Note that if it returns 0, we assume activation of any location unit above a threshold of. To produce a less dis- location. Settling times for our model. Activation served experimentally. However, this cost would be very dynamics similar to those produced by the kWTA func- small, since only very large contributions from noise tion have been shown to result from simulated inhibito- could overcome the lack of top-down support.
It is thus possible 3. Results to speed the settling process at the cost of accuracy. We Our model initially produced results quantitatively chose to vary the starting value of the membrane poten- similar to those of the previous model, and to behavioral tial. It also seems that this is a likely var- settle with additional distractors in conjunction search iable for online adjustment by the cognitive system; pro- Fig. A Location process times for varying starting states.
Locating a potential target is dramatically speeded by larger starting membrane potentials, corresponding to a lowered threshold. B Error rates rise rapidly as the location process becomes faster. Even though that process is fairly costly, rounding distractors.
Guided Search as- 4. We replicated earlier work allowed to that process. Thus, guidance is not inaccurate indicating that such a process can produce the linearly because it must be, but because it may be faster to quick- increasing reaction times with set sizes. Informal although some information from the previous parallel experimentation suggest that these changes can produce process may be retained.
High Like the Guided Search model, our model does not threshold theories have been convincingly rejected in the specify the conditions under which search is terminated.
We therefore Duncan, J. Psychological Review, 96 3. Horowitz, T. Search for multiple targets: the identity of the object at the selected location, and re- Remember the targets, forget the search. Abstract Visual search is central to the investigation of selective visual attention. Publication types Review. School of Psychological Sciences. Overview Fingerprint. Abstract Visual search is central to the investigation of selective visual attention.
Access to Document Link to publication in Scopus. Penalizing the models for complexity, AIC still prefers the parallel model for Participants 4 and 7. For the conjunction-search task, too, the model fits provide strong support for the CGS model see Table 3 for the best-fitting parameters.
As shown in Fig. However, the model fails with respect to target-absent displays: it underestimates the inter-quantile range of RTs for the large set size 12, 18 items; top right panel and falsely predicts an increasing FA rate with increasing set size bottom right panel. Additionally, CGS accounts better for the miss rates bottom left panel. A model comparison Table 2 showed that for all participants except for Participant 1 as well as for the group as a whole, CGS yielded lower deviance values despite its lower number of parameters.
Model fits for the conjunction-search task of Wolfe et al. The arrangement of the figure is identical to Fig. For the feature-search task, too, the model fits provide strong support for the CGS model see Table 4 for the best-fitting parameters.
To understand the reasons for this, we focus below on the fits of the parallel model. Considering first the target-present displays, we find that the parallel model provides a good fit for the hit RTs Fig. Remarkably, as in the data, there are no observable set size effects on the predicted hit RTs. Table 4 shows that with increasing set size, the threshold separation hardly changes, while the starting point moves closer to the lower target-absent boundary.
With everything else being equal, this effect would lead to an increase in hit RTs since the target has to traverse a longer distance to reach the upper boundary. This weak super-capacity could arise if the larger number of display items increased the target's bottom-up salience. Why does the starting point move downwards, however? Model fits for the feature-search task of Wolfe et al. Arrangement of the figure is identical to that of Fig. To understand this, we need to consider the target-absent condition.
Figure 4 shows that when the target is not found, the search is exhaustive. Thus, all other things being equal including boundaries and starting point , RTs for CRs would increase with set size it takes longer for more distractors to reach the lower boundary. However, unlike the data, the model predicts a speed-up in the two upmost 0.
This intricate trade-off provides further demonstration for why stronger model constraints can be gleaned by fitting search models to RT distributions, rather than only to central-tendency measures Wolfe et al. Finally, a model comparison Table 2 showed that for all participants except for Participant 6 as well as for the group as a whole, CGS yielded lower deviance values despite its lower number of parameters.
This finding is striking, taking into account that for a long time, feature search has been considered the prototypical task for a parallel search architecture. The parallel-model fits to the feature-search task that we presented above correspond to a highly flexible model, which assumes that boundaries, starting points, and drift rates can vary with set size and which also included the capacity and the quit-termination parameters.
Interestingly, the inclusion of the latter did not help the parallel model in this case because the fit always converged to large q-values that correspond to exhaustive search Table 4 ; Fig.
As expected, the fits were worse than for the flexible model that we presented in Fig. Notably, this model was able to account for the traditional property of flat mean-RT with set size, but not for the full RT distribution and the error rate functions see Supplemental information. We focused on three classical search tasks from a rich data set Wolfe et al. Importantly, both the spatial configuration and the conjunction tasks exhibit robust set-size effects, thus allowing for probing the origin s of those effects.
Methodologically, we embraced Wolfe et al. The results showed that the fits of the parallel model were problematic. In the 2-vs. For the conjunction task, the parallel model failed to account for performance on target-absent displays with respect to both RT distributions and error rates. Indeed, despite its larger number of free parameters 13 vs.
This finding is striking, especially when taking into account that CGS provided adequate fits with parameters that were invariant with respect to set size, whereas the parallel model allowed for flexible set-size adjustments in boundary separation and identification bias.
Thus, our model comparisons show that the serial, two-stage CGS model Moran et al. Having compared the models with respect to these traditional serial search tasks, we next compared the models based on their fits to the feature task. Given that this task has traditionally been considered to epitomize a parallel search architecture, it provides a stringent test for the serial model.
Strikingly, we found consistent superiority for CGS Table 2 , especially in its ability to provide a better account for miss rates and correct-rejection RTs.
As explained by Moran et al. On target-present trials, for any set size, the target is almost certainly identified as the first item.
On target-absent trials, for any set size, the quit unit is almost always selected after the rejection of the first distractor. In other words, if the target failed to pop out, observers safely terminate the search, deciding that a target is absent.
Thus, in both target-present and target-absent displays, a single item is identified; consequently, there are no set-size effects. The rightmost panel in Fig.
Why, then, can it not successfully mimic the serial model? Interestingly, this question highlights a fundamental distinction between the serial and parallel models we compared. Whereas in our CGS parameterization, identification time was invariant with respect to set size, this was not the case with the parallel model. Imagine we would maintain all the parameters of the parallel model invariant across set size and set a zero quit-unit exponent so that it quits after the first distractor reaches the lower boundary.
Notably, everything else is not necessarily equal as the parallel model was endowed with ample flexibility to apply set size modulations with respect to threshold separation, starting point, and capacity. The results of our quantitative model fits show, however, that the empirical RT distributions and error rates provide strict constraints such that a policy of exhaustive search when the target is not found yielded the best fits.
Ceteris paribus, search-exhaustiveness induces a plethora of set-size effects: a slowdown in CRs due to the 'need to wait' for the last distractor to reach the lower boundary , a speedup in hits due to statistical facilitation; note that a 'hit' can be triggered by a distractor, rather than the target, mistakenly reaching the upper bound an increase in FA-rate higher likelihood that one of the distractors will mistakenly reach the upper boundary in target absent displays and a reduction in miss rates once more, due to the higher probability that one of the distractors will mistakenly reach the upper boundary in a target present display and will trigger a correct hit response.
These fits, alas, were inferior to those produced by CGS, because they failed to provide a satisfactory tradeoff in accounting for miss rates and they generated an unobserved set-size related speedup in the high quantiles of the CR distributions.
As shown in the Supplement, more constrained fits which impose a limit on the quit parameter failed to improve the model fits. While our results favor the two-stage serial CGS model, they need to be taken with caution with regard to concluding an unequivocal superiority for a serial over a parallel architecture of attentional selection. First, extensions of our parallel model need to be explored.
For example, within the framework of parallel-diffusor models, it would be important to probe the possibility that different items are processed with different drift rates due to attentional gradients. Because such investigations will depend on a number of critical assumptions e. Additionally, in the current model, we adopted the simplifying assumption that people set nonbiased drift rate criteria for the item-identification process and that any identification-biases are reflected in the starting point see also Footnote 3.
Consequently, the identification drift-rates for the target and the distractors are equal in magnitude. This assumption, however, could be relaxed in future studies to allow for different target-distractors drifts. Future investigations may also explore alternative termination rules for target-absent responses. It should be noted that our model comparison study is parametric in that it makes specific distributional assumptions with respect to the components of the model e.
In this respect, our approach is modest in its ambition as compared with non-parametric, model-free attempts to identify the visual-search cognitive architecture. Alas, prior model-free attempts have produced inconclusive conclusions, because they highlighted the possibility for serial-parallel mimicry for a recent review, see Algom et al.
Still, one limitation of our study is that it cannot rule out the possibility that different distributional assumptions in future serial and parallel models will improve visual search models and that such future parallel models will outperform future serial models.
This, however, does not imply that our current findings are trivial. On the contrary, we contend that the advantage of our approach is that—as a consequence of making parametric assumptions—it avoids the risk of model mimicry. Furthermore, our parametric assumptions are well motivated: By grounding our parallel model on a diffusion-type architecture—the currently most popular approach for modeling speeded decisions across a wide range of cognitive tasks—we believe that our findings are highly informative in the context of current research.
Finally, these results provide a challenge that more sophisticated parallel models will need to rise to if they wish to compete with Guided-Search type serial models in accounting for visual search data. An alternative approach to testing the adequacy of the parallel model of visual search that may avoid the pitfall of specific assumptions associated with the model we explored here e.
One such promising signal-detection model was developed by Verghese to account for accuracy with brief search displays. Unlike the current parallel model, in the Verghese model, the individual items are not separately identified. Rather, search decisions are based on a global match between the search display and a target template. This global match in turn is based on the maximal value of the local matches between each display item and the target. While this model was shown to account for set-size effects on accuracy, it has not yet been formally extended and tested on its ability to account of RT distributions.
Footnote Furthermore, conclusions favoring the serial model may need to be qualified to visual search displays that are available until response. It thus is possible that the strategy that observers rely on in visual search varies with task contingencies: While for briefly presented displays observers may rely on the maximal value of saliency, with time-unlimited and difficult search displays, they may use the salience map to engage in serial attentional selections that guide a high-resolution identification process to verify target presence.
To better understand the nature of the operating processes in visual search, future studies comparing serial and parallel models are required. Such studies should examine additional data-sets based on experimental manipulations that are designed to differentiate between these types of models.
For example, it would be important to test how these types of models account for visual-search performance in displays in which target salience is manipulated on a continuum Liesefeld et al.
Furthermore, the understanding of the nature of attentional processes in visual search will have to include efficiency considerations. For example, once attentional gradients are assumed Williams et al.
Finally, while serial and parallel theories describe two prototypical search mechanisms, future research also should consider the possibility of hybrid mechanisms. Typically, the slope is roughly twice as steep for target-absent compared to target-present displays.
This assumption implies that observers set non-biased drift rate criteria for interpreting target-match vs. In principle, observers could bias their drift rate criterion so that distractors and targets generate drift rates that are unequal in their magnitude, implementing a 'dynamic integration bias' e.
However, here we assume that any bias in identification is fully reflected in the diffusion starting point see the parameter z below , but otherwise integration proceeds in a non-biased manner. The notion of a race between diffusion processes captures the intuition that each item-identification is competitive in terms of evidence-accumulation for or against the target, while the different diffusors operate independently of each other except for the capacity constraint on the drift, which we discuss below.
The mapping of diffusion-model parameters to psychological constructs has been demonstrated behaviorally in perceptual-decision paradigms Schwarz, ; Voss et al. Additionally, there is electrophysiological evidence Philiastides et al. Adjusting two decision criteria is mathematically equivalent to adjusting the boundary separation and the starting point. Moran et al. Here, we focus on the fits of the non-constrained general 8-free- parameter model. This is plausible for the present data set, because displays with more items were also more densely packed.
In line with such an increase in iso-feature suppression, several studies actually reported a decrease instead of the more typical increase! We have performed preliminary explorations of a sequential-sampling extension of this model, which yielded a lower poorer fits as compared with the CGS model Moran et al.
One challenge that the test of this model involves is that, unlike the one presented, it does not allow analytical calculations and thus requires more laborious, slow and noisy, model simulations. In fitting the feature task we sometimes encountered numerical problem e. Thus, we also fit the average observer of this task with an alternative methods were the single diffuser CDF was estimated based on a simulation of K diffusion trials, obtaining similar results i. After fitting our models, we verified that our analytical derivations described below yield predictions in terms of RT quantiles and error rates that are very similar to these produced by a mechanistic trial-by-trial simulation of the model based on the best fitting parameters.
Akaike, H. Information theory and an extension of the maximum likelihood principle.
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