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Limited Capacity Hypothesis Statement

We found that varying the number of to-be-remembered features from a single object affected performance on a memory task. The key innovation of this study was that memory for multiple features was measured within a single object, rather than memory for features across multiple objects (see also Vogels et al., 1988). The special case of a single object is important, because it eliminates any possibility of the effects being mediated by the presence of multiple objects. For example, there was no opportunity for effects to arise from interference between multiple objects (e.g., McConnell & Quinn, 2000) or from confusion regarding which features went with which objects (e.g., Wheeler & Treisman, 2002). In general, using a single object is a way to study the effects of having to remember multiple features, with no possibility of confounding effects due to multiple objects. That the number of to-be-remembered features affected memory performance with a single object indicates that feature memory does not have unlimited capacity, and thus a discrete-object limit on visual memory cannot be the only limitation in visual memory. In addition, the relatively small effects found in Experiment 2 allow one to reject the fixed-capacity model, as well. The effect of the number of features falls between the two extreme models.

The following discussion has four parts. The first part relates our study of a single object to the larger literature on multiple objects. The next two parts address the theoretical interpretation of the effect of the number of relevant features, and the fourth part discusses the possible reasons for the difference in the magnitudes of the effects found in Experiments 1 and 2.

Effect of the number of features with multiple objects

An influential study on visual working memory (Luck & Vogel, 1997) came to a contrasting conclusion, that visual working memory is not limited by the number of to-be-remembered features, but only by the number of objects in which those features are instantiated. In those experiments, subjects were presented with brief study displays of two to six colored lines, followed 0.9 s later by a test display that was either unchanged or different for one object. The subjects responded either “same” or “different” to the test display. In different blocks of trials, the subjects were instructed to detect changes in color, orientation, or both. Performance decreased as the number of objects increased, but little if any effect was apparent of the number of relevant features on performance. This result with multiple objects is in apparent conflict with the present study.

Later studies, however, have indicated that features do play a role (Cowan, Blume, & Saults, 2013; Davis & Holmes, 2005; Marshall & Bays, 2013; Olson & Jiang, 2002; Wheeler & Treisman, 2002; Xu, 2002). A particularly simple demonstration of an effect of the number of relevant features was reported in Fougnie et al. (2010). They presented three stimuli that varied in color and orientation, and probed the memory of one feature in one object. Subjects had to report the relevant feature by using the adjustment method of Wilken and Ma (2004; see also Zhang & Luck, 2008, 2011), which allows for estimates of both the precision of memories and the number of items remembered. In different blocks of trials, subjects had to remember the color, the orientation, or both. Increasing the number of relevant features resulted in a decrease in precision but no effect on the number of remembered objects. Fougnie and colleagues (Fougnie et al., 2010; see also Fougnie, Cormiea, & Alvarez, 2013) suggested a hybrid model in which visual memory is limited both by the number of to-be-remembered objects and, separately, by the number of to-be-remembered features. The number of objects influences both storage capacity and precision, whereas the number of features influences only precision. The present results are also consistent with such a hybrid model, in that we found that processing was limited by the number of to-be-remembered features. Our single-object experiments do not speak to whether or not a further limit is imposed by the number of to-be-remembered objects.

The nature of the capacity limits: Storage capacity versus processing capacity

The capacity limitations observed in the present study might concern processing capacity, in the sense of the amount of information processed per display (Broadbent, 1958), rather than storage capacity, defined by the number of objects per display (Miller, 1956). Discussions regarding the capacity limitations of visual memory have often focused on limitations in the storage of visual information. This is perhaps a natural focus when thinking about memory. But, it is important to also consider possible processing limitations on the encoding, maintenance, and retrieval of visual information (see Cowan & Morey, 2007; Fougnie & Marois, 2009).

For an intuition regarding a precision limit due to limited processing capacity, consider Shaw’s (1980) sample size model, which was the basis for our fixed-capacity predictions. According to this model, one can make n samples of a stimulus representation per unit time. For a single relevant feature, these samples can all be on one feature. For four relevant features, the samples must be divided, which results in a less precise estimate for the individual features. For the case of evenly divided samples, the variance of the estimate is inversely related to the number of samples, and thus the standard deviation doubles when the memory set size increases by a factor of 4. Thus, the capacity limits observed in this study could reflect a processing capacity limitation like that captured in this model, which would manifest as a limit on the precision of the representation of the visual information. This sampling intuition is a start, but it does not speak to what specific aspect of processing is limited: Is it encoding, maintenance, retrieval, or all of the above?

A specific processing-capacity hypothesis has been suggested for the effect of multiple features by Bays, Gorgoraptis, Wee, Marshall, and Husain (2011). They suggested a combination of a memory storage limit for objects and a memory encoding limit for the features within an object. To test this idea, they varied both stimulus duration and the numbers of features and objects, and found results consistent with this two-component hypothesis. Recently, this idea has been elaborated by Sewell, Lilburn, and Smith (2014).

A discrete-object limit can sometimes mimic a precision limit. Zhang and Luck (2008) suggested that the effects on precision that they inferred through a cue estimation procedure could be accounted for under a model that assumed a discrete-object limit on storage. Specifically, they proposed a model in which, when the memory set size is below the storage capacity limit, multiple copies of some objects can be stored, resulting in a measured improvement in precision. This solution does not work for the present study, because multiple copies of the (single) study object would improve the precision of all of the features of the object; there would be no advantage for specifying a single feature as relevant, rather than all four features.

The tendency to focus on storage limitations when considering memory might be a reason why the special case of a single object has been neglected. If one is focused only on possible limitations of memory storage, then it would be unlikely to consider a single-object case, because it would be unlikely to reveal the limits of the system.

Memory or perception?

The study–test paradigm used here was intended to measure visual memory, but might the observed effect of set size have been due to perception? This is a difficult question, and few studies have directly addressed it (e.g., Bays et al., 2011; Fougnie & Marois, 2009; Mazyar, van den Berg, & Ma, 2012; Sewell et al., 2014). Consider two opposing arguments. An argument for a perceptual account comes from the experiment of Mazyar et al. (2012), in which they found similar effects of the number of objects/features using matched search and memory paradigms (but see McLean, 1999). Mazyar and colleagues interpreted this result as being consistent with perceptual limits and no memory limits.

An argument against the perceptual account is that some experiments have shown no effect of the number of simultaneous objects/features using search tasks (e.g., Huang & Pashler, 2005; Scharff, Palmer, & Moore, 2011). The authors of these studies interpreted their results as showing no perceptual limits for these kinds of simple stimuli and tasks, and thus that memory must be the limit in study–test paradigms. Critically relevant to memory, this simultaneous–sequential procedure has been applied to the effect of multiple objects on memory performance by Sewell et al. (2014; see also Liu & Becker, 2013; Mance, Becker, & Liu, 2012). Sewell and colleagues found equal performance for simultaneous and sequential displays, consistent with no limit on perception, despite an effect of the total number of items to be remembered. The next step would be to use these methods to study the effect of the number of features with a single object. Sorting out this issue will be important, because one way to “save” a simple memory hypothesis is to attribute to perception any exception to the memory hypothesis.

Experiment 1 compared to Experiment 2

Experiments 1 and 2 yielded effects that differed markedly in magnitude. The effect in Experiment 1 was as large as that predicted by fixed-capacity models, whereas the effect in Experiment 2, though inconsistent with unlimited-capacity models, was much less than predicted by fixed-capacity models. Several procedural differences distinguished the two experiments, and therefore we cannot say with certainty what is the source (or are the sources) of the difference. We offered some speculations in the discussion of Experiment 2.

A broader view is that whatever the specific cause for the difference in effect sizes between the two experiments, it is an example of how the details of the procedure can change the effect of the number of relevant features. The task can change, for example, how the number of decisions varies with the number of features (see Busey & Palmer, 2008, for an example of this in visual search). The task can simplify or complicate the retrieval process (see Anderson & Bower, 1972, and Kintsch, 1970, for examples of this in verbal memory). The experiments reported here, for example, used a cued recognition task in which subjects had to judge a particular cued aspect of the study display. Specifically, one of four features was cued. In prior studies, an entire object (or set of objects) had been cued (e.g., Palmer, 1990). This cued recognition task was chosen because it minimizes the potential for contributions from decision and retrieval processes to the magnitude of the observed memory-set-size effects. The more common task of probe recognition, in which subjects judge whether a given stimulus was present anywhere in the memorized display (e.g., Mazyar et al., 2012) probably presents a more difficult retrieval and decision problem, because all of the elements of the study display are relevant to the response. But that task, in turn, presents a simpler decision and retrieval problem than does other change detection (e.g., Keshvari et al., 2013; Luck & Vogel, 1997; Scott-Brown & Orbach, 1998), which presents the subject with many decisions, since all of the elements of the study and test display are relevant. It remains to be worked out how the specific task influences the effect of the number of to-be-remembered features.

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