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Model test In this study, the mean difference between the semantically related and unrelated conditions under a strict serial-recall criterion was 0.107. This value was used to estimate λ in the model. As can be seen in Fig. 2, the model reproduces the impact of the semantic relatedness dimension on overall recall performance. At the same time, semantic relatedness in the model also enhances order-recall performance (M = 0.841 and M = 0.729 in the related and unrelated conditions, respectively). This is not observed in the empirical data. Instead, order-recall performance among human subjects remains relatively unchanged (M = 0.782 and M = 0.812 in the related and unrelated conditions, respectively). The semantic effect found in the simulations (see Fig. 3) is a logical consequence of the model. As order-recall performance is driven by the activation level in long-term memory, increased activation leads to better between-item discriminability and hence higher order-recall performance.

Dataset #2: Kowialiewski, Lemaire, and Portrat (2021)

Data It was recently shown (Kowialiewski et al., 2021) that the presence of semantic relatedness in a to-be-remembered list frees up WM resources, as previously observed using chunks (Portrat, Guida, Phénix, & Lemaire, 2016; Thalmann, Souza, & Oberauer, 2019). In this study, semantic relatedness was manipulated by presenting triplets of semantically related items either at the beginning (T1) or at the end (T2) of a six-item to-be-remembered list. These conditions were compared to lists of unrelated items (NT). The semantically related triplets proactively enhanced recall performance for the subsequent, unrelated items, compared to the same items not preceded by a related triplet. However, the semantically related triplet did not retroactively impact recall performance. As we will see, the T2 condition is a critical test of the model.

Model test The mean difference between the T1 and NT conditions over positions 1, 2, and 3 was 0.122. This value was used to estimate λ in the model. Without modifying any of the

Fig. 2 Recall performance across a serial position for the empirical data (left panel) and the model (right panel) in the Kowialiewski and Majerus (2020) study. The experimental conditions involved the presentation of semantically related (green line) or unrelated (mauve line) items

Fig. 3 Order-recall performance as a function of semantic condition for the empirical data (left panel) and the model (right panel) in the Kowialiewski and Majerus (2020) study

basic parameters, the model predicts the recall advantage observed over the semantically related triplet in the T1 condition (Fig. 4). However, the model does not predict the proactive impact of semantic relatedness on the subsequent unrelated items. This latter result, we think, is not critical. Proactive effects could emerge by modeling maintenance mechanisms in a fine-grained manner (Portrat et al., 2016) or by including a limited-resource mechanism (Popov & Reder, 2020), which is beyond the scope of the present study. The critical result of these simulations is to show that the semantically related triplets have a retroactive deleterious impact on recall performance: when the semantically related triplet occurs at the end of the list (T2), recall performance of the third item is worse than in the neutral condition. This is a direct consequence of the modification of the pattern of activation in the model: since the related items in positions 4, 5, and 6 are more activated than other items, they are also more likely to be recalled towards earlier serial positions. In this case, items 3 and 4 are the most likely to be erroneously transposed due to their similar activation level. This pattern is absent in the empirical data. Instead, an absence of retroactive impact is observed.

Dataset #3: Poirier et al. (2015)

Data Poirier et al. (2015) observed that the manipulation of semantic relatedness changed the way items are transposed. In Experiment 1, they presented items of which the first three were semantically related. The manipulation concerned the fifth item that was related as well in the experimental condition, as described in the Introduction. Critically, the fifth item was more often transposed towards position 3 in the experimental condition than in the control condition.

Model test These data do not contain a non-semantic condition that prevents the estimation of the basic parameters of the model. We, therefore, reused the parameters estimated from the second dataset (see above). Figure 5 displays the results. Thepresenceofsemanticrelatednessinthecontrolcondition (i.e., the first three items being semantically related) pro- duces good patterns of recall performance. However, once the fifth item is semantically related to the triplet, a strong drop in performance is observed over positions 4 and 5.

This drop in performance over positions 4 and 5 in the experimental condition is explained by the pattern of serial

Fig. 4 Recall performance across a serial position for the empirical data (left panel) and the model (right panel) in the Kowialiewski, Lemaire, and Portrat (2021) study. The experimental manipulations involved the presence of semantically related triplets of words at the beginning (T1) or the end (T2) of the list and compared this to a semantically unrelated condition (NT)

Fig. 5 Recall performance across a serial position for the empirical data (left panel) and the model (right panel). Each line represents the two experimental conditions originally manipulated by Poirier et al. (2015)

order errors, displayed in Fig. 6. Critically, the vast majority of serial order errors in the experimental condition occurred in position 4. This is contrary to the empirical data where those transpositions tend to increase over position 3. This phenomenon is a core property of the model: serial order errors are constrained by the pattern of activation in long-term memory. Increasing the activation level of one item results in an automatic and obligatory increase of transposition errors toward the directly preceding item.

One may argue that these results merely reflect the property of the model only for the specific set of parameters we found using the simulated annealing algorithm. Instead, there might be some configurations of parameters that could reproduce the results observed by Poirier et al. (2015). We explored this possibility by testing the model across a large sample of parameters. As reported in Appendix A, the model always fails to predict the increased transposition errors over position 3, and the absence of increased transposition errors over position 4.

Discussion

This study used a computational modeling approach to investigate the hypothesis that serial order maintenance results from patterns of activation in long-term memory. The model successfully captured the overall impact of semantic relatedness effect on WM performance. However, it failed to predict the specific influence of semantic relatedness on the processing of serial order information. The model failed to predict the absence of semantic relatedness effects on order-recall performance, and instead predicted better order-recall performance for semantically related items. In addition, while human participants tend to erroneously recall an item at the position of its, semantic neighbors, the computational model produced transposition errors involving migrations towards unrelated items. The problem lies in the architecture's lack of dissociation between serial order information and the activation in long-term memory. Simulation of Dataset #1 showed that

Fig. 6 Transposition rate of item 5 across a serial position for the empirical data (left panel) and the model (right panel)

the increased level of activation of items led to better memory for order information, contrary to what is usually found in the literature (Ishiguro & Saito, 2020). This occurred in the model because the higher level of activation protects items against the deleterious effect of decay occurring at recall, decay following an exponential decay function as implemented in many computational architectures (Burgess & Hitch, 2006; Oberauer & Lewandowsky, 2011; Page & Norris, 1998). In addition, simulations of Dataset #2 and Dataset #3 suggest that if serial ordering errors are at least minimally constrained by an item’s relative level of activation in long-term memory, then a retroactive impact of semantically related items on re-call performance should have been observed. Instead, empirical evidence from the WM literature converges towards an absence of retroactive impact of psycholinguistic factors on serial-recall performance (Cowan et al., 1992; Miller & Roodenrys, 2012; Portrat et al., 2016; Thalmann et al., 2019), a result that our activation-based architecture cannot reproduce. Hence, a purely activation-based architecture appears to be problematic to solve the problem of serial order in WM, contrary to what has been previously assumed (Acheson et al., 2011; Martin & Saffran, 1997; Poirier et al., 2015).

More generally, maintenance of serial order information via a primacy gradient in long-term memory is problematic for several reasons. First, it is not clear how the model would perform simple tasks, such as rehearsal/refreshing(Barrouillet, Bernardin, & Camos, 2004). This is because item selection is performed by choosing the most activated information. The model would be continuously stuck on the most activated item, which in most situations is the first one. Instead, participants can rehearse several items, and cumulatively (Tan & Ward, 2008). The original primacy model assumes rehearsal as being performed within a phonological loop (Page & Norris, 1998), but that does not solve the problem of serial order in the first place. Second, and as mentioned by Norris (2017), a purely activation-based model would never be able to recall an item twice (e.g., recalling “9-2-5-4-9-7”). This task requires temporary representations lying outside long-term memory. Note that this study does not rule out the Primacy model itself as a general mechanism through which serial order information could be coded outside long-term memory, as postulated by the original Page and Norris (1998) model. The present study simply rules out a primacy gradient of ac- activation in long-term memory as an exclusive mechanism to maintain serial order information.

How is serial order represented?

Many theoretical models of WM postulate independence between the nature of the representational codes involved in the maintenance of serial order information and those involved in item information. This relative independence is explicitly as- summed by positional models of WM (Burgess & Hitch, 2006; Oberauer et al., 2012; Oberauer & Lewandowsky, 2011). Critically, these models should also consider potential interactions between item and serial ordering codes, but these interactions are not yet well understood. Jefferies et al. (2006) demonstrated a tendency for phonemes to migrate be- tween nonwords, at the syllabic structure level (e.g., recalling “dug-fal” instead of“dag-full”). Similarly, the pattern of transposition errors observed by Poirier et al. (2015) could be explained by assuming that WM also encodes semantic features. Because semantically related items share overlapping semantic features and/or are also more similar (Dell, Schwartz, Martin, Saffran, & Gagnon, 1997; Ishiguro & Saito, 2020), transposition errors between semantically related items from more distant positions could theoretically occur at the moment of retrieval. Alternatively, as soon as participants detect the presence of a semantically related triplet, they might chunk the information and maintain a single semantic representation (e.g., “nature” instead of “leaf-tree-branch”). At the re-call, due to the decompression of the semantic chunk, the arbitrary order of the items themselves may be lost (Kowialiewski & Majerus, 2020), leading to the erroneous recall of a related word3.

This study fails to support the idea that serial order info- motion is maintained via item-relative activation in the linguistic system. At the same time, this study does not discard the possibility that maintenance of serial order could be completely constrained by the statistical regularities learned from language exposure (Schwering & MacDonald, 2020). According to this account, the linguistic system possesses its serial order maintenance mechanisms. This is, for in- stance, supported by studies showing that statistical regularities derived from linguistic corpora can predict serial-recall performance in verbal WM tasks (Jones & Macken, 2015, 2018). Critically, the plausibility of a purely language-based serial order maintenance mechanism has been demonstrated using a recurrent neural network (Botvinick & Plaut, 2006), the emerging behavior of which is shaped via the adjustment of connections weights using simple learning rules. At a conceptual level, this is radically different from the activation-based architecture we built, which is based on item-relative activation in long-term memory.

Conclusion

This study looked at the range of plausible mechanisms involved in the temporary retention of serial order information. Through a computational modeling approach, we demonstrated that maintenance of serial order information via a primacy gradient of activation in long-term memory is implausible. Whether serial order is coded via independent serial order mechanisms or directly through the statistical regularities occurring in language processing or both remains to be formally established.

Appendix A

In this analysis, we performed a grid search on 16,807 points of the parameter space of our model with λ = 0. The range of parameters explored is displayed in Table A1. We selected the combination of parameters (N = 13,103) that successfully reproduced a primacy effect on recall performance across both the strict serial- recall and item-recall criteria. The recency effect was not considered to ensure the analysis covered a broad range of points in the parameter space.

Next, we performed a new grid search on that combination of parameters by modulating λ (4 values) on each of them, both on the control and the experimental conditions from Experiment 1 of Poirier et al. (2015). Each set of parameters was estimated using 10,000 simulations. We then computed the number of transposition errors (corrected for the total number of times the target had been recalled) of the fifth item that occurred in positions 3 and 4 in each of these experimental conditions. For a result to be valid, we reasoned that there should be at least an increase of transposition errors in the experimental condition over position 3 superior to a potential increase of transposition over position 4. We counted the number of times these versions of the model corresponded to this criterion. There were none.

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