Part 2:Transsaccadic Integration Relies On A Limited Memory Resource

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Results and discussion

The distributions of color responses relative to the pre-and post-saccadic colors are shown for each set size inFigure 2A. We defined bias toward the post-saccadic color value and response variability as the circular mean and circular SD) on a within-observer level (results in figures 2B, 2C, respectively).

Color estimates were increasingly biased toward the post-saccadic stimulus asset size increased, ranging from 4.90 degrees ± 3.13 degrees (mean ± SD) at set size one to 14.3 degrees ± 5.4 degrees at set size four. A series of Bayesian paired-samples t-tests found that bias at set size two exceeded bias at set size one (BF10 = 11.7), and bias at set size three, in turn, exceeded bias at set size two (BF10 = 15.1). We obtained weak evidence favoring no difference between set sizes three and four (BF01 = 1.30). Likewise, response variability also increased with set size, ranging from 21.9 degrees ± 8.1 degrees at set size one to 37.2 degrees ± 10.6 degrees at set size four. Bayesian paired-samples t-tests found

that the SD at set size two exceeded the SD at set size one (BF10 = 292). The SD at set size three in turn

Figure 2. Results of experiment 1. (A) Color response distributions for each set size, plotted concerning pre-and post-saccadic feature values (indicated by dotted lines). Arrows under the x-axis indicate the circular mean of each distribution. (B) Mean circular bias toward the post-saccadic feature as a function of set size. (C) Mean circular standard deviation as a function of set size. Error bars denote 95% within-subjects conﬁdence intervals (O’Brien & Cousineau, 2014).

exceeded the SD at set size two (BF10 = 5.35). We found weak evidence favoring no difference between set sizes three and four (BF01 = 2.76).

To address potential confounds, we investigated whether our results could be influenced by saccadic behavior. Differences in saccade latency could affect pre-saccadic exposure duration, as the color changed only after a saccade was initiated. We found that saccade latencies increased with set size, ranging from

four. This effect was supported by Bayesian paired samples t-tests, finding shorter latencies from set size one to two (BF10 = 96.9), two to three (BF10 = 61.1), and three to four (BF10 = 7.26). This rules out saccade latency as an alternative explanation for our results: longer saccade latencies imply longer exposure to the pre-saccadic stimulus, which should be associated with a stronger bias toward the pre-saccadic color. Our results show the opposite effect. Furthermore, we found no systematic relationship between saccade latencies and bias (within-subjects Pearson’s r = 0.015 ± 0.043; Bayesian t-test on Fisher-transformed correlations versus no correlation, BF01 = 1.82).

The eccentricity of the post-saccadic stimulus relative to the post-saccadic fixation point varied depending on whether it occupied one of the inner or outer array locations. A previous study (Oostwoud Wijdenes et al., 2015) found that biases in integration reflected differences in the relative eccentricity of a stimulus before and after the saccade. Although the eccentricity difference was small, we hypothesized there might be a stronger bias toward the post-saccadic color for items in the inner than outer locations. However, our results did not support a difference in bias (inner = 9.68 degrees; outer = 9.99 degrees; BF01 = 3.52), although there was weak evidence for a difference in SD (inner = 30.82 degrees; outer = 33.88 degrees; BF10 = 2.06). To confirm this was not contributing to our results, we re-analyzed the main effects of set size with the inclusion of an interaction effect with target location (inner versus outer). We found that the model with the interaction was less likely than the best model without, BF01 = 29.82 and 6.52 for bias and SD, respectively.

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Although the stimulus locations were chosen to be equidistant from the pre-saccadic fixation point, small differences in gaze direction during the pre-saccadic fixation period could have affected our findings as they determined the retinal eccentricity of the pre-saccadic color array (Oostwoud Wijdenes et al., 2015). We found a general tendency for fixations to be horizontally displaced away from the stimuli as set size increased. Differences in gaze angle ranged from 0.02 degrees ± 0.11 degrees at set size one to 0.07 degrees ± 0.15 degrees at set size four, where positive values denote gaze displacements toward the edge of the screen. Bayesian t-tests found weak evidence favoring no difference in horizontal displacements between set sizes one and two (BF01 = 1.24) and two and three (BF01 = 3.04), but evidence indicating that horizontal displacement at set size four was further from the stimuli than at set size three (BF10 = 4.21). Given the

unaware participants. We found that the observed difference was greater than the 95th percentile of shuffled data only in one case (for bias at set size 2).

In conclusion, we demonstrate that increasing the number of items presented before the saccade led to a monotonic decrease in the degree to which pre-saccadic information influenced post-saccadic color judgments. Combined with a concurrent increase in response variability, this suggests that the fidelity of pre-saccadic information available for transsaccadic integration declined with set size, consistent with a

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magnitude of the differences in fixation and that the greatest difference in fixation was between set sizes three and four, where the smallest effect in bias and SD was observed, we feel confident in ruling out variations in pre-saccadic fixation as an explanation for our results. In line with this, we found weak evidence against a correlation between horizontal pre-saccadic fixation displacement and bias in color estimates across all trials (r = 0.015 ± 0.052; Bayesian t-test on Fisher transformed correlations versus no correlation, BF01 = 2.20). Similar analyses of post-saccadic fixation location with respect to the lone post-saccadic stimulus found only evidence against effects of set size (r = 0.046 ± 0.042; correlations versus no correlation: BF01 = 3.44).

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Given the amplitude of the required saccade, strong reproducibility of saccade velocity profiles (e.g., Harwood, Mezey, & Harris, 1999), and low latencies of the eye-tracker and display, we can be confident that the large majority of color changes occurred while the eye was moving. However, we cannot rule out the possibility that some changes occurred before or after the saccade, particularly on trials that were aborted due to aberrant eye movements. To investigate whether any changes had been visible to participants and whether this could have influenced our results, we performed a structured debriefing after the experiment, which revealed that most participants were unaware of the color change. Four out of 14 participants indicated that they were aware that the color of the disk could change during a trial. Excluding these participants did not change the overall pattern of results. For a formal comparison between participants who reported being aware and unaware of the change, we performed a mixed-effects Bayesian ANOVA, which found no main effect of awareness on either bias (BF01 = 1.39) or SD (BF01 = 1.81). The model constrained to the main effect of set size was favored over the model, including effects of set size, awareness, and their interaction (for bias: BF = 4.24; for SD: BF = 7.11). Moreover, we performed a permutation test by randomly shuffling aware and unaware labels between participants and computing the difference in bias and SD between the randomly assigned groups. This process was repeated 10,000 times to estimate the expected distribution of different measures if there was no real difference between aware A second key property of visual working memory is that resources can be flexibly allocated to stimuli according to their priority for storage. Studies using attentional pre-cues (Bays, 2014; Bays & Husain, 2008; Oberauer & Lin, 2017; Schmidt et al., 2002; Yoo et al., 2018) have demonstrated enhanced recall of items that are visually salient or task-relevant. If pre-saccadic information is held in a resource-limited store, then we would expect that the pre-saccadic color of an item cued before the saccade would similarly be stored with higher fidelity. As a consequence, integrated estimates would be biased more strongly toward the pre-saccadic color. Experiment 2constitutes a test of this prediction.

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Method

Participants

Fifteen participants (11 female) aged between 18 and 34 years (mean = 26.1) participated inExperiment 2.

Design and procedure

Example trial sequences for experiment 2 can be seen in figure 3. The design was identical to the set size four condition in experiment 1, with the following exceptions: we introduced three cueing conditions of equal frequency: “valid,” “invalid,” and “no cue.” Invalid and invalid conditions, after the initial 500 ms of fixation, a darker grey (54.9 cd/m2) arrow cue was presented for 500 ms, pointing to one of the four stimulus locations. The cue did not overlap with the stimulus location, to avoid contrast changes around the cued item that could interfere with color processing. On valid trials, the item indicated by the cue was subsequently probed (example inFigure 3, bottom panel). On invalid trials, one of the other three items was probed with equal probability. Because there were four items and an equal probability of the cue being

Figure 3. Example trial sequences for experiment 2depicting three of the possible nine combinations of conditions (not to scale). Dashed red circles represent gaze ﬁxations. The dashed red arrow represents the saccade vector. The color change was introduced as soon as the gaze position crossed the vertical midline of the screen. Color changes are exaggerated for illustrative purposes.

valid or invalid in any single trial, the cued item was three times more likely to be probed than any uncued item, providing an incentive to prioritize its storage. Participants were explicitly told about the probabilistic validity of the cue. The no cue trials followed the same timings as valid and invalid trials, with the only difference that no arrow was shown.

The task included trials in which only the pre-or only the post-saccadic stimulus was presented, in

which the probed stimulus was presented before and after the saccade, labeled BOTH trials (see the example in Figure 3, bottom panel), proceeded in the same way as the set size four trials in experiment 1. That is,

four items were presented before the saccade, only one remained visible after the saccade (the cued item on valid trials, and uncued item on invalid and no cue trials) and that item was indicated for a report by the letter corresponding to its location appearing inside a color wheel.

PRE-only trials were identical to BOTH trials with the exception that the probed item was removed during the saccade (see the example in figure 3, top panel). No placeholder appeared in its stead to avoid any influence of backward masking. In POST-only trials, the pre-saccadic items were replaced with four placeholder dots during the eye movement (see the example inFigure 3, middle panel).

Figure 4. Results of experiment 2. (A) Mean circular bias towards the post-saccadic color in the BOTH condition, as a function of cue validity. (B) Mean circular standard deviation in each presentation condition, as a function of cue validity. (C) Color report distributions in the BOTH condition for all cue validities. Arrows under the x-axis indicate the circular mean of the distribution. The purple dashed line denotes model prediction of the BOTH condition derived from the PRE- and POST-only conditions. Error bars denote 95% within-subjects conﬁdence intervals (O’Brien & Cousineau, 2014).

Manipulations of cue validity and presentation time were fully counterbalanced, resulting in a total of nine conditions. Participants completed eight blocks distributed across two experimental sessions of four blocks each. Each block comprised 99 trials (11 per condition, randomly interleaved) amounting to a total

of sessions were performed within 1 week. At the beginning of the first session, participants completed an eye movement practice block (sexperiment 1), followed by a practice block of 33 trials involving no cue trials only, and a second practice block of 27 trials involving all experimental conditions.

Analysis

Bias and variability were calculated in the same way as experiment 1. Note that color responses were reflected only for trials in the BOTH condition.

Results and discussion

We expected that cueing a pre-saccadic item would prioritize its processing and enhance the fidelity of the stored memory content. On valid trials, this should decrease bias toward the post-saccadic color value and reduce error variability compared to no cue trials.

To confirm that the cue was effective in modulating behavior, we analyzed the color error variability in the PRE-only and POST-only conditions. In the PRE-only condition (cyan symbols in figure 4B), the SD was lower on valid trials (47.4 degrees ± 25.4 degrees) than on no cue trials (77.0 degrees ± 19.7 degrees; BF10 = 212). The SD on invalid trials was on average higher (86.2 degrees ± 24.6 degrees), although there was only weak evidence for a difference from no cue trials (BF10 = 2.05). In the POST-only condition, as shown by the blue symbols in figure 4B, no difference in SD was found between cue conditions (repeated-measured Bayesian ANOVA, BF01 = 4.44). This pattern of results confirms that the cueing manipulation was effective in modulating the fidelity of the pre-saccadic representation of the cued item, but did not influence post-saccadic processing.

We next examined the effect of cues on integration in the BOTH condition. Color estimates on valid trials were less biased toward the post-saccadic color than on no cue trials (14.2 degrees ± 4.0 degrees vs. 20.0 degrees ± 3.4 degrees; BF10 = 1.49 × 105), consistent with a reliability-based increase in the weighting of the pre-saccadic color of the cued item. Color bias on invalid trials (19.9 degrees ± 3.90 degrees) did not differ from no cue trials (BF01 = 3.79). This is broadly consistent with the weak effect of invalid cues on variability observed in the PRE-only condition.

The flexible resource account predicts that the increased infidelity for a cued item should be matched by a decrease in infidelity for uncued items, and this has been observed in previous studies of visual working memory (e.g., Bays, Gorgoraptis, Wee, Marshall, & Husain, 2011; Gorgoraptis, Catalao, Bays, & Husain, 2011). The failure to find a clear invalid cue effect in the present study may reflect the fact that, whereas the benefit of a valid cue accrues only to the cued item, the corresponding cost of an invalid cue is distributed between all uncued items (3 in this case). As a consequence, the expected effects of invalid cues are smaller and more difficult to detect than those of valid cues.

The variability estimates for the BOTH condition are shown by purple symbols in figure 4B. The SD on valid trials (22.6 degrees ± 3.9 degrees) was lower than the SD on no cue trials (29.3 degrees ± 6.5 degrees; BF10 = 35.63). Numerically, the SD on invalid trials exceeded the SD on no cue trials (32.8 degrees ± 9.1 degrees), although evidence for this difference was only weak (BF10 = 2.43). Variability in BOTH trials was lower than variability in PRE-only trials in every cueing condition (lowest BF10 = 22.4). However, we did not find a consistent decrease in variability compared to the POST-only condition: for invalid (BF10 = 26.6) and no cue (BF10 = 13.5) trials, the BOTH condition showed a higher SD, whereas there was evidence for no difference in the valid condition (BF01 = 3.55).

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Given that the SD in the BOTH condition was higher than in the POST-only condition, it is clear that performance did not demonstrate the benefit predicted by optimal integration, in contrast to some previous studies testing a single stimulus (Ganmor et al., 2015; Wolf & Schutz, 2015). The purple dashed line in Figures 4A and 4B correspond to predicted performance based on an optimally weighted average of PRE- and POST-only data. While the effects of cue condition were as expected (decreased bias toward post-saccadic color and decreased SD for valid cues) and qualitatively matched the empirical data from the BOTH condition, the optimal integration model consistently overestimated the bias toward

post-saccadic color and underestimated the SD. We will consider possible explanations for this in the General Discussion.

As in Experiment 1, the eccentricity of the post-saccadic stimulus relative to the post-saccadic fixation point varied depending on whether it occupied one of the inner or outer array locations, possibly leading to a stronger bias toward the post-saccadic color for items in the inner than outer locations. Again, our results did not support a difference in bias (inner = 17.21 degrees; outer = 18.61 degrees°; BF10 = 1.01), although there is now stronger evidence for a difference in SD (inner = 26.39 degrees; outer = 30.58 degrees; BF10 = 5.72). To confirm this was not contributing to our results, we re-analyzed the main effects of set size with the inclusion of an interaction effect with target location (inner versus outer). We found that the model with the interaction was less likely than the best model without, BF01 = 5.44 and 1.86 for bias and SD, respectively.

The movement of the eyes is key to being able to see the world clearly (Yarbus, 1967). These eye movements compensate for the limited resolution of human peripheral vision by supporting the accumulation of relevant visual information across successive fixations (Irwin & Andrews, 1996). Across two experiments, we investigated the nature of the representation of the pre-saccadic input available for integration. In Experiment 1, we found that increasing the number of pre-saccadic items monotonically decreased the relative weighting of the pre-saccadic representation in the integrated estimate, consistent with a decline in the infidelity of the pre-saccadic representation. experiment 2, we found that a valid pre-cue highlighting one item in the pre-saccadic display led to an increase in the relative weighting of the pre-saccadic representation in integration, compared to a condition with no cue. This suggests that the prioritized item was represented

with enhanced fidelity in the pre-saccadic store. Both the decline infidelity with set size (Bays & Husain, 2008; Schneegans et al., 2020; van den Berg et al., 2012; Zhang & Luck, 2008) and the flexibility in the allocation

(Gorgoraptis et al., 2011; Oberauer & Lin, 2017; Schmidt et al., 2002;Yoo et al., 2018) are characteristic qualities of visual working memory, often theorized pre- and post-saccadic reliability was truly as great