No Evidence for an Item Limit in Change Detection
[['Visual working memory , the ability to buffer visual information over time intervals of the order of seconds , is a fundamental aspect of cognition .', 'It is essential for detecting changes [1]–[3] , integrating information across eye fixations [4]–[5] , and planning goal-directed reaching movements [6] .', 'Numerous studies have found that visual working memory is limited , but the precise nature of its limitations is subject of intense debate [7]–[14] .', 'The standard view is that visual working memory cannot hold more than about four items , with any excess items being discarded [7]–[9] , [15]–[18] .', 'According to an alternative hypothesis , working memory limitations take the form of a gradual decrease in the encoding precision of stimuli with increasing set size [10]–[11] , [13] , [19]–[23] .', 'In this view , encoding precision is a continuous quantity , and this hypothesis has therefore also been referred to as the continuous-resource hypothesis .', 'Historically , the leading paradigm for studying visual working memory has been change detection , a task in which observers report whether a change occurred between two scenes separated in time [2]–[3] , [24] .', 'Not only humans , but also non-human primates can perform multiple-item change detection [25]–[28] , and physiological studies have begun to investigate the neural mechanisms involved in this task [27] .', 'Findings from change detection studies have been used widely to argue in favor of the item-limit hypothesis [2] , [8] , [15]–[18] .', 'The majority of these studies , however , used stimuli that differed categorically from each other , such as line drawings of everyday objects or highly distinct and easily named colors .', 'The logic is that for such stimuli , changes are large relative to the noise , avoiding the problem of “comparison errors” [1] , [18] , [29]–[30] that would be associated with low encoding precision ( high noise ) .', "When encoding precision is limited , an observer's stimulus measurements are noisy and will differ between displays for each item , even if the item did not change .", 'The observer then has to decide whether a difference in measurements is due to noise only or to a change plus noise , which is especially problematic when changes are small .', 'This signal detection problem results in comparison errors .', 'Attempts to avoid such errors by using categorical stimuli run into two objections: first , using such stimuli does not guarantee that comparison errors are absent and can be ignored in modeling; second , there is no good reason to avoid comparison errors , since the pattern of such errors can help to distinguish models .', 'Ideally , change detection performance should be measured across a wide range of change magnitudes , including small values , as we do here .', 'Comparison errors can , in fact , be modeled rather easily within the context of a Bayesian-observer model .', "Bayesian inference is the decision strategy that maximizes an observer's accuracy given noisy measurements [31]–[32] , and was recently found to describe human decision-making in change detection well [33] .", 'We conducted two change detection experiments , in the orientation and color domains , in which we varied both set size and the magnitude of change .', 'We rigorously tested five models of working memory limitations , each consisting of an encoding stage and a decision stage .', 'The encoding stage differed between the five models: the original item-limit model [2] , [15]–[16] , two recent variants [9] , and two continuous-resource models , one with equal precision for all items [20] , [23] , and one with item-to-item and trial-to-trial variability in precision [13] , [33] .', 'The decision stage was Bayesian for every model .', 'To anticipate our results , we find that variable precision coupled with Bayesian inference provides a highly accurate account of human working memory performance across change magnitudes , set sizes , and feature dimensions , and far outperforms models that postulate an item limit .'], ['We model a task in which the observer is presented with two displays , each containing N oriented stimuli and separated in time by a delay period .', 'On each trial , there is a 50% probability that one stimulus changes orientation between the first and the second display .', 'The change can be of any magnitude .', 'Observers report whether or not a change occurred .', 'We tested five models of this task , which differ in the way they conceptualize what memory resource consists of and how it is distributed across items ( Fig . 1a ) .', 'We conducted an orientation change detection task in which we manipulated both set size and change magnitude ( Fig . 2a ) .', 'Consistent with earlier studies ( e . g . [10] , [15] , [17] ) , we found that the ability of observers to detect a change decreased with set size , with hit rate H monotonically decreasing and false-alarm rate F monotonically increasing ( Fig . 2b ) .', 'Effects of set size were significant ( repeated-measures ANOVA; hit rate: F ( 3 , 27 ) =\u200a52 . 8 , p<0 . 001; false alarm rate: F ( 3 , 27 ) =\u200a82 . 0 , p<0 . 001 ) .', 'The increase in F is inconsistent with the IP model , as this model would predict no dependence .', 'For a more detailed representation of the data , we binned magnitude of change on change trials into 10 bins ( Fig . 2c ) .', 'All no-change trials had magnitude 0 and sat in a separate bin .', 'These psychometric curves clearly show that the probability of reporting a change increases with change magnitude at every set size ( p<0 . 001 ) .', 'From Fig . 2c we could , in principle , compute a naïve estimate of memory capacity using the well-known formula from the IP model , K\u200a=\u200aN ( H−F ) / ( 1−F ) [16] .', 'However , since H depends on the magnitude of change , the estimated K would depend on the magnitude of change as well , contradicting the basic premise of a fixed capacity .', "For example , at set size 6 , for change magnitudes between 0° and 9° , Cowan's formula would estimate K at exactly zero ( no items retained at all ) , while for magnitudes between 81° and 90° , it would estimate K at 3 . 8 , with a nearly linear increase in between .", 'This serves as a first indication that the IP model in general and this formula in particular are wrong .'], ['Five models of visual working memory limitations have been proposed in the literature .', 'Here , we tested all five using a change detection paradigm .', 'Although change detection has been investigated extensively , several of the models had never been applied to this task and no previous study had compared all models .', 'Compared to previous studies , our use of a continuous stimulus variable and changes drawn from a wide range of magnitudes enhanced our ability to tell apart the model predictions .', 'Our results suggest that working memory resource is continuous and variable and do not support the notion of an item limit .', 'The variable-precision model of change detection connects a continuous-resource encoding model of working memory [13] with a Bayesian model for decision-making in change detection [33] .', 'This improves on two related change detection studies that advocated for continuous resources .', 'Wilken and Ma [10] introduced the concept of continuous resources , but only compared an EP model with a suboptimal decision rule to the IP model .', 'Although the EP model won in this comparison , the more recent item-limit models ( SA and SR ) had not yet been proposed at that time .', 'Our present results show that the SA and SR models are improvements over both the EP and IP models , but lose to the VP model .', 'In a more recent study , we compared different variants of the Bayesian model of the decision process and found that the optimal decision rule outperformed suboptimal ones [33] , but we did not vary set size or compare different models of working memory .', 'Other tasks , such as change localization [13] , visual search [21] , [23] , and multiple-object tracking [19] , [46] , can also be conceptualized using a resource-limited front end conjoined with a Bayesian-observer back end .', 'Whether such a conceptualization will survive a deeper understanding of resource limitations remains to be seen .', 'It is instructive to consider each model in terms of the distribution over precision that it postulates for a given set size .', 'In the IP model , this distribution has mass at infinity and , depending on set size , also at zero .', 'In the SA and SR models , probability mass resides , depending on set size , at one or two nonzero values , or at zero and one nonzero value .', 'The EP model has probability mass only at one nonzero value .', 'The VP model is the only model considered that assigns probability to a broad , continuous range of precision values .', 'Roughly speaking , the more values of precision a model allows , the better it seems to fit .', 'Although we assumed in the VP model that precision follows a gamma distribution , it is possible that a different continuous distribution can describe variability in precision better .', 'However , the amount of data needed to distinguish different continuous precision distributions using psychophysics only might be prohibitive .', 'Work by Rouder et al . used a change detection task to compare a continuous-resource model based on signal detection theory to a variant of the IP model [8] .', 'Manipulating bias , they measured receiver-operating characteristics ( ROCs ) .', 'The IP variant predicted straight-line ROCs , whereas the continuous-resource model predicted regular ROCs ( i . e . , passing through the origin ) .', 'Unfortunately , each of the ROCs they measured contained only three points , and therefore the models were very difficult to distinguish .', 'We ourselves , in an earlier study , had collected five-point ROCs using confidence ratings , allowing for an easier distinction between different ROC types; there , we found that the ROCs were regular [10] , in support of a continuous-resource model .', 'A difference between the Rouder study and our current study is that Rouder et al . used ten distinct colors instead of a one-dimensional continuum; this again has the disadvantage of missing the stimulus regime in which the signal-to-noise ratio is low .', 'Moreover , the decision process in their continuous-resource model was not optimal; an optimal observer would utilize knowledge of the distribution of the stimuli and change magnitudes used in the experiment .', "It is likely that the optimal decision rule would have described human behavior in Rouder et al . 's experiment better than an ad-hoc suboptimal rule [33] .", 'Finally , Rouder et al . did not consider variability in precision .', 'In short , our current study does not contradict the results of Rouder et al . , but offers a more plausible continuous-resource model and tests all models over a broader range of experimental conditions .', 'The notion of an item limit on the one hand and continuous or variable resources on the other hand are not mutually exclusive .', 'In the SR model , for example , a continuous resource is split among a limited number of items .', 'Although this model was not the best in the present study , many other “hybrid” models can be conceived – such as a VP model augmented with an item limit , or an IP or SA model with variable capacity [47]–[48] – and testing them is an important direction for future work .', 'Our results , however , establish the VP model as the standard against which any new model of change detection should be compared .', 'The neural basis of working memory limitations is unknown .', 'In the variable-precision model , encoding precision is the central concept , raising the question which neural quantity corresponds to encoding precision .', 'We hypothesize that precision relates to neural gain , according to the reasoning laid out in previous work [13] , [19] , [33] .', 'To summarize , gain translates directly to precision in sensory population codes [49] , increased gain correlates with increased attention [50] , and high gain is energetically costly [51] , potentially bringing encoding precision down as set size increases .', 'The variable-precision model predicts that the gain associated with the encoding of each item exhibits large fluctuations across items and trials .', 'There is initial neurophysiological support for this prediction [52]–[53] .', 'Furthermore , if gain is variable , then spiking activity originates from a doubly stochastic process: spiking is stochastic for a given of value of gain , while gain is stochastic itself .', 'Recent evidence points in this direction [54]–[55] , although formal model comparison remains to be done .', 'The variable-precision model also predicts that gain on average decreases with increasing set size .', 'We proposed in earlier work that this could be realized mechanistically by divisive normalization [19] .', 'Divisive normalization could act on the gains of the input populations by approximately dividing each gain by the sum of the gains across all locations raised to some power [56] .', 'When set size is larger , the division would be by a larger number , resulting in a post-normalization gain that decreases with set size .', 'A spiking neural network implementation of aspects of continuous-resource models was proposed recently [57] .', 'Taken together , the variable-precision model has plausible neural underpinnings .', 'Our results have far-reaching implications for neural studies of working memory limitations .', 'Throughout the field , taking a fixed item limit for granted has been the norm , and many studies have focused on finding its neural correlates [12] , [58] .', 'Even if we restrict ourselves to change detection only , a fixed item limit has been assumed by studies that used fMRI [59]–[65] , EEG [66]–[72] , MEG [67] , [72]–[73] , voxel-based morphometry [74] , TMS [68] , [75] , lesion patients [76] , and computational models [77]–[78] .', 'Our present results undermine the theoretical basis of all these studies .', 'Neural studies that questioned the item-limit model or attempted to correlate neural measures with parameters in a continuous-resource model have been rare [27] , [57] .', 'Perhaps , this is because no continuous-resource model has so far been perceived as compelling .', 'The variable-precision model remedies this situation and might inspire a new generation of neural studies .'], ['Stimuli were displayed on a 21″ LCD monitor at a viewing distance of approximately 60 cm .', 'Stimuli were oriented ellipses with minor and major axes of 0 . 41 and 0 . 94 degrees of visual angle ( deg ) , respectively .', 'On each trial , ellipse centers were chosen by placing one at a random location on an imaginary circle of radius 7 deg around the screen center , placing the next one 45° counterclockwise from the first along the circle , etc . , until all ellipses had been placed .', 'Set size was 2 , 4 , 6 , or 8 .', 'Each ellipse position was jittered by a random amount between −0 . 3 and 0 . 3 deg in both x- and y-directions to reduce the probability of orientation alignments between items .', 'Stimulus and background luminances were 95 . 7 and 33 . 1 cd/m2 , respectively .', 'Ten observers participated ( 4 female , 6 male; 3 authors ) .', 'All were between 20 and 35 years old , had normal or corrected-to-normal vision , and gave informed consent .', 'On each trial , the first stimulus display was presented for 117 ms , followed by a delay period ( 1000 ms ) and a second stimulus display ( 117 ms ) .', 'In the first display , set size was chosen randomly and the orientation of each item was drawn independently from a uniform distribution over all possible orientations .', 'The second display was identical to the first , except that there was a 50% chance that one of the ellipses had changed its orientation by an angle drawn from a uniform distribution over all possible orientations .', 'The ellipse centers in the second screen were jittered independently from those in the first .', 'Following the second display , the observer pressed a key to indicate whether there was a change between the first and second displays .', 'A correct response caused the fixation cross to turn green and an incorrect response caused it to turn red .', 'During the instruction phase , observers were informed in lay terms about the distributions from which the stimuli were drawn ( e . g . , “The change is equally likely to be of any magnitude . ” ) .', 'Each observer completed three sessions of 600 trials each , with each session on a separate day , for a total of 1800 trials .', 'There were timed breaks after every 100 trials .', "During each break , the screen displayed the observer's cumulative percentage correct .", 'Methods for model fitting and model comparison are described in the Text S1 .']]
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['Change detection is a classic paradigm that has been used for decades to argue that working memory can hold no more than a fixed number of items ( “item-limit models” ) .', 'Recent findings force us to consider the alternative view that working memory is limited by the precision in stimulus encoding , with mean precision decreasing with increasing set size ( “continuous-resource models” ) .', 'Most previous studies that used the change detection paradigm have ignored effects of limited encoding precision by using highly discriminable stimuli and only large changes .', 'We conducted two change detection experiments ( orientation and color ) in which change magnitudes were drawn from a wide range , including small changes .', 'In a rigorous comparison of five models , we found no evidence of an item limit .', 'Instead , human change detection performance was best explained by a continuous-resource model in which encoding precision is variable across items and trials even at a given set size .', 'This model accounts for comparison errors in a principled , probabilistic manner .', 'Our findings sharply challenge the theoretical basis for most neural studies of working memory capacity .']
['Working memory is a fundamental aspect of human cognition .', 'It allows us to remember bits of information over short periods of time and make split-second decisions about what to do next .', 'Working memory is often tested using a change detection task: subjects report whether a change occurred between two subsequent visual images that both contain multiple objects ( items ) .', 'The more items are present in the images , the worse they do .', 'The precise origin of this phenomenon is not agreed on .', 'The classic theory asserts that working memory consists of a small number of slots , each of which can store one item; when there are more items than slots , the extra items are discarded .', 'A modern model postulates that working memory is fundamentally limited in the quality rather than the quantity of memories .', 'In a metaphor: instead of watering only a few plants in our garden , we water all of them , but the more plants we have , the less water each will receive on average .', 'We show that this new model does much better in accounting for human change detection responses .', 'This has consequences for the entire field of working memory research .']
['working memory', 'cognitive neuroscience', 'computational neuroscience', 'psychophysics', 'biology', 'sensory perception', 'neuroscience']