The ins and outs of working memory

Figure 5.1 An illustration of focus-switching effect (data from Verhaeghen and Basak 2005, Experiment 1). The top of the figure illustrates the two-tier structure of working memory (McElree 2001): within working memory, only the items held in the focus-of-attention (FoA) are immediately accessible. If the number of items present in working memory exceeds the capacity of the focus, item-swapping becomes necessary. The bottom of the figure shows data from our identity-judgment N-Back task, indicating that the focus has a size of one: there is a step function in response times, with the step occurring between N = 1 and N = 2. The decline in accuracy, which does not measure focus switching, is monotonic over increasing values of N, but not a step function.

the object of the next cognitive operation; (b) a capacity-limited region of direct access corresponding to Cowan’s focus of attention, where a limited number of items is stored that are likely to be selected for subsequent processing; and (c) the activated part of long-term memory, that is able to store additional items over brief periods of time. According to this reasoning, narrow-focus results will be obtained when researchers tap into the first store; wide-focus results will be obtained when the second store is being measured.

The limitations imposed on the focus of attention by both the serial-attention explanation and the tripartite-architecture explanation are hard and fast. Both theories treat a focus-of-one as built into the working memory machinery. It seems to us that this view may be excessively rigid. A different perspective comes from theories that view working memory as an attentional system. A basic supposition from this perspective is that attentional capacity can be allocated flexibly across the perceptual/cognitive field, following the needs of the participant, the demands of the task, or both (e.g., Kahneman 1973; Wickens 1984). This points to a third resolution of the (p.84)

Figure 5.2 An example of what a trial in the 4-back version of the task would look like if all stimuli remained onscreen. In the experiment, stimuli were shown one at a time, in a reading pattern (left to right, then on the next line, etc.); each column was depicted in a different color. The first row was presented at a 2 s/item pace; presentation of subsequent stimuli was participant-paced. The response required was a judgment whether the digit currently projected was identical to the digit previously shown one row higher in the same column.

narrow-focus/wide-focus controversy: perhaps the different values represent the two ends of an underlying continuum of resource allocation (Verhaeghen, Cerella and Basak 2004). Perhaps the focus of attention can vary in size, shrinking to one item when all resources are channeled to the processing of a single item, and expanding up to a size of four when several items can be processed in parallel. On this view, a focus-of-one is not due to a structural limitation of the cognitive system, but rather to the way attention is distributed over the task and stimuli.

One way to test the immutability of the size of the focus of attention is by means of a practice manipulation. Garavan (1998, Experiment 2) enlisted extended practice as a test for a resource-allocation explanation of the focus-of-one outcome in a symbol-counting task. In his study, a substantial focus-switch cost remained after practice: this result has since been replicated by Basak (2005). Both results point to the immutability of the focus size, and by implication, to the existence of a structural limitation.

We took up Garavan’s practice manipulation and applied it to our columnized identity-judgment N-Back task (Verhaeghen, Cerella and Basak 2004). This task is simpler than Garavan’s or Basak’s, especially because the item to be accessed next is always predictable. We hoped that extended practice might lead to automaticity in some of the task components; this in turn should free up resources that could then be applied towards storage inside the focus of attention. The empirical test of this reasoning is straightforward: if the limit on the size of the focus of attention is structural, then we would expect that the N-Back step function (with the step at N = 2) will endure over the course of practice (although the height of the step may be diminished). If, however, the location of the step shifts over the course of practice (perhaps settling finally at N = 5), this would suggest that a focus-of-one derives from resource limits not structural limits.

In our study, five adults practiced the N-Back task for ten hours each, spread over five consecutive days. Figure 5.3 depicts the evolution over sessions of average response time (RT) and accuracy (Verhaeghen, Cerella and Basak 2004). The critical data are again the response time data (top panel). It can be seen that at the onset of practice, the data conform to the focus-of-one account of working memory: There is a sudden jump from N = 1 to N = 2, and a flat RT profile thereafter. After ten hours of practice with the task, however, the pattern of response times differed considerably from that of the first session. There is no longer evidence for privileged access in the (p.85)

Figure 5.3 Average response times and accuracy over sessions in a study in which participants practiced the identity-judgment N-Back task over ten sessions (Verhaeghen, Cerella and Basak 2004). Error bars denote standard errors calculated at the group level. Response times initially showed a step function indicating a focus of size one; at the end of practice, however, the step has disappeared and the focus has expanded to hold four items.

N = 1 condition. Rather, the response time increases linearly over the range N = 1 to N = 4, with a shallow slope of about 30 ms/N. The breakpoint is now situated at N = 5: going fromN = 4 to N = 5 the increment in response time is about twice as large as that extrapolated from the linear trend. In other words, it appears that with extended practice participants were able to expand the focus of attention to accommodate four items.

This result suggests that with extended practice the focus of attention can be expanded to hold four items, even in a task requiring serial attention which initially limits processing to a single item. Two additional points are worth noting. First, our data suggest that four may be the ultimate limit of the size of the focus. This may reflect a limit on total activation in the relevant storage structures of the cortex (e.g., Vogel and Machizawa 2004; see Usher, Cohen, Haarmann et al. 2001, for a mathematical model of flexible allocation). Second, research has shown that not every task showing an initial focus of one is amenable to a practice-related focus expansion: Garavan’s symbol-counting task is not (Garavan 1998; Basak 2005, Experiment 3); neither do all subject groups show this expansion: Basak, Cerella and Verhaeghen (2004 failed to obtain focus expansion in the N-Back task in a group of older adults).

(p.86) To summarize, we believe that the size of the focus of attention is not fixed, but may take any value between one and four. (Put facetiously, the correct magical number may be ‘2.5 plus-or-minus 1.5’). The size obtained in any particular case appears to be a function of both task characteristics and individual differences, as well as their interaction, the many dimensions of which have yet to be explored.

Focus switching and retrieval dynamics within working memory: a walk down working memory lane

The focus-switching pulse partitions working memory into two zones: a variable-size part characterized by fast access times, and a surrounding part of indefinite size with slower access times. The division raises the question of what type of access process operates within each zone. Interestingly, our studies reveal different retrieval dynamics for the two cases.

Retrieval dynamics within the focus of attention

The extended practice data allow us to examine retrieval processes within the expanded focus of attention. At first blush, one might expect that they are all accessed at the same speed, but this is not necessarily true. In a limited-capacity system, items will compete for activation, and the competition might be greater when the system has to maintain a larger set of items. For instance, in support of a focus size of four, Cowan (1999) cites Trick and Pylyshyn (1994) on the subitizing span, and Fisher (1984) on parallel channels in consistently mapped visual search; both are processes characterized by shallow, positive, load functions. Another memory process showing the same load function is short-term memory scanning (Sternberg 1966). Mathematical models of this process are highly developed, and may converge on the schema of parallel, limited-capacity memory access (Murdock 1971; Ratcliff 1978; Van Zandt and Townsend 1993).

Our data conform to Cowan’s expectation: as can be seen over the last sessions in Figure 5.3, there is a significant response time over N slope of about 30 ms/item over the N = 1 to N = 4 range. The positive slope strongly suggests that the focus of attention is not content-addressable: rather, its contents need to be searched.

Pursuing the hypothesis that the search process within the focus is of a parallel and limited-capacity nature, we conducted an ex-Gaussian decomposition of the response time distributions. The ex-Gaussian model assumes that each response time can be represented as the sum of a Gaussian or normally distributed random variable and an independent exponentially distributed random variable. The ex-Gaussian distribution is described by three parameters: mu and sigma are the mean and standard deviation of the normal distribution and tau is the mean of the exponential distribution. Mu and sigma determine the location of the leading edge of the distribution; tau reflects slow responses at the tail of the distribution (the skew). Hockley (1984, Experiment 1) has shown that the ex-Gaussian signature of the Sternberg search process is a linear increase in tau over memory load, while mu and sigma remain constant. Figure 5.4 (middle panel) presents the results of the ex-Gaussian decomposition for Session 10 of the Verhaeghen, Cerella and Basak study (2004). Clearly, the linear increase in response time over N within the expanded focus of attention is due to an increase in tau, as would be expected when a limited-capacity parallel search process is involved.

Thus three operations – our version of N-Back, memory scanning and subitizing – show shallow load functions with about equal slopes, and at least two of these operations – N-Back and memory scanning – have the same ex-Gaussian signature. The processing involved in all three cases may be traceable to the same modus operandi within the focus of attention – an hypothesis that merits more research. The conceptualization of within-focus search as a parallel limited-capacity (p.87)

Figure 5.4 Ex-Gaussian decomposition of response times in our identity-judgment N-Back task, under three types of circumstances: predictable switching with a focus size of one (Session 1 data from Verhaeghen et al. 2004), predictable switching with a focus size of four (Session 10 data from Verhaeghen et al. 2004), and unpredictable switching with a focus size of one (data from Basak 2005, Experiment 4). Error bars denote within-individual standard errors for the leftmost and center panel, and group standard errors for the rightmost panel.

(p.88) process may further explain why the capacity of the focus is not fixed. If access occurs in parallel but capacity-demanding channels, the number of supportable channels is likely to be a function of the total resources available to the working memory system. If a task is very demanding, the residual may allow only a single active channel. As a task becomes automated resources are freed up, allowing the system to open more channels to simultaneous search.

Retrieval dynamics in working memory outside the focus of attention

What about search outside the focus of attention? So far the story seems simple: both Verhaeghen and Basak (2005), and Verhaeghen, Cerella and Basak (2004, Session 1) obtained statistically flat slopes over values of N larger than 1 (see Figures 5.1 and 5.3). Items outside the focus of attention therefore appear to be directly content-addressable, much in the way elements stored in long-term memory are (see also McElree 2001).

However, this conclusion needs to be qualified. First, Verhaeghen and Basak (2005) observed a flat slope only for college-age adults; older adults showed a slope of about 70 ms/item. Second, Basak (2005, Experiment 1) found a slope of about 240 ms/register in focus-switch costs over N in a version of Garavan’s counting task. Third, Basak (2005, Experiment 4) found a slope of about 90 ms/N in a modification of the N-Back task in which the item to be accessed could be from any position 1-back to N-Back (making this a hybrid between an N-Back task and a memory scanning task). Taken together, these results suggest that although the region outside the focus of attention can be content-addressable, it will actually be so only under optimal circumstances – predictable switching performed by high-functioning subjects. Under other circumstances, an explicit search process is needed.

This search process is clearly slower, by a factor of at least three, than the limited-capacity parallel search process that seems to govern the focus of attention. Additionally, it has a different ex-Gaussian signature, as can be seen in the right-hand panel of Figure 5.4 (data from Basak 2005, Experiment 4). Whereas the search cost within the focus is due to an increase in the skew parameter alone, the search cost outside the focus seems to involve the mean and standard deviation of the Gaussian parameters as well. Thus, the latter process is probably not a capacity-limited parallel search. Its signature resembles that of a visual search task (Hockley 1984), which is typically considered to be serial and self-terminating. More research is needed to confirm this conclusion, but it is an intriguing hypothesis.

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