) at encoding.c) Time courses of spa,al biases in gaze toward the cued memory item when this item was near (light) or far (dark) at encoding.d) Heatmaps of two-dimensional gaze posi,on following leG vs. right cues.Shading in panels b-c indicate ±1 SEM calculated across par,cipants (n = 25).

Figure 3 .
Figure 3.Our findings are driven by spa,al scaffolding demands, not the mere presence of near and far items.a) Representa,ve encoding displays used in Experiment 3. Experiment 3 replicated Experiment 2 except that in Experiment 3, the "direc,on-sufficient à distance-redundant" condi,on (right-top panel) now always also had two near items (on one axis) and two far (on the other axis).b-c) Time courses of spa,al biases in gaze toward the cued memory item when this item was near (light) or far (dark) at encoding, when direc,on was insufficient and distance useful as a spa,al scaffold (panel b) or when direc,on was sufficient and distance redundant as an addi,onal spa,al scaffolding feature (panel c).d) Gaze bias averaged across the a-priori defined window from 400 to 1000 ms aGer the cue (based on 36 ).e-f) Heatmaps of two-dimensional gaze posi,on following leG vs. right cues (top row) or top vs. bo\om cues (bo\om row) across our four condi,ons.Shading in panels b-c and error bars in panel d indicate ±1 SEM calculated across par,cipants (n = 25).