Target Fidelity, but not Inducer Fidelity, Modulates Repulsive Serial Dependence of Visual Working Memory Representations

doi:10.21203/rs.3.rs-7835332/v1

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Target Fidelity, but not Inducer Fidelity, Modulates Repulsive Serial Dependence of Visual Working Memory Representations

https://doi.org/10.21203/rs.3.rs-7835332/v1

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Visual representations are open to systematic functional biases. In visual working memory, representations of serially presented stimuli can either attract or repel each other. Such serial dependence biases are thought to reflect adaptive Bayesian processes yielding optimal perceptual decisions under uncertainty. This perspective suggests that serial dependence should adapt to the degree of uncertainty in both the current target and the inducer (previous target) representations. When the current target representation is noisy, attractive serial dependence increases, but the effect of uncertainty in the inducer is not clear. Furthermore, less is known about the effect of inducer or target uncertainty, especially in tasks where repulsive biases would optimize performance. In an orientation estimation task, we presented three consecutive targets (T1, T2, T3) in rapid succession, with the T1-T2 Lag of 3 or 7; T3 always followed T2 at lag 7. T2 fidelity was lower at Lag 3 due to attentional blink. This design allowed us to test the impact of representational noise on serial dependence effects when T2 is both a target, and an inducer (for T3). We are the first to demonstrate that reduced attentional resources increased the repulsive serial bias in T2; inducer noise in T2 did not modulate the bias in T3. Repulsive biases extended beyond immediate perceptual history, as T3 estimates were repelled by T1 orientation. T2 estimates were also repelled from the subsequent T3 orientation, demonstrating a repulsive effect emerging during working memory maintenance. Our findings show adaptive error reduction in working memory, beyond Bayesian optimality.

serial bias

serial dependence

visual adaptation

visual working memory

attention

Prior information and experiences can implicitly influence perceptual decisions. Many recent studies have found evidence for a bias called serial dependence, which is typically defined as an attractive bias toward the immediately preceding stimulus (1,2,3 for reviews). The serial dependence bias is thought to optimize perceptual representations by drawing on the pervasive temporal correlation between the immediate past and the current state of the physical world (4). Although assimilative serial dependence attracted much attention, evidence suggests that repulsive serial dependence also exists, where perceptual estimates are biased away from recent perceptual history (e.g., 5). This repulsive bias is often considered to be a consequence of negative adaptation (e.g., 6–8) which can be considered as a predominantly perceptual effect (9). The serial dependence bias goes beyond the immediate perceptual realm as revealed by modulation of the bias during working memory-related processes (e.g., 6,10,11). Yet, the influence of working memory-related processes was characterized as an exclusively attractive effect that compensates for uncertainty in the stimulus representation (e.g., 12–15). Popular Bayesian accounts of the serial dependence bias predict that the attractive bias should increase when the current target representation is noisy and decrease when the bias inducer is noisy, optimizing representations (1,6,16). On the other hand, working memory models (e.g., 17,18) suggest that repulsive biases can also be adaptive to minimize error in representations, when the noise is high (19). This conclusion was based on data from tasks where a set of items presented concurrently, leaving open the question of whether such repulsive biases can also adaptively minimize errors in tasks where items are presented sequentially. In the present study, we tested whether the target and inducer uncertainty modulates the serial bias in representations. To test this, we used an orientation reproduction task in which we presented three targets serially, where a target could also serve as an inducer for a subsequent target. We manipulated the uncertainty in the target representations by using an attentional blink manipulation. This task rendered individuating representations more optimal for the ultimate goal of error reduction. This, in turn, enabled us to test for the effect of uncertainty in target and inducer items on the repulsive serial bias, going beyond the immediate perceptual realm.

Major accounts of serial dependence emphasize the possible functions of such a bias. One major argument is that the serial dependence bias optimizes perceptual estimates in the face of ambiguity to achieve stability over time. Bayesian accounts of serial dependence (e.g., 6,16) suggest that bias adapts to the uncertainty in the current target as well as the inducer (i.e., the preceding target) that serves as a prior. Cicchini et al. (1) claimed that the serial dependence bias operates like an adaptive Kalman filter¹, suggesting that the bias toward the past is maximal when the current stimulus representation is noisy, the previous stimulus representation is reliable, and the feature difference between successive stimuli are relatively low. Therefore, the first critical prediction of the Bayesian account is that when the current input is noisy or unreliable due to internal or external factors, the serial dependence bias should be greater. This is followed by the prediction that the estimate should be less informed by the prior (indicating a weaker serial dependence bias) when the prior is noisy or unreliable.

There is mixed evidence regarding Bayesian accounts of serial dependence. There is considerable evidence supporting the former prediction showing that attractive serial dependence is greater when the uncertainty in the current target representation is high (e.g., 16,21–23). There are attentional blink studies showing an increase in the serial dependence-like attractive effect in target representations when attention allocation to the target is reduced (24,25). On the other hand, evidence regarding the latter prediction of the Bayesian accounts is scarce. In fact, many studies have found that manipulations of uncertainty (e.g., 21,22,cf. 26), working memory load (11), or decisional uncertainty in the inducer (12,cf. 27) did not influence the magnitude of the serial dependence bias towards the inducer. Therefore, it appears that attractive serial dependence is strongly modulated by uncertainty in the current trial and not by uncertainty in the prior.

Studies on factors related to working memory on serial dependence suggest the effect of working memory processes is exclusively attractive. For instance, the attractive bias magnitude increases when the working memory delay (6,13–15) and load increases (11,12), along with findings of a shift in an initially repulsive bias into an attractive bias with increased working memory load (10,14). All suggest that the serial dependence bias in working memory is exclusively attractive. Moreover, many studies consider the effect of post-perceptual processes including working memory-related processes to have an exclusively attractive influence and not be repulsive (6,7,15). We argue that methodological factors may lead to a disproportionate attractive pattern. First, in many serial dependence studies, the feature difference between successive targets is restricted, usually within 30° to 40° in the orientation domain (11,12,28–30). In this case, the attractive bias is rendered optimal for minimizing errors especially when successive stimuli are similar enough and the current target representation is noisy. On the other hand, the experiments that are designed to yield a repulsive serial dependence usually use discrete orientations with large increments that span throughout a wide range of the available range of orientations, where successive targets are unlikely to have similar orientations across the trials (8,10,14). In the current design, we sampled orientations such that only in a small proportion of trials successive items had similar orientations. A second factor that we believe contributes to the reports connecting working memory-related factors with an increase in attractive biases is whether the task encourages individuation of representations or not. Critically, our task encouraged further individuation of target representations since we presented multiple targets within the same event (trial) serially and asked participants to reproduce all in order. In contrast, typical serial dependence studies present a single target (e.g., 10,14,16) per event, there is no need for further segregating representations presented in successive events. The possible effects of working memory-related processes on the repulsive bias have not yet been tested in such a task in which separating out individual target representations would yield more accurate estimates. Therefore, the evidence reviewed above does not provide sufficient data to assume that working memory-related processes are exclusively attractive.

To summarize, Bayesian accounts of serial dependence proposed that the attractive bias magnitude should increase when the working memory representation of the current target is noisy and it should decrease when the inducer representation is noisy (6,16,26). Although the effect of noise in the target or the inducer representation on attractive serial dependence has been investigated (e.g., 11,12), it has not been extensively tested in a task that is designed to produce repulsive serial dependence. For the same reason, even though the effect of working memory-related processes (e.g., increase in load or delay) are considered to increase the attractive serial effect (6,10,13–15) the evidence is not sufficient to assume that this is necessarily the case. Given the literature on working memory representations indicating that repulsive biases help reduce error in stimulus representations (17–19), in the current work, we addressed this possibility.

In the current study, we manipulated the fidelity of item representations using a novel paradigm which requires differentiating between serially presented items on a single trial. We then tested whether the magnitude of repulsive serial dependence is influenced by the noise in the inducer representation or in the target representation. Our paradigm enabled us to manipulate attention allocation to a single target per trial, which then served as the inducer or the target depending on the analytical approach to trial-wise data.

We used a variant of a continuous-measure attentional blink paradigm to address the effect of noise in successive target representations on the repulsive serial bias. In the current paradigm, we presented three oriented teardrop objects on each trial. We varied the lag between the first (T1) and the second target (T2) to be within the attentional blink period (Lag 3) or after (Lag 7). A third target (T3) always followed T2 at a fixed lag outside to the attentional blink period. See Figure 1 for the trial sequence of the present study. The orientation difference between T1 and T2 as well as between T2 and T3 varied between -75° to +75° with increments of 15°. This is following experiments that aimed to produce repulsive serial dependence (8,10,14). This meant that subsequent targets in our study had identical or highly similar orientations only in a very small proportion of trials (smaller than 30° only in 3 in every 11 trials), and in the remaining trials, their orientations were highly different. We expected to observe a repulsive serial dependence effect, rendering three working memory representations separable from each other, optimizing the task performance (19). Following this logic, we expected that when there was less attention available to process a target item (T2), there would be a stronger repulsion effect (away from T1), drawing an inference based on the trial history (as target orientations are different from each other in most trials). In line, when attention allocation to the inducer (T2) was restricted, we expected to observe a weaker repulsion in T3 targets². This aligns with the idea of adaptive optimization of visual judgments (11,19), which would suggest that a low fidelity target should exert less influence as a bias inducer. The current experiment was preregistered (https://aspredicted.org/gsyg-jw2t.pdf). We had conducted a pilot to the current experiment, and a detailed report can be found in Supplementary.

To preview the results, we found that the repulsive bias increased when the current target representation was noisy. However, the inducer fidelity did not strongly modulate the repulsive bias. This is in line with the recent findings on attractive serial dependence suggesting that the noise in the inducer representation does not modulate the effect, adding to the literature challenging the popular Bayesian accounts (e.g., 12,14) of the serial bias.

Attentional Blink

T2. A paired-samples t-test revealed that absolute T2|T1 error was significantly lower in the Lag 7 condition (M = 11.35, SD = 2.23) compared to the Lag 3 condition (M = 13.01, SD = 2.20), t(21) = 4.62, p < .001, Cohen’s d = .75. The Bayesian paired-samples t-test also showed decisive evidence in favor of the alternative hypothesis over the null, with the BF₁₀ of ~194. We observed the typical attentional blink effect for T2 representations.

T3. A paired-samples t-test revealed that absolute T3|T1 error did not differ significantly across the Lag 3 (M = 13.13, SD = 2.09) and the Lag 7 (M = 12.78, SD = 2.77) conditions, t(21) = 1.03, p = .31, Cohen’s d = .14. The Bayesian paired-samples t-test suggested that the data is 2.78 times more likely under the null hypothesis than the alternative. Absolute T3|T1 error was comparable across Lag 3 and Lag 7 conditions, suggesting that error in T3 estimates was not influenced by the T1-T2 Lag manipulation, as expected.

Serial Dependence

T2 – Effect of Target Fidelity. To test whether there is a serial bias in T2 estimates, and if so, whether it differed across Lag conditions, we conducted a paired-samples t-test on α values estimated based on individual data by fitting a first derivative of the Gaussian function (DoG). The results indicated a repulsive serial dependence effect which was greater in the Lag 3 (M = -8.17, SD = 4.53) condition compared to the Lag 7 condition (M = -5.05, SD = 4.52), t(21) = -4.03, p < .001, Cohen’s d = -.69. The Bayesian paired-samples t-test suggested that the data was ~55 times more likely under the alternative model including Lag as a factor compared to the null model.

We also conducted a nonparametric permutation analysis on the aggregated data pooled over participants as there is a limited number of observations per condition per participant. In doing so, we followed the literature (6,11). The observed parameter α values were -7.60 in the Lag 3 condition and -4.92 in the Lag 7 condition, again confirming the repulsive effect. The results suggested that the α difference between Lag 7 and Lag 3 conditions was significant, α_Lag7-Lag3 = 2.68, 95% CI [-1.15, 1.15], p_perm < .001. The fitted curves as well as the observed data can be seen in Figure 2. The results suggested that the magnitude of the repulsive serial dependence bias was greater when the target fidelity was rendered low due to the attentional blink effect compared to when the target fidelity was higher (outside the attentional blink window). Overall, estimates based on both individual and aggregated data suggested that there is an effect of target fidelity on the repulsive bias. We had also observed very similar findings in the pilot experiment (Figure S2).

T3 – Effect of Inducer Fidelity. Next, we tested whether the serial bias in target (T3) estimates was influenced by the fidelity of the inducer (T2). Attentional blink analysis suggested that the inducer, T2, varied in fidelity as a function Lag whereas the target T3 fidelity remained constant across Lag conditions. To determine whether there was any change in the serial bias based on inducer fidelity, we compared bias for T3 across Lag conditions. A paired-samples t-test on individual α values revealed that the repulsive serial bias in T3 estimates did not differ across Lag 3 (M = -8.59, SD = 4.49) and Lag 7 (M = -7.33, SD = 4.25) conditions, t(21) = -1.97, p = .063, Cohen’s d = -.29. Bayes factor analysis showed anecdotal support for the alternative hypothesis compared to the null, with a BF₁₀ of 1.13.

The analysis based on the aggregated data suggested that the α parameter values estimated based on the observed data were -8.22 in the Lag 3 condition and -6.40 in the Lag 7 condition. The results suggested that the difference in the parameter a across the Lag conditions was significant, α_Lag7-Lag3 = 1.82, 95% CI [-1.26, 1.28], p_perm = .005, suggesting that the repulsive bias in the target T3 was stronger when the inducer (T2) had low fidelity due to the attentional blink, compared to when the inducer fidelity was better (outside the attentional blink window). DoG fits and the observed data can be seen in Figure 3. This finding was unexpected as it is on the contrary to the optimal strategy. In detail, as the Bayesian accounts of serial dependence suggest (e.g., 6,16), an ideal observer would put more weight into the current sensory input in case the uncertainty in the prior (inducer) is high. However, what we observed here suggested that the observers relied more on the inducer while responding to the current target when their representation of the inducer orientation was more inaccurate compared to when the inducer representation was less inaccurate. On the other hand, it is important to note that the results of the individual fits suggested no differences in terms of the magnitude of the repulsive bias in T3 estimates across Lag conditions. In addition, as seen in Figure 3, although we applied a correction to eliminate orientation-specific biases, the intercept of T3|T1 estimation error in the Lag 3 condition is off in the repulsion side compared to the Lag 7 condition. This might have influenced the fit and artificially increased the half-amplitude estimate of the DoG function. In a planned exploratory analysis, we aimed to further investigate other possible effects that might have influenced participants’ reports of T2 and T3, possibly leading to this discrepancy.

The current design required participants to hold on to three target representations briefly in working memory until they were prompted to reproduce these targets in the presented order. The typical serial dependence analyses reported above focused only on the effect of the relative orientation of the immediately preceding target on estimation error in a given target representation. While this effectively quantifies the effect of the relative difference between two successive targets in the stream on the subsequent target’s representation, it leaves out the possibility that the other target in the stream might have also influenced the target representation. To account for this, in a planned exploratory analysis, we fitted linear mixed-effects models to our data to predict estimation error while accounting for the effect of the relative difference between the given target and the remaining two targets as well as the effect of Lag, simultaneously. We fitted nested mixed models to predict T2|T1 error and T3|T1 error separately. For the ease of interpretation, we mutated three categorical predictors based on the relative orientation difference between T1 and T2 (T1 vs T2: T1 > T2 and T1 < T2), the relative orientation difference between T3 and T2 (T3 vs T2: T3 > T2 and T3 < T2), and the relative orientation difference between T1 and T3 (T1 vs T3: T1 > T3 and T1 < T3). In these predictors, the target that precedes the “bigger than” sign has a more clockwise orientation than the target that follows it. In this case, negative error indicates repulsive bias. The target that precedes the “smaller than” sign is more counterclockwise than the one following. Figure 4 and Figure 5 present T2|T1 and T3|T1 estimation errors as a function of these predictors based on relative orientation differences.

To predict T2|T1 estimation error, we fitted linear mixed models with Lag, T1 vs T2 , and T3 vs T2 as fixed effect predictors and participant as the only random effect predictor. We followed a stepwise approach. Table 1 shows the nested model structure and model diagnostics. The likelihood ratio tests revealed that the model including T1 vs T2, T3 vs T2, Lag, and the interaction of T1 vs T2 and Lag as fixed predictors was the best fitting model, χ²(1) = 14.49, p < .001. The model's intercept corresponds to the Lag 3 condition where both T1 and T3 were more clockwise than T2 (T1 vs T2: T1 > T2 and T3 vs T2: T3 > T2). Within the best fitting model, Type II Wald Chi-square tests suggested that there was no significant main effect of Lag, χ²(1) = 0.36, p = .55, but there were significant main effects of T1 vs T2, χ²(1) = 418.94, p < .001, and T3 vs T2, χ²(1) = 73.55, p < .001. Moreover, the interaction between Lag and T1 vs T2 was significant, χ²(1) = 14.51, p < .001. The results suggested that T2 estimation error shows repulsion away from both T1 and T3 (Figure 4; explained in detail below). Critically, however, attention manipulation further amplified the repulsion in T2 from the preceding target T1 but not from the succeeding target T3. These findings were consistent with the results based on both individual and aggregate DoG fits.

In Figure 4, overall, the positive slope of the lines indicates the repulsive effect of relative T1 orientation on T2 estimates. The vertical offset of the green line, shifted upward, and the orange line, shifted downward, indicates the repulsive effect of relative T3 orientation on T2 estimates. The steeper slope in the lines in the Lag 3 condition (left panel) compared to Lag 7 (right panel) shows the modulation of the T1-induced bias by Lag. In contrast, the similar vertical separation between the green and orange lines across panels indicates no modulation of the T3-induced bias by Lag.

To further explain this based on Figure 4, let’s focus on the left panel corresponding to the Lag 3 condition. The bottom left point (in orange) is the intersection where both T1 and T3 were more clockwise (+°) compared to T2 (T1 > T2 & T3 > T2). It can be seen that the error is further counterclockwise (–°) in this condition. The exact opposite is on the top right point (in green) in the left pane. When both T1 and T3 are more counterclockwise (–°) than T2 (T1 < T2 & T3 < T2), the error is further clockwise (+°). This suggests that when both T1 and T3 repelled T2 in the same direction the observed repulsion was stronger. The remaining two points show conditions where T1 and T3 repelled T2 in opposite directions. These two points are closer to y = 0, reflecting that when T1 and T3 repelled T2 in opposite directions, the overall bias appears to reduce. The same logic applies to the Lag 7 condition as well.

Table 1 Linear mixed-effects models of T2|T1 estimation error

Predictors of T2\|T1 Error	n parameters	Δ_AIC	Δ_BIC	χ²
~ T1vsT2 + (1 \| participant)	4	80.98	63.74	-
~ T1vsT2 + T3vsT2 + (1 \| participant)	5	10.85	0	72.13***
~ Lag + T1vsT2 + T3vsT2 + (1 \| participant)	6	12.49	8.04	0.36
~ Lag x T1vsT2 + T3vsT2 + (1 \| participant)	7	0	1.94	14.49***
~ Lag x T1vsT2 x T3vsT2 + (1 \| participant)	10	3.84	24.97	2.15

Note. *** indicates statistical significance at p < .001. Intercept corresponds to the Lag 3 condition where both T1 and T3 were more clockwise than T2 (T1 vs T2: T1 > T2 and T3 vs T2: T3 > T2).

As above, also for T3 we explored whether the relationship between T2 and T3 and T1 and T3 impacted the bias in T3 estimates. We fitted linear mixed models to predict T3|T1 error with Lag, T2 vs T3 , and T1 vs T3 as fixed effect predictors and participant as the only random effect predictor, adopting a stepwise approach. The model including T2 vs T3 and T1 vs T3 as fixed effect terms showed better fit to the data compared to the simpler model with T2 vs T3 as the sole fixed term, χ²(1) = 79.20, p < .001. As seen in Table 2, adding additional predictors did not significantly improve the model fit, all ps > .05, suggesting that T2 vs T3 and T1 vs T3 captured the critical variance in T3|T1 estimation error. Within the best fitting model, both T2 vs T3, χ²(1) = 149.37, p < .001, and T1 vs T3, χ²(1) = 100.27, p < .001, were significant predictors. This suggested that T3 estimates were not only influenced by the relative orientation between T2 and T3, but they were also repelled away from T1 presented earlier in the stream (Figure 5). However, in line with the results of the analysis based on individual DoG fits, neither the effect of T2 vs T3 nor the effect of T1 vs T3 varied across Lag conditions. In Figure 5, the positive slope of the lines demonstrates the repulsive effect of relative T2 orientation on T3 estimates. The vertical offset of the yellow line, shifted upward, indicates that T3 estimates are more clockwise when T1 is more counterclockwise relative to T3. Conversely, the purple line, shifted downward, indicates the repulsive effect of relative T1 orientation on T3 estimates shift errors toward more counterclockwise direction when T1 is more clockwise relative to T3. Therefore, it is apparent that the T1-induced and T2-induced effects on T3 estimates are additive.

To summarize, the planned exploratory analysis revealed that both T2 and T3 representations repelled away not only from the immediately preceding target (T1 and T2, respectively) in the stream but also from the other target (T3 and T1, respectively) in the stream³. Critically, in T2 representations, when attention allocation to T2 was restricted, repulsion from the preceding target T1 was greater. This was consistent with the findings of the DoG-based analyses. However, the repulsion from T3 did not vary depending on the attention allocation to T2 and was an additive effect (Figure 4). Similarly, repulsive effects in T3 estimates away from T1 and T2 did not vary significantly depending on the attention allocation to the inducer T2 (Figure 5). This was also in line with the results of the analysis based on individual DoG fits but not the one based on aggregate DoG fits.

Table 2 Linear mixed-effects models of T3|T1 estimation error

Predictors of T3\|T1 Error	n parameters	Δ_AIC	Δ_BIC	χ²
~ T2vsT3 + (1 \| participant)	4	97.13	90.74	-
~ T2vsT3 + T1vsT3 + (1 \| participant)	5	0	0	99.13***
~ Lag + T2vsT3 + T1vsT3 + (1 \| participant)	6	1.75	8.15	0.25
~ Lag x T2vsT3 + T1vsT3 + (1 \| participant)	7	0.66	13.46	3.09
~ Lag x T2vsT3 x T1vsT3 + (1 \| participant)	10	5.53	37.52	1.14

Note. *** indicates statistical significance at p < .001. Intercept corresponds to the Lag 3 condition where both T1 and T2 were more clockwise than T3 (T1 vs T3: T1 > T3 and T2 vs T3: T2 > T3).

We investigated the effect of attention allocation to the target and to the inducer on the serial bias in an orientation estimation task, in which three targets had to be reproduced from memory in order. Overall, with a variety of analytical techniques, we showed that the repulsive bias in target estimates was modulated by attention allocation. We reported, for the first time, that as the target representation (T2) got more noisy due to restricted attention, the repulsive serial bias (in T2) increased (cf. 10,14). On the other hand, there was no modulatory effect of inducer noise (in T2) on the repulsive serial bias on the target (T3). Critically, our findings regarding the repulsive serial bias went beyond the immediately preceding target, as indicated by a repulsive bias in T3 estimates contingent on the relative orientation of T1 (Figure 5). Another pivotal finding was that target (T2) estimates were further repelled away from a subsequent target (T3) orientation. This repulsive effect emerged during working memory maintenance. Even though there was sufficient time for consolidation of T2 targets, we demonstrated that the subsequently encoded T3 further impacted the T2 representation resulting in further repulsion. This was the case even though T2 was always reported before T3, which indicates that this effect is free from the effect of response. This showed that the repulsive bias can emerge during visual working memory maintenance, a possibility which has not been previously considered in the serial dependence literature. We argue that our findings revealed adaptive error-minimizing dynamics of working memory processes which are not necessarily entirely explained by Bayesian optimal processes. In addition, as a manipulation check, we reported that the attention manipulation selectively influenced the fidelity of T2 representations –as indicated by greater absolute estimation error at Lag 3– and not the fidelity of T3 representations⁴. We actually had conducted a pilot experiment where we replicated the repulsive bias reported for T2 and T3 representations at Lags of 3 and 7 (Supplementary). It is also noteworthy that we observed repulsive biases exclusively, even when all stimuli were task-relevant and attended to (cf. 31–33). Our findings add to the prior work (e.g., 12,22) that contrast predictions that can be drawn from a Bayesian perspective (e.g., 6,16) and are more consistent with accounts that emphasize goal-driven adaptability (19). We believe our findings have important implications for understanding how temporal context, stimulus history, and task demands bias perceptual decisions in a way that is adaptive but not necessarily optimal in Bayesian terms.

Our findings align with those in the literature demonstrating an increase in the serial bias when target uncertainty is high (16,21–23) and little to no impact of inducer fidelity on the bias (11,12,21). Though, note that these studies reported an increase in the attractive serial bias, not repulsive. The only effect we observed of the inducer on the target was contradictory to Bayesian account predictions (6,16); instead of observing a decrease in the reliance on the inducer with increased noise in the current target, we observed the opposite. There was no such evidence in the analysis based on individual DoG fits and the mixed model analysis, nor in the pilot data. Moreover, we believe the aggregated DoG fit for the T3|T1 error in the Lag 3 condition may have an inflated half-amplitude due to the overall underestimation effect observed in this condition (Figure 3). Therefore, we refrain from speculating on this increase in the repulsive bias. Critically, unlike studies showing an increase in attractive serial bias under uncertainty (e.g., 12,22) or working memory load (e.g., 10,11), we reported an increase in the repulsive bias in the current study for the first time. To summarize, our findings are at odds with the Bayesian accounts of the serial dependence bias (16,26,34). Not only this, but merely the fact that we exclusively observed repulsive biases, challenges simple Bayesian models of serial dependence (e.g., 16), as they only allow for integration of information which necessarily leads to attractive biases.

To understand why we may be observing a pattern of results contradicting those of typical Bayesian predictions, one must be reminded of the differences between earlier work and the paradigm adapted in this task. In a typical study investigating serial dependence, a single target is presented on each trial, and the task is to replicate the critical target feature (e.g., orientation) of this target following a brief delay (e.g., 16,33). Within the orientation domain, many studies reporting an attractive serial bias limit the successive orientation difference (11,12) to be relatively similar or sample orientations with smaller increments (33) or in a continuous manner (29). Others reporting a repulsive bias (8,14) usually sample from the whole range of available orientations with larger increments, including the current study. This suggests that the biases observed across studies may reflect different factors impacting earlier perceptual and later working memory representations (31). We believe these differences to be important, and we further discuss these in relation to debates surrounding the locus of processing of serial dependence.

One of the most debated issues in the serial dependence literature has been the locus of processing. Several alternatives have been proposed: The locus of serial dependence could be at early perceptual stages (e.g., 33,35,36), at post-perceptual stages involving working memory and decisional stages (e.g., 13,15,37), or the bias can operate at both early and late stages (e.g., 7,38). More recently, there has been a growing interest in the role of mnemonic processes in serial dependence (11,12,39). Earlier studies have found that the attractive serial bias increases as the working memory delay increases (e.g., 13,15,40). Several recent studies investigated the mouse trajectory of responses in continuous-measure estimation tasks (10,14,39). Findings suggested that the initially repulsive bias which arises from early perceptual processes transitions towards attraction or even becomes an attractive bias as time passes. This is consistent with the visual system’s goal of optimizing perceptual performance in a balanced manner, promoting stability in perceptual decisions while remaining sensitive to changes in the environment. Accordingly, during the preparation of a response, while the representation is being held in working memory an attractive bias accumulates indicating that post-perceptual processes balance out the effect of early repulsive bias (8). Calling further attention to working memory processes, some studies reported that when working memory load increased with an additional task such as the Stroop task, the otherwise repulsive bias became an attractive bias (10,14). This is also consistent with the effect of working memory load in the studies reviewed in the paragraph above (11,12). In fact, the increase in the attractive bias under high working memory load could be explained by Bayesian models (e.g. 6,16) as additional working memory load likely renders target representations more uncertain. However, the effect being repulsive in the absence of an additional task (10,14 but see 11,12) cannot be accounted for by a simple Bayesian model (16) but requires a combination of Bayesian computation with processes such as efficient coding (14), as in the model by Fritsche et al. (6).

Apart from the underlying computation that leads to serial bias, the evidence reviewed above characterizes the influence of working memory processes as purely attractive. However, the results of a planned exploratory analysis suggested that a target T2 representation is not only repelled away from the immediately preceding item T1 in the stream but also from the item T3 that followed the target T2. As the item that followed the target was displayed during working memory maintenance of the target, this is direct evidence that repulsive bias can emerge during working memory processes. Moreover, this same analysis further confirmed the DoG-based findings that repulsive serial bias in T2 target estimates repelled farther away from the inducer T1 when attention to the target was restricted at Lag 3. Critically, the repulsive effect of the item T3 that followed the target T2 was not modulated by Lag. This might be hinting at a difference between the purely post-perceptual effect of T3 on T2 and the effect of T1 on T2 which likely has a perceptual component too, especially at Lag 3 where T1-T2 SOA is 300 ms. Turning to the computational models of the bias, these findings cannot be explained even by the Bayesian efficient coding model (6) unlike others showing an increase in the attractive effect during post-perceptual processes (10,14), as we observed that target representations repelled away from an item presented during working memory maintenance (Figure 4).

It is entirely possible that what we conceptualize as the repulsive serial bias here might arise as a result of visual adaptation, which manifest as a repulsive bias away from the adaptor stimulus (i.e., inducer) that can occur at timescales as short as milliseconds (7–9). Negative effects arising from visual adaptation can be modeled within a Bayesian framework as a shift in the likelihood function away from the adaptor (41). This leads to allocation of more resources for processing features in the vicinity of the adaptor value. This, in turn, increases measurement reliability near the adaptor value, which may account for the increase in the repulsive bias magnitude under restricted attention to the target in the current study. This is also consistent with the decrease we observed in the repulsive bias as successive target values further apart from each other (Figures 2 and 3). Furthermore, Chopin and Mamassian (42) reported a repulsive bias in perceived orientation away from the recent past and an attractive bias toward the remote past. Critically, repulsive bias was further away from a certain orientation as it occurred more often in the recent past. The authors argued that this repulsive bias indicates a mechanism that predicts the upcoming stimulus based on the stimulus distribution in the recent past. We consider our findings to be consistent with these findings. Therefore, although the current results cannot be explained by Bayesian models of serial dependence (6,16), this does not necessarily imply that they cannot be explained within any Bayesian framework.

Chunharas and colleagues (19) proposed an adaptive framework for explaining biases in visual working memory representations of multiple simultaneously presented stimuli. In a series of experiments the authors reported a repulsive bias when simultaneously presented target stimuli were similar to each other in the feature domain. They also found an increase in the repulsive bias when there is a longer working memory delay and when target representations were more noisy. According to this framework, both attractive and repulsive biases are a consequence of the system’s goal of reducing error in representations. Critically, if an individual item representation is rendered more noisy due to manipulations such as increasing working memory delay, by default, more attraction should occur (19). However, when the task demands individuated representations, as in our case, segregating the representations to reduce overlap between them provides a more effective means of error reduction. This framework was not meant for explaining biases between serially presented stimuli. Yet, we believe the fundamentals of this framework may reconcile the apparent discrepancy between our study and those reporting a flip to an attractive bias from an initially repulsive bias (10,14), observed under conditions where target representations were noisier. Although stimuli and design choices were quite similar across these two studies and the present work, a critical difference was that our design required segregation of successive stimuli for error minimization, whereas this was not the case in the others. We believe that this divergence in the results is completely in line with error reduction in working memory, it defaults to more attraction under uncertainty but when the task demands individuation it switches to more repulsion.

There are several limitations of the current study. As we effectively manipulated the T1-T2 Lag to be 3 and 7, we also altered the working memory delay for T2 and T3. This is because in the Lag 3 condition, not only T2 but also T3 were presented in a closer temporal succession to T1, which was followed by more masking patterns until the end of the 24-item long stream. Therefore, the working memory delay was longer for T2 and T3 when the T1-T2 Lag was 3 as compared to when it was 7⁵. This might be problematic given there is evidence in the working memory literature that repulsion biases grow with longer delays (19). Although this may indicate that delay may have contributed to the increase in the repulsive bias in T2 in the Lag 3 condition, we believe it is not very likely for a couple of reasons. First, there are reports of an opposite effect or no effect of delay. For instance, Fritsche et al. (6) showed that the repulsive bias is not modulated by working memory delay. Findings in the serial dependence literature showing that the attractive bias, not the repulsive bias, increases as the working memory delay increases (e.g., 13,15). Moreover, Chen and Bae (8) reported that the repulsive effect was stronger when the working memory delay was shorter. Second, and perhaps more critically, although the Lag condition changed the working memory delay also for T3, we did not observe such a difference in the magnitude of the repulsive bias as we did for T2.

Another possible limitation of the current study is that the response order was always the same and we asked for reproduction of the targets in the presented order. Previous responses can have influence on the reported orientation of a given stimulus. In fact, prior decisions and therefore, responses are considered to drive the attractive serial dependence bias (e.g., 7,15,43). To test for a possible effect of responses, in alternative nested linear mixed model analyses we included response to the previous target as a predictor of T2 and T3 estimation error. While estimates of these predictors indicated an attractive influence, the prior response was a significant predictor neither for T2 nor for T3 estimation error. Although a response-based explanation is unlikely for the observed modulation of the repulsive bias magnitude by target fidelity, we believe that this does not entirely disregard the possibility that prior responses may have influenced our findings especially as it is very difficult to disentangle response-contingent effects from stimulus-contingent effects.

The current findings call attention to the role of error-reducing dynamics of working memory which has a strong influence on the direction of the bias between representations of serially presented items and the bias magnitude under uncertainty. Our findings demonstrate serial dependence is not merely a perceptual phenomenon. Consistent with earlier findings (e.g., 12,22) we found that uncertainty in the inducer has a weak to no effect on the serial bias, contradicting simple Bayesian explanations. Unlike prior work (10,14), we found an increase in the repulsive bias when attention allocation to the target is restricted. We believe the current set of findings offers an opportunity to reconsider the computational and conceptual models of serial dependence.

The current study aimed to investigate the effect of attention allocation to the target and to the inducer on the serial bias in a task where three targets are presented in close temporal proximity in rapid serial visual presentation (RSVP). The task was to reproduce the orientation of each individual target in the presented order. We analyzed the bias in target estimates. The second target (T2) in the RSVP stream served as the target in the analysis of the bias in T2 estimates induced by the first target (T1) in the stream. T2 served as the inducer in the analysis of the bias it introduced to the third target (T3) in the stream. To manipulate attention allocation we varied the Lag between T1 and T2 to be 3 and 7, respectively the attentional blink condition and outside the attentional blink. T3 followed T2 at a fixed lag (of 7) outside the attentional blink window. We also varied the orientation of successive targets in RSVP from -75° to +75° with steps of 15°.

Participants

22 Koç University undergraduate students (M_age = 21.18, SD_age = 2.15, 19 females and 3 males) participated in the current experiment. We determined the sample size following an a priori power analysis in GPower (44) which suggested a sample size of 24 with 80% probability of detecting a medium to large attentional blink effect (Cohen’s d of .6) with an alpha of .05. Participants were not diagnosed with a neurological disorder and had normal or corrected-to-normal vision. All participants were compensated with 1 course credit in exchange for participating in the experiment.

Apparatus & Stimuli

We collected data in person at Koç University Cognition and Behavior Lab. We programmed and ran the experiment in OpenSesame (45) on computers running under Windows 10 OS. Target stimuli were colored teardrop objects (red: #EE6677, green: #228833, blue: #4477AA). The orientation of the first target item (T1) in the stream was determined randomly between 0° to 359°. The orientations of the remaining targets (T2 and T3) were determined based on the relative orientation difference variables, Δ_T1−T2 and Δ_T2−T3, on each trial. We created mask stimuli by randomly shuffling an equal number of red, blue, and green 3x3 pixel-squares. Target stimuli had the width of 28 pixels and the length of 80 px whereas masks were 81 x 81-px squares. Response probes consisted of a colored ring with 40 px radius and a colored dot (both either red, green, or blue). The color of the first (T1), second (T2), and third (T3) target in the stream was fixed across trials for each participant and pseudo-randomly sampled from 6 possible combinations (red-green-blue, green-red-blue etc.). The color of three response probes on each trial matched the color of the respective targets. Color-coding was done to prevent swap errors. All stimuli were displayed centrally on a gray (#393939) background using 22-in. monitors with 60 Hz refresh rate and 1920 x 1080 px resolution with participants seated approximately 60 cm away from the monitor (1 px corresponds approx. to .02° of visual angles).

Design and Procedure

We employed a within-subjects design with a single factor with two levels (Lag: 3 and 7)⁶. We varied the relative difference between successive target orientations, T1-T2 and T2-T3 orientations. Accordingly, Δ_T1−T2 and Δ_T2−T3 varied from − 75° to + 75° with steps of 15°. Each level of Δ_T1−T2 paired with each level of Δ_T2−T3, adding up to 242 permutations in total. Anticipating trial loss after applying trial-based exclusion criteria, we randomly sampled 58 additional trials from unique permutations. Thus, participants completed 300 experimental trials and 10 practice trials in a single experiment session taking approximately 51 minutes on average.

We adopted the RSVP technique to present three target stimuli (T1, T2, and T3) on each trial. The RSVP stream consisted of 24 displays in total, in which all stimuli (3 targets and 21 masks) were presented at the center of the screen alone for ~ 83 ms, with ~ 17 ms blank interval in between each display. Lags 3 and 7 corresponded to stimulus onset asynchronies (SOAs) of ~ 300, and ~ 700 ms. We set the T1-T2 Lag variably as 3 or 7 and used a fixed T2-T3 Lag of 7.

Each trial began with the presentation of two successive fixation crosses at the center of the screen (approx. for either 300 ms or 500 ms each). The first fixation cross was green, indicating the beginning of the trial, and the second cross was white. Following the white fixation cross, the RSVP stream took place. T1 was randomly presented as the 4th or 5th item in the RSVP stream. There were either 2 or 6 masks between T1 and T2 in Lag 3 and Lag 7 conditions, respectively. There were always 6 masks between T2 and T3. Following the offset of T3, mask items were presented until the end of the RSVP stream. After a 500 ms blank display, three response probes were presented successively. Participants reproduced the orientation of the corresponding target, one by one, in the presented order. In doing so, participants adjusted the position of the dot on the ring to match the direction that the teardrop object pointed at, using the mouse cursor. The initial orientation of each response probe was determined randomly between 0° and 359°. The trial sequence can be seen in Fig. 1.

Data Preprocessing and Analytical Approach

All analyses were performed in R (46). We conducted Bayes factor analyses using the BayesFactor package (47), we considered a BF₁₀ of 1 or greater as evidence for the alternative hypothesis, and a BF₀₁ of 1 or greater as evidence supporting the null hypothesis. We used the Jeffreys-Zellner-Siow (JZS) prior for all Bayesian analyses. We fitted linear mixed-effects models using lme4 (Bates et al.). To further investigate the simple effects of predictors we used the car package (48). We used likelihood ratio rests, Akaike information criterion (AIC) and Bayesian information criterion (BIC) for model comparison.

We used the following criteria to perform trial-based exclusion. First, we applied the recursive outlier elimination procedure (49) for reaction time of T2 and T3 responses resulting in exclusion of approximately 4% of trials. Next, we excluded trials where absolute T1 estimation error exceeded 22.5° (an additional ~ 14%) and absolute T2 and T3 estimation errors exceeded 60° (an additional ~ 3%). We only kept trials where T1 estimation is low to ensure the attentional blink effect which requires T1 fidelity to be high (25,50). This resulted in 80.17% of all trials to be included in the analysis.

Our analyses focused exclusively on orientation estimation error for the second (T2) and the third (T3) target in the RSVP stream. Signed estimation error was computed by subtracting the response from the presented orientation of a target. Accounting for the circularity of the variable, we ensured that signed error spans from − 180° to + 179° (i.e., modulo 180°). To test our hypotheses, we benefited from a variety of analytical methods. To clean the data from orientation-dependent biases such as cardinal or intercardinal biases (e.g., 5,51), we residualized T2 and T3 error by fitting a weighted sum of first- and second-harmonic components to the plot of estimation error (\(\:y\)) by presented target orientation (θ). A₁ and A₂ correspond to the amplitude of sine and cosine functions, respectively, and b is the intercept parameter. We fitted the model [1] to the data using the nonlinear least squares (nls) method.

[1] \(\:y=\:{A}_{1}\text{sin}\left(\frac{2\pi\:\theta\:}{180}\right)+{A}_{2}\text{cos}\left(\frac{4\pi\:\theta\:}{180}-\frac{\pi\:}{2}\right)+b\)

As a final preprocessing step for the serial dependence analysis, we folded T2 and T3 errors by multiplying them with the sign of Δ_T1−T2 and Δ_T2−T3, respectively. By doing this, we mirrored the estimation error in the negative range of Δ_T1−T2 and Δ_T2−T3 to the positive range. Further details of the serial dependence analyses are below.

For the serial dependence analysis, as is common in the literature (33), we fitted a simple first derivative of Gaussian function (DoG) without intercept [2]. Our approach was two-fold: We fitted the DoG function to both individual data and the aggregate data to assess serial dependence. The DoG function in both cases was the same and as follows:

[2] \(\:y=\:\alpha\:\times\:w\times\:c\times\:x\times\:{e}^{-{(w\times\:x)}^{2}}\:\)

In the DoG function, y indicates estimation error on a given trial for a given target. x indicates the relative orientation difference between successive targets (i.e., Δ). The constant c is equal to \(\:\frac{\sqrt{2}}{{e}^{-.05}}\). The parameter w is the inverse of the half-width of the curve. The parameter \(\:\alpha\:\) quantified the magnitude of the serial bias as the half-amplitude of the curve. First, we fitted the DoG function to the individual data by creating a matrix of multiple initial values for parameters \(\:\alpha\:\), from − 10 to 10 with steps of 5, and w, from .03 to .06 with steps of .01. We used the L-BFGS-B method from the optimx package (52) for parameter estimation, setting the lower and upper boundaries for \(\:\alpha\:\) as [-20–20] and w as [.01 – .08, allowing for curve peaks between 12.50° to 100°], with 1000 maximum iteration per starting parameter pair. In doing so, we adopted the maximum likelihood estimation approach to estimate the best fitting parameter values.

We used the very same DoG function [2] to fit the aggregate data pooled over all participants per unique Lag condition. In doing so, first, we estimated the observed difference in the parameter \(\:\alpha\:\) between Lag conditions. Next, following the permutation test procedure described in (11), we shuffled Lag condition labels 10,000 times and at each iteration we fitted the DoG function to the aggregate data computing the difference between Lag conditions for the parameter \(\:\alpha\:\). The estimated difference values from these permutations then served as the empirical null distribution for the parameter \(\:\alpha\:\). Finally, we compared the observed \(\:\alpha\:\) difference between Lag conditions with the empirical null distribution to estimate the proportion of permutations where such a difference occurred by chance, yielding the permuted p value. We used an alpha level of 5% for all statistical tests.

Ethics approval and consent to participate: Participants provided written consent prior to participating in experiments. The ethical approval was obtained from the Institutional Review Board in Social Sciences and Humanities of Bogazici University.

Consent for publication: NA.

Availability of data and materials: Both the pilot experiment (https://aspredicted.org/nzdn-fthj.pdf) and the present study (https://aspredicted.org/gsyg-jw2t.pdf) were preregistered at AsPredicted. The data and experiment files will be made available in OSF upon acceptance of the manuscript for publication.

Competing interests: The authors have no competing interests to disclose.

Funding: The current study was supported by TUBITAK (The Scientific and Technological Research Council of Turkey) 1001 programme (112K291) granted to AB.

Authors' contributions: BY: Conceptualization, Methodology, Software, Data collection, Analysis, Writing, Review & editing.

AB: Conceptualization, Methodology, Analysis, Writing, Review & editing, Funding acquisition. All authors have read and approved the final manuscript.

Acknowledgements: BY acknowledges the support of TUBITAK 2211-A PhD scholarship.

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The Kalman filter is a linear estimation algorithm (20). First, it keeps track of a series of observations over time which forms the prior knowledge. Next, by weighting the prior knowledge and the new noisy input, it allows for an estimation of an unknown variable which is more accurate than an estimation made solely based on the new input. Finally, the prior distribution is updated with each new input weighted by its noise. This procedure continues recursively.
In the current paradigm, T2 serves as both the target and the inducer within the same trial depending on the part of the trial that the analysis focuses on. In analyzing T2 responses in terms of bias induced by T1, T2 is the target. Turning to T3 responses, T2 is now the bias inducer.
In an alternative analysis, we applied the same model structure for both T2|T1 error and T3|T1 error, additionally including the response to the immediately preceding target as a predictor, which did not significantly predict either estimation error variable. We also fitted alternative nested models to predict both T2|T1 error and T3|T1 error, where we introduced the interaction term of the relative orientation difference predictors prior to adding Lag as a predictor. However, these interaction terms also failed to significantly improve the model fit.
We also investigated target representation precision (inverse of the standard deviation in estimation error) across Lag conditions. The results replicated those of absolute estimation error, revealing that precision in T2 estimates was lower in the Lag 3 condition (M = .10, SD = .02) compared to the Lag 7 condition (M = .11, SD = .03), t(21) = -3.45, p = .002, Cohen’s d = − .67, BF₁₀ = 16.81. This was not the case for precision in T3 estimates, t(21) = -1.20, p = .24, Cohen’s d = − .24, BF₀₁ = 2.37.
Depending on T1 position (the 4th or the 5th item in the RSVP), the working memory delay for all targets was either 100 ms longer or shorter regardless of the Lag condition.
Δ_T1−T2 and Δ_T2−T3 were not considered factors as the serial dependence analysis already accounts for the relative orientation difference between successive targets.

No competing interests reported.

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Target Fidelity, but not Inducer Fidelity, Modulates Repulsive Serial Dependence of Visual Working Memory Representations

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The Present Study

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Attentional Blink

Serial Dependence

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Participants

Apparatus & Stimuli

Design and Procedure

Data Preprocessing and Analytical Approach

[1] \(\:y=\:{A}_{1}\text{sin}\left(\frac{2\pi\:\theta\:}{180}\right)+{A}_{2}\text{cos}\left(\frac{4\pi\:\theta\:}{180}-\frac{\pi\:}{2}\right)+b\)

[2] \(\:y=\:\alpha\:\times\:w\times\:c\times\:x\times\:{e}^{-{(w\times\:x)}^{2}}\:\)

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