Context information supports serial dependence of multiple visual objects across memory episodes

Serial dependence is thought to promote perceptual stability by compensating for small changes of an object’s appearance across memory episodes. So far, it has been studied in situations that comprised only a single object. The question of how we selectively create temporal stability of several objects remains unsolved. In a memory task, objects can be differentiated by their to-be-memorized feature (content) as well as accompanying discriminative features (context). We test whether congruent context features, in addition to content similarity, support serial dependence. In four experiments, we observe a stronger serial dependence between objects that share the same context features across trials. Apparently, the binding of content and context features is not erased but rather carried over to the subsequent memory episode. As this reflects temporal dependencies in natural settings, our findings reveal a mechanism that integrates corresponding content and context features to support stable representations of individualized objects over time.


Supplementary Figure 1.
Interaction results of Experiments 1-4. Panels in a) to d) depict the group mean bias aggregated across two levels of a single factor (previous role, serial/spatial position and color) or plotted separately for each condition to illustrate the absence of 2-way (Panel 1 to 3 from left to right) or 3-way-interactions (rightmost panel), respectively. Panels in a) and b) show results for Experiments 1 and 2 and in c) and d) for Experiments 3 and 4, respectively. The y-axis indicates the mean response bias in degrees with a positive bias indicating attraction toward a previous item. Box-plots depict the area between the first and the third quartile (box edges) and the median (box center, solid line). Whiskers depict maximally 1.5 times the Interquartile Range (IQR), with the endpoint of the whisker adjusted to the minimum/maximum data point, if it falls below 1.5*IQR. Data points that fall outside of 1.5*IQR are depicted as colored circles. Additionally, the mean is depicted as a solid black circle within the boxes (four experiments with independent samples; Exp. 1: n=20, Exp. 2: n=49, Exp. 3: n=20, Exp. 4: n=20). This figure illustrates the relationship between context features and the previous role of an item for all four experiments (see Supplementary Tables 1-4

Supplementary Figure 2.
Results for Experiments 1 and Experiment 2 with respect to whether the previous and the current item was presented as first or second stimulus in a trial (S1 or S2). In Experiments 1 (a) and Experiment 2 (b), the stimuli were presented sequentially. Previous studies observed that serial dependence is affected by the time that has passed between the previous and the current item, i.e. the closer in time two items are together, the stronger the serial dependence between them (Fischer & Whitney, 2014). Thus, in addition to our main analysis, we split the data with respect to whether the previous and the current item was S1 or S2. The figure depicts the resulting group mean response biases separately for each experimental condition. Please note that due to the reduction of trials per condition by splitting the data further, the mean bias was calculated using the same procedure as described for the interaction analysis (for details see Methods Experiment 1). The y-axis indicates the mean response bias in degrees with a positive bias indicating attraction toward a previous item. Solid lines represent the group mean with the surrounding opaque area indicating ± 1 standard error of the group mean (two experiments with independent samples; Exp. 1: n=20, Exp. 2: n=49) (see Supplementary  Tables 5 and 6  Non-Target

Same Color Different Color
Current S1 Current S2 Previous S1 Previous S2

Previous S2
Target Current S1 Current S2 Previous S1 Previous S2 Previous S1 Previous S2 Previous S1 7 Supplementary Splitting the data with respect to whether the previous and the current item were S1 or S2 resulted in a 4-way ANOVA with the factors color (same/different), previous role (target/non-target), previous item position (previous S1/previous S2) and current item position (current S1/current S2). Please note that the factor "serial position" of our main analysis, which referred to whether the current and the previous item shared the same serial position or not (regardless of their actual position), was split here into two new factors: previous item position and current item position. As in our main analysis, we found a significant effect of the task-relevant context feature color and of the previous role. Interestingly, the 4-way ANOVA showed that serial dependence was similar for current S1 and current S2 and was also similar when the previous item was actually S1 or S2. In addition, the ANOVA showed a significant interaction between current item position and previous role: the current S1 was more strongly attracted toward previous targets than toward previous non-targets as compared to the current S2. The second-last column lists Bayes Factors (BFincl) which indicate the contribution of a single factor or interaction. Bold accentuation indicates p-values < .05. Source data are provided as a Source Data file.
8 Supplementary Splitting the data with respect to whether the previous and the current item were S1 or S2 resulted in a 4-way ANOVA with the factors color (same/different), previous role (target/non-target), previous item position (previous S1/previous S2) and current item position (current S1/current S2). For details, see Supplementary Table S1. As in our main analysis, we found a significant effect of the task-relevant context feature serial position (revealed by the interaction between Previous Item Position × Current Item Position) and of the previous role. In addition, we also observed an effect of current item position, i.e. the current S1 showed a stronger attraction bias than the current S2. In contrast, serial dependence was similar for previous S1 and S2. We observed two additional interactions. First, there was a significant interaction between color and previous item position, i.e. color modulated serial dependence when the previous item was S1, but not when previous item was S2. While this interaction was significant, the Bayes Factor (BFincl) indicated only inconclusive evidence. Second, we observed a significant interaction between the current item position and the previous role similar to Experiment 1, hinting at a stronger influence of the previous role on serial dependence for the current S1 than the current S2. Taken together, the present additional analyses (Supplementary Tables S1 and S2) showed that the current S1 was more strongly impacted by previous targets than the current S2. This is in line with the finding that temporal proximity facilitates serial dependence (Fischer et al., 2014), as S1 was closer in time to the previous trial. As the current S1 was also maintained in working memory for a longer duration before report than S2, our results are also in accordance with the observation that serial dependence is increased by working memory

Supplementary Note 1
The DoG fitting procedure initially introduced by Fischer and Whitney 1 incorporates both amplitude and width as separate parameters. However, it is possible that especially under higher noise levels their estimation is not independent from each other. To test whether amplitude and width estimates were interdependent in our data, we ran a simulation. We started with the effect of previous non-targets that just fell short of significance (p = .0519), observed in Experiment 1. To obtain realistic noise data, we subtracted the group-level serial dependence bias as fitted with the DoG method (amplitude: 0.71°, width: 0.1) from each subject's individual response error in the non-target condition of Experiment 1. Given this individual "baseline noise", a small amplitude effect as the one subtracted (a = .71°) is just at the border of significance. Higher noise levels will therefore not lead to significant results. For simulation, we reduced this baseline noise in five levels, from 100% of its original size to 20% in steps of 20% by multiplying the individual baseline noise with the reduction factor (e.g. with 0.8 for the 80% condition). On this noise, we individually added a serial dependence bias by adding a DoG function. We used three artificial biases with different amplitudes (the original ones from the contrast, .71° and 2.99° as well as the mean 1.85° of both) and a fixed w value of .065, which is the mean of the original w estimates of this contrast. To assess the effect the amplitude has on the estimation of the width parameter, we fitted the DoG model in each of these 5 (noise level) x 3 (amplitude) conditions and examined the relationship between amplitude and width (Supplementary Figure 3a). We observed merely statistical trends for differences between the three amplitude conditions (low vs. high: p = .072; low vs. medium: p = .075; medium vs. high: p =.087; two-sided paired t-tests, Bonferroni corrected; see Supplementary Figure  3b). The different noise levels affected the width estimation mainly in the low-amplitude condition. Based on this finding we concluded that the amplitude might have a slight effect on the width estimation at a high noise level. However, when the amplitude was low, the variability of the width estimation was in a very small range (<1°). This range was far below any significant FWHM difference as observed in our four experiments (the lowest significant FWHM difference was 8.86°). This demonstrates that our results concerning the w parameter were not driven by amplitude differences.
Supplementary Figure 3. Interdependence between amplitude and width estimates with the DoG fitting method under different noise levels. Panel a) shows the simulated data with their fittings. The individual mean response errors (ordinate; grey lines) are shown as a function of the motion direction difference (abscissa) between an item of the previous trial and the target of the current trial. Red, purple and blue lines depict the fitted DoG models, whereas red indicates the low amplitude condition, purple the medium amplitude condition and blue the high amplitude condition. b) The fitted parameters are depicted as colored dots, where the color indicates the amplitude of the artificial bias and the brightness the underlying noise level, from high (dark color) to low (light color). The x-axis indicates the estimated amplitude and the y-axis the estimated width expressed as full width at half maximum (FWHM). The grey shaded area shows a zoomed-in fraction of the y-axis to make the small differences visible. We observed merely statistical trends for differences between the three amplitude conditions (low vs. high: p = .072; low vs. medium: p = .075; medium vs. high: p =.087; two-sided paired t-tests, Bonferroni corrected). Source data are provided as a Source Data file.