An assessment of fixed-capacity models of visual working memory

Abstract

Visual working memory is often modeled as having a fixed number of slots. We test this model by assessing the receiver operating characteristics (ROC) of participants in a visual-working-memory change-detection task. ROC plots yielded straight lines with a slope of 1.0, a tell-tale characteristic of all-or-none mnemonic representations. Formal model assessment yielded evidence highly consistent with a discrete fixed-capacity model of working memory for this task.working memory ͉ capacity ͉ mathematical models of memory ͉ short-term memory T he study of the nature and capacity of visual working memory (WM) is both timely (1) and controversial (2, 3). A popular conceptualization is that visual WM consists of a fixed number of discrete slots in which items or chunks are temporarily held (2, 4, 5). Nonetheless, there are dissenting viewpoints in which the discreteness is taken as, at most, a convenient oversimplification (6, 7). In this article, we provide a rigorous test of the fixed-capacity model for a visual WM task. Herein, we apply this test to items that differ in color, although the test is suitable to examine the generality of capacity limits across various materials.We used a common version (8-15) of the task popularized by Luck and Vogel (4, 16) (see Fig. 1A). At study, participants are presented with an array of colored squares. At test, a single square is presented; this square is either the same color as the corresponding square in the study array (a "same trial") or a novel color (a "change trial"). Participants simply decide whether the test square is the same as or different from the corresponding studied square. In this task, where the color of each square is unique and the colors are well separated, capacity is the number of squares (objects) that may be held in visual WM. This object-based view of capacity is supported by previous research (4), in which performance does not vary with the number of manipulated features per object.Previous demonstrations of fixed capacity have relied on plotting capacity estimates as a function of the number of to-be-remembered items. Fixed capacity is claimed because capacity estimates tend to asymptote at three to four items for array sizes of four to six items. This approach, however, is not the most rigorous for this model. There are three weaknesses in previous demonstrations: (i) The asymptote of the capacity estimated may be mimicked by models without recourse to fixed capacity; (ii) previous demonstrations are made with aggregate data, and an asymptote in the group aggregate does not necessarily imply asymptotes in all or any individuals; and (iii) the stability of these asymptotes has not been formally assessed. These weaknesses motivate a more constrained test, to be presented subsequently.The Fixed-Capacity Almost-Ideal Observer Model. We define the fixed-capacity ideal observer as one who maximizes the probability of a correct response given the constraint that visual WM is discrete and limited in the number of items that may be held. Here, we derive th...

Interference and memory capacity limitations.

“…Participants' memory thus seems to be capacity-limited as predicted by a slot-model. In this and the following literature, fixed and limited capacities have thus been used as diagnostic of slotlike memory representations vs. continuous resource-like representations, often based on sophisticated mathematical analyses (e.g., van den Berg et al, 2012;Rouder et al, 2008; W. Zhang & Luck, 2008).…”

“…With these assumptions, the estimated memory capacity K is given by P × (H − FA), where P is the total number of presented items, and H and FA are the hit rate and the false alarm rate, respectively (see e.g. (Rouder et al, 2008)). With an equal number of "old" and "new" test items, the formula can be written as K = P (2pcor − 1), where pcor is the proportion of correct responses.…”

“…Examples include Endress and Potter's (2014a) interference-rich conditions, or the change detection paradigm (Luck & Vogel, 1997) that has probably become the most prominent test case of visual WM in recent years (e.g., Alvarez & Cavanagh, 2004;van den Berg et al, 2012;Piazza et al, 2011;Rouder et al, 2008;Vogel et al, 2006;W. Zhang & Luck, 2008).…”

“…For example, is WM better characterized as a set of discrete memory "slots" in which items can be placed (see, among many others, Cowan, 2001;Hartshorne, 2008;Luck & Vogel, 1997;Piazza, Fumarola, Chinello, & Melcher, 2011;Rouder et al, 2008; W. Zhang & Luck, 2008) or rather as a continuous resource (e.g., Alvarez & Cavanagh, 2004;Bays & Husain, 2008;van den Berg, Shin, Chou, George, & Ma, 2012;Just & Carpenter, 1992;Ma, Husain, & Bays, 2014)?…”

Discrete-Slots Models of Visual Working-Memory Response Times

“…An alternative approach is to constrain those parameters by imposing assumptions involving fixed memory capacity across the different set-size conditions. For example, in fitting their discrete-slots models to ROC data, Rouder et al (2008) denoted the number of available slots by K and assumed that the value of K was constant across the different memory set sizes N. Thus, across the different set size conditions, they assumed that the probability that any given study item would occupy one of the slots when memory was probed would be given by m = min(K/N, 1). Because they estimated fractional values of K in fitting the model, they were clearly assuming that the number of available slots in visual WM was variable across trials but that the mean of this variable number of slots was fixed across set sizes.…”