nature neuroscience VOLUME 17 | NUMBER 3 | MARCH 2014 347
Working memory refers to the short-term storage and manipulation
of sensory information lasting on the order of seconds1. It has been
associated with persistent neural activity in many brain regions2 and
is considered to be a core cognitive process that underpins a range
of behaviors, from perception to problem solving and action control.
Deficits in working memory have been reported in many brain disorders;
whereas performance on working memory tasks improves with brain
development from childhood to early adulthood, it declines in the
elderly, and is closely related to measures of intelligence.
The classic view has been that working memory is limited in capacity,
holding a fixed, small number (K) of items, such as Miller’s ‘magical
number’ seven3 or Cowan’s four4. Such hypotheses have arisen from
tasks such as letter recall or change detection that use a discrete or
categorical stimulus set, such as a small number of easily identifiable
colors5,6. For vision, a highly influential proposal has been that items
retained in working memory are held in three or four independent
object ‘slots’, one for each item stored5. This slot conceptualization of
working memory is all or none: an object either gets into a memory
slot and is then remembered accurately, or it does not, in which case
it is not remembered at all. This framework7 has had a huge influence
on interpretation of neural data—imaging, monkey neurophysiology
and human electrophysiology—as well as on studies of normal
development and aging, the effects of training working memory, and
Resource models of working memory
Recent work has led to substantial advances in our understanding
of the structure and organization of working memory. In particular,
compelling reasons to reconsider the classic view have arisen from
psychophysical studies showing that the precision of recall declines
continuously as the number of items to be remembered increases
(Fig. 1a–c), and increasing the salience or goal relevance of a stimulus
causes it to be stored with enhanced precision, at the cost of poorer
memor y for other stimuli (Fig. 1d–f). Although interpretation
of these results remains an active area of debate, neither of these
findings would have been predicted on the basis of the original slot
model5, in which every item is either stored with high precision or
not at all (Fig. 2a).
In contrast, the results are naturally accommodated by models that
consider working memory to be a limited resource, distributed flex-
ibly between all items in a scene8–16 (Fig. 2b–d). Crucially, although
resource models consider working memory to be extremely limited,
they do not invoke a fixed item limit on the number of objects that can
be stored. Thus, for these models, K is not the fundamental metric with
which to measure working memory. According to these views, it is not
the number of items remembered, but rather the quality or precision
of memory that is the key measure of working memory limits.
Resource models of working memory8,11,17 are based on two
premises. First, the internal representations (or measurements) of
sensor y stimuli are noisy, that is, they are corrupted by random,
unpredictable fluctuations. Second, the level of this noise increases
with the number of stimuli in memory. This increase is attributed
to limitations in the supply of a representational medium that is
distributed between items; thus, the more resource is allocated to
an item, the less noise is present in its representation and the more
precise the recall of that item. Resource models have strong links to
other areas of neuroscience and psychology. The premise that internal
representations are noisy is common to all signal detection theory and
many Bayesian models of perception, whereas the increase in noise
with set size is also shared with models of attention.
Just as is common in perceptual psychophysics, one way to test
working memory models based on the concept of noise in memory
representations is to vary stimuli on a fine scale, thereby manipulat-
ing the signal-to-noise ratio (see below). Wilken and Ma modified
the method of adjustment, long employed in perceptual studies, to
multiple-item working memory8 (Fig. 1a). In this delayed-estimation
technique, both the stimulus and the response space are analog
(continuous) rather than discrete. This is very different from conven-
tional methods for probing visual or other types of working memory
(for example, change detection or digit span in verbal working
memory), where the stimulus or change in stimulus is held constant
to obtain a discrete measure of K or span.
The delayed-estimation technique has now been used to study
memory of a range of visual features, including color, orientation and
1Center for Neural Science and Department of Psychology, New York University,
New York, New York, USA. 2Department of Experimental Psychology and Nuffield
Department of Clinical Neurosciences, University of Oxford, Oxford, UK. 3Institute
of Neurology, University College London, London, UK. 4Institute of Cognitive
and Brain Sciences, University of California Berkeley, Berkeley, California, USA.
Correspondence should be addressed to W.J.M. (email@example.com).
Received 21 October 2013; accepted 23 January 2014; published online
25 February 2014; doi:10.1038/nn.3655
Changing concepts of working memory
Wei Ji Ma1, Masud Husain2 & Paul M Bays3,4
Working memory is widely considered to be limited in capacity, holding a fixed, small number of items, such as
Miller’s ‘magical number’ seven or Cowan’s four. It has recently been proposed that working memory might better be
conceptualized as a limited resource that is distributed flexibly among all items to be maintained in memory. According to
this view, the quality rather than the quantity of working memory representations determines performance. Here we consider
behavioral and emerging neural evidence for this proposal.
npg © 2014 Nature America, Inc. All rights reserved.
34 8 VOLUME 17 | NUMBER 3 | MARCH 2014 nature neuroscience
motion direction8–10,15,16,18–21. Rather than exhibiting the abrupt, step
decline that would be expected on reaching a capacity limit of a fixed
number of items5, in every case, recall variability has been shown to
gradually and continuously increase as set size increases (Fig. 1b,c),
as predicted if working memory resources are shared between items.
Across a range of studies, this relationship between precision of recall
and set size has been shown to follow a power law9,11,15,17.
Although the concept of a limited working memor y resource
has considerable explanatory power for behavioral data (discussed
below), the exact nature of the representational medium remains
to be established and is an important goal for neurophysiological
investigation. The majority of electrophysiological and computational
studies have confined themselves to studying memory for a single
object. However, understanding the neural effects of increasing set
size will be crucial for determining the cognitive architecture underly-
ing working memory and distinguishing between competing models
(Fig. 2b–d). Resource models are already beginning to have an effect
on systems neuroscience. Animal studies have started to measure
working memory behaviorally in non-human primates using set
sizes >1, with testing of resource models in mind22–25. Looking ahead,
interpretation of such neural data will crucially depend on having a
sound theoretical framework for behavior. In this review, we focus on
emerging data from studies that have employed simple visual memo-
randa, as they are the easiest to model and have been used in both
human and animal studies.
Flexible resource allocation
Flexibility in memory allocation11 represents a crucial distinction
between competing slot and resource accounts of working memory.
Rather than being limited to a fixed storage resolution, a growing body
of evidence indicates that memory resources can be unevenly distrib-
uted so that prioritized items are stored with enhanced precision com-
pared to other objects. Voluntary control over resource allocation has
been demonstrated by studies in which one stimulus in a memory array
is indicated as more likely to be selected for test, resulting in a robust
gain in recall precision for the cued stimulus10,18,26. Critically, this
recall advantage appears to come with a corresponding cost to other
stimuli in memory, which are recalled with less precision10,11,26.
These findings are consistent with an unequally distributed, but
limited, resource: when more resource is devoted to a prioritized item,
less is available for other objects. Notably, these effects cannot be
explained simply by biased competition for sensory processing favor-
ing a prioritized item27, for several reasons. First, equivalent find-
ings are observed for stimuli presented one at a time in sequence10,
eliminating competition in sensory input (Fig. 1d–f). Second, cues
presented following prolonged examination of a stimulus array are
of similar effectiveness as those presented before the array26, indicat-
ing that working memory resolution can be changed after the initial
encoding is complete. Finally, recall precision can be influenced by
retrospective cues, presented long after the array is extinguished, that
is, when there is no sensory input available28.
These results indicate that the allocation of limited working
memory storage can be controlled and updated with changing
behavioral priorities. Similar recall advantages and costs have been
observed for objects that are visually salient11,26,29, even when test
probability is equal, indicating an automatic component to memory
allocation that might be linked to visual attention. Further evidence
that resource is associated with allocation of visual attention has
arisen from demonstration of recall advantages for targets of
saccades11,29,30 and for targets of covert shifts of attention, as inferred
In oculomotor areas, including frontal eye field (FEF) and lateral
intraparietal area (LIP), neural activity is modulated by both stimulus
salience and task relevance to produce retinotopic maps of stimulus
priority31. Such priority maps have been implicated in the guidance
of visual attention and eye movements, but could also be involved in
determining how working memory resources are distributed between
objects. When eye movement sequences are interrupted, the upcom-
ing saccade target is held in memory with high resolution, whereas
objects that had previously been the focus of attention are represented
more coarsely11. This allocation may reflect a dual role of working
memory representations in visual exploration, whereby memory for
the saccade target is compared with post-saccadic input to correct
inaccurate eye movements, and a record of attended locations is main-
tained to inhibit re-examination of previously explored locations32.
Sources of noise
Errors in recollection of a stimulus could arise from multiple sources:
noise in the initial stage of sensory processing, in storing or main-
taining information in a stable state once the sensory input has been
Figure 1 Evidence from delayed estimation
challenging the slot model. (a) Example of a
color delayed-estimation task8. Observers must
report the color in memory that matches a probed
location by selecting from a color wheel. (b) The
distribution of responses relative to the correct
(target) color depends on the number of items
in the sample display. (c) Recall variability as
measured by the standard deviation (SD) of
error increases gradually and continuously with
set size. In the item-limit (slot) model, this
function would be flat up to set size 4. Adapted
with permission from ref. 9. (d) Example of
an orientation delayed-estimation task with
sequential presentation10. Observers must
report the orientation in memory that matches a
probed color by adjustment of the probe, using
a response dial. An item of the cue color (here,
green) is more likely to be probed than items of
other colors, making it higher priority for accurate
storage. (e,f) Response distributions and standard deviation of errors for the orientation estimation task. When an item of the cue color is present in the
sequence, it is remembered with enhanced precision (lower standard deviation) compared with other items in the sequence. Comparison with trials on which
the cue color is absent (no cue) shows that uncued items are recalled with lower precision when a cued item is present. Adapted with permission from ref. 10.
Number of items
1 2 3 4 5 6
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nature neuroscience VOLUME 17 | NUMBER 3 | MARCH 2014 349
removed, or in the final stage of decoding (retrieval) and response
generation. It is important to distinguish between these possibilities.
Working memory precision is inevitably limited by the precision
afforded by early sensory representations, which is influenced by stimu-
lus factors such as contrast. Moreover, encoding of sensory information
is not instantaneous26,33, so recall errors following brief exposure to
multiple or complex stimuli may reflect incomplete encoding. The
quality of encoding might also depend on attentional limitations34,35
instead of, or in addition to, storage capacity limitations. Indeed,
when the time available for encoding items into working memory
is systematically varied, the rate at which recall precision increases
over short exposures depends on the number of visual elements26,
consistent with a continuous parallel accumulation of sensory infor-
mation into memory36. However, with prolonged exposures, precision
does not continue to increase, but rather approaches a maximum
value that depends on the number of items stored, which is consist-
ent with a limit on how much information can be simultaneously
represented in working memory26.
During the maintenance stage, additional noise might be added.
Recall variability has been shown to increase with the duration of
the delay period (for example, see ref. 28), which is consistent with a
gradual accumulation of error resulting from noise in memory, but
is difficult to explain solely in terms of noise at encoding or decoding
stages. The possibility that noise in working memory recall arises pre-
dominantly at the decoding or response stage has generally received
less attention. However, it is unlikely to be a major contributor in
delayed-estimation tasks, as only one of the items in memory is speci-
fied for recall; thus, noise arising at this stage would not be expected
to produce set size–dependent effects.
The search for a neural basis for limits on working memory
performance has primarily focused on brain areas that are active
during the delay period of memory tasks. Investigations using
functional magnetic resonance imaging (fMRI) have identified regions
of human prefrontal and posterior parietal cortex that show elevated
blood oxygen level–dependent (BOLD) signals during working
memory maintenance37–39 (Fig. 3a), whereas electroencephalogra-
phy (EEG) studies have observed a sustained negativity over posterior
electrodes contralateral to memorized stimuli21,40 (the contralateral
delay activity, CDA). Both BOLD and CDA signals are sensitive to the
number of items in memory, displaying increasing37,38,40 or inverted
U–shaped21,39,41 responses to increasing load.
Within the slot framework, an increase in neural activity with
memory load has been considered to be the signature of a working
memory store, based on the assumption that increasing load engages
more of a store’s capacity. Indeed, a number of studies37,38,40 have
reported that neural signals reach an abrupt plateau at higher memory
loads, potentially corroborating the hypothesis of a maximum number
of objects that can be stored5. However, unambiguously identifying a
signal plateau in the presence of noise is not trivial, and the methods
used to date have not been rigorous, either relying on appeals to
subjective visual judgment or on the statistical error of accepting the
It therefore remains to be established whether these neural signals
reach a maximum at a particular set size and then plateau, or increase
continuously toward an asymptotic limit (for example, according to
a saturation function; Fig. 3b). One perspective is that increases in
CDA amplitude may actually be explained by amplitude modula-
tion asynchrony, whereby a systematic decrease in the peak, but not
trough, of alpha-band oscillation can produce the appearance of a
sustained negativity (the CDA) when trial averaged42.
At the level of individual differences, the rate at which neural
signals change with load is correlated with working memory per-
formance measures40,43, although the common assumption that this
reflects differences in signal plateau has again not been rigorously
examined. Notably, both BOLD and CDA measures show effects of
the complexity as well as the number of visual stimuli in the memory
array37,44, suggesting that the amplitude of neural signals may reflect
both information content and object number. Consistent with this,
the amplitude of the CDA is correlated with precision of recall45, even
when only a single item is held in memory46 (Fig. 3c).
In contrast with the slot framework, resource models of working
memory dictate that the same resources are engaged whether one
or multiple visual items are stored. This is also true for the latest
revisions of the slot model, which effectively distribute resource in
discrete quanta19 (see below). Thus, increases in neural activity with
load should not be considered the definitive marker of a working
Figure 2 Models of working memory. (a) In the slot (or item limit) model of
working memory4,5, each visual item is stored in one of a fixed number of
independent memory slots (here, 3) with high resolution (left, illustrated,
by narrow distribution of errors around the true feature value of a tested item).
When there are more items than slots, one or more items are not stored and
the slot model predicts that errors in report of a randomly chosen item will be
composed of a mixture of high-precision responses (right, blue component of
distribution corresponds to trials when the chosen item received a slot) and
random guesses (green component corresponds to trials where it did not get
a slot). (b) Resource models of working memory8,11,17 fundamentally differ:
they propose a limited supply of representational medium that is shared out
between items, without a limit to the number of items that can be stored.
Crucially, the precision with which an item can be recalled depends on the
quantity of resource allocated to it. If resources are equally distributed
between objects, error variability (width of the distribution) increases
continuously with the number of items (compare distribution of error for one
versus four items), with a normal distribution being commonly assumed.
(c) In discrete-representation models19, the working memory medium is divided into a discrete number of quanta, similar to the slot model. However, these
slots are shared out between items; in this respect, this type of model is much closer to resource models than the original slot model (a). For low set sizes
(for example, one item shown at left), the quanta combine to produce a high-resolution memory of an item. However, for higher set sizes, above the number
of slots available (right), all items get either one or zero quanta, predicting a mixture of low-resolution recall and random guesses. Note how this distribution
differs from those in a and b. (d) Variable-precision models15,16 propose that working memory precision varies, from trial to trial and item to item, around
a mean that decreases with increasing number of items as a result of limited resources. This model predicts that recall errors will be made up of an infinite
mixture of distributions (assumed normal) of different widths. Variability in precision could stem from variability in resource or from bottom-up factors.
representations Variable precision
npg © 2014 Nature America, Inc. All rights reserved.
35 0 VOLUME 17 | NUMBER 3 | MARCH 2014 nature neuroscience
memory store. Nonetheless, there are several reasons why load-dependent
signals might arise in a resource-based memory system. At the neu-
ronal level, BOLD and EEG signals are believed to primarily reflect
synaptic conductances, rather than spiking activity, with both excita-
tory and inhibitory conductances contributing to the amplitude of
these signals47. As a consequence, a working memory network whose
spiking activity level is independent of memory load, for example, as
a result of divisive normalization (see below), may nonetheless dem-
onstrate increases in BOLD and EEG amplitude with load simply as a
result of an increase in synaptic processing with increasing set size.
Alternatively, load-sensitive signals might not be associated with
coding of object features directly, but instead with maintenance of
‘meta-information’ that is required to control resource allocation or
maintain bindings between features in dimension-specific stores48,49.
Thus, if features that belong to an object need to be maintained bound
veridically, increases in signal with working memory load might
reflect greater demands resulting from feature binding rather than
increasing number of items per se (see below).
Single-unit recordings in monkeys have identified neurons with
persistent delay period activity in frontal and parietal areas, consistent
with analogous regions displaying elevated BOLD signals in humans.
A recent study46 combining intracranial recording and EEG demon-
strated that the magnitude of the local field potential in prefrontal
areas is correlated with precision of recall, and may contribute to the
CDA signal observed in humans.
In another investigation, recordings from prefrontal and posterior
parietal neurons under varying working memory load revealed that
the ability to decode stimulus parameters from persistent activity
declined continuously with increases in memory load22. In other
words, the information about a stimulus that can be extracted
from delay period activity gradually decreases as the total number of
stimuli in memory increases. This observation of graded degradation
is consistent with division of working memory resource between
items. However, memor y items appear to compete for resources
only with other stimuli presented in the same hemifield, suggest-
ing a degree of hemispheric independence in monkeys that is much
greater than that observed in humans50.
Recent advances in multivariate analysis of fMRI have widened the
search for working memory representations to include earlier cortical
areas. Studies based on multivoxel techniques have successfully decoded
simple visual features held in memory from signals in visual areas,
including V1, where the BOLD signal is not globally elevated above
baseline levels during working memory maintenance51–53 (Fig. 3d).
Furthermore, inter-subject differences in the information content of
BOLD signals in visual cortex are correlated with the precision of
an individual’s recall54,55. Atlhough the factors that determine the
decodability of BOLD signals are still being explored56,57, these results
highlight the importance of looking beyond simple elevated delay
activity as a unique marker of working memory representation.
Before slot models of working memory were called into question,
neural modeling studies proposed that a neural basis of slots could
be found in the number of oscillatory states that can be superimposed
0 21 3 5 74 6 8 9
Number of items in memory array
BOLD signal relative to rest (%)
0 4 8 12 16 20 24 28
0 4 8 12 16 20 24 28
0 4 8 12 16 20 24 28
0 4 8 12 16 20 24 28
Lateral occipital Medial occipital
Endpoint error (°)
Endpoint error (°)
Figure 3 Neural correlates of storage in working memory. (a) Short-term maintenance of visual information is associated with sustained elevated BOLD
signals (hot colors) in prefrontal and posterior parietal regions, whereas the signal in occipital visual cortex is the same or below that observed at rest
(but see d). BOLD signals are displayed on an inflated brain surface, showing gyri in light gray and sulci in dark gray. (b) During maintenance, BOLD
amplitude in posterior parietal regions varies with the number of features held in memory (data are from ref. 38). A neural capacity limit has typically been
inferred by looking for increases in memory load that are not accompanied by a statistically significant (P < 0.05) increase in signal (here, above four items).
However, there are many continuously increasing functions (for example, exponential saturation function, dashed line) that would be incorrectly identified as
reaching a plateau by this method. (c) In both humans and monkeys, a lateralized EEG signal at posterior electrodes (the CDA) is correlated with precision of
recall, as measured by the error in reproducing a single remembered stimulus location. (d) The information content of BOLD signals is dissociated from signal
strength during memory maintenance. In occipital areas (left), visual parameters held in memory can be accurately decoded (blue lines) from voxels that are
not consistently elevated above baseline during the delay period (red lines). Decoding from these occipital areas is more effective than from prefrontal and
posterior parietal voxels (right) that show elevated delay-period responses. Adapted with permission from refs. 51 (a,d), 38 (b) and 46 (c).
npg © 2014 Nature America, Inc. All rights reserved.
nature neuroscience VOLUME 17 | NUMBER 3 | MARCH 2014 351
without interference58. These models made a connection to the
binding problem, as cortical synchronization has been proposed as a
mechanism for binding features of an object59. However, they did not
describe the contents of working memory, let alone contain a descrip-
tion of the precision of encoding. Physiological evidence supporting
oscillation-based models has so far been sparse.
In the context of resource models, a possible neural basis for
resource lies in the number of action potentials used to encode work-
ing memories15,60 (Fig. 4). Cortical firing is highly variable from trial
to trial61, and this variability might underlie the (encoding and main-
tenance) noise seen in working memory recall. A correspondence
between resource and the amplitude of neural activity (gain) in a
neural population representing an item is suggested by several lines
of evidence. First, theoretical models of early sensory representation
have proposed that neural gain is proportional to the precision of
encoding of the stimulus62,63. Second, working memory resource
is often considered to be similar to attentional resource4,34,64, and
attention modulates neural gain65. Third, there is neurophysiological
evidence that firing rate decreases with increasing set size66 and varies
from trial to trial67. Fourth, neural spiking is energetically costly and,
at large set sizes, the performance benefits of investing more spikes in
encoding stimuli might be outweighed by the energy spent, leading
to a decrease of precision per item15.
One way to realize a decrease of precision with set size arises from
the relationship between precision and neural gain. It has been pro-
posed that neural gain could be related to the number of items in
memory through a mechanism of divisive normalization60. The idea
is that activity in the population encoding a particular item is divided
by the grand sum of the activities of neurons in all populations encod-
ing items. Thus, the larger the number of items, the larger this sum
and the lower the gain of the population encoding each item. This is
a directly testable physiological hypothesis.
A recent neural network model managed to capture a decrease
of precision with set size using biologically realistic neurons68. In
this network, all items are encoded as persistent activity ‘bumps’
in a shared feature-selective population, causing working memory
errors to arise from competition between and merging of these
bumps. However, neurons in this simulated network had no spa-
tial selectivity, and stimuli were therefore artificially spaced out in
the feature space to be retained as distinct bumps. It remains to be
seen whether the proposed mechanism can account for performance
when (potentially similar) visual items are remembered in distinct
Making sense of memory errors
So far we have considered some key behavioral, neural and modeling
data that have led to a reconceptualization of working memory. Recent
studies have gone further and started to examine whether the pattern
of recall errors might provide even deeper insights into the nature of
working memory representations.
A crucial advantage of the delayed-estimation technique for
probing working memory (Fig. 1) is that it provides the experi-
menter not just with an estimate of error precision, but with an entire
error distribution. Theoretical models of sensory representation
typically assume that errors have a normal (Gaussian) distribution,
and early instantiations of resource models likewise assumed that
recall errors would be normally distributed8,17. However, recent
studies have shown that errors in recall from working memory often
deviate substantially from normality. Beyond changes in precision,
accounting for the shape of the error distribution has become a new
testing ground for comparing working memory models (Figs. 2 and 5).
In addition, an important new trend is to fit models to raw, individual-
trial data using maximum-likelihood estimation, instead of relying
on summary statistics69.
Discrete representation. An influential study19 proposed that
the shape of the error distribution in delayed estimation could be
reproduced by a mixture of two classes of error: some resulting from
noisy recall (with a normal distribution) and some resulting from
random guessing (with a uniform distribution) (Fig. 2c). Fitting this
normal + uniform mixture to the data, the authors showed that the
proportion of errors accounted for by the uniform distribution (which
they interpreted as guessing rate) increased with set size. The standard
deviation of the normal component, denoted SDnormal, increased for
the first three items, then reached a plateau (Fig. 5b)21, although this
plateau has not always been replicated9,11,26. To explain this, the inves-
tigators proposed that the same item could be stored in more than
one slot1 9. When a single item is held in memory, there would then
exist several independent representations of it in the brain (depicted
as three overlapping quanta in Fig. 2c), which could be averaged at
recall to boost precision.
While attempting to retain the terminology of the slot model, this
account actually differs fundamentally from the classic slot model.
Here, all the representational medium (that is, every slot) is engaged
for all set sizes and shared out between items. Furthermore, the authors
reported flexible allocation in response to a predictive cue, which they
interpreted as some objects being allocated more slots than others19.
This makes the model equivalent to a discrete or quantized resource
model. The key distinction from continuous-resource models8,11
is that it predicts a fixed upper limit on how many objects can be
Error in decoded
Error in decoded
Spike countSpike count Spike count
a b c
N = 1
N = 2
Error in decoded
Figure 4 Putative neural basis of set size effects in resource models of
working memory. (a) Example displays for an orientation delayed-estimation
task with one or two items. (b) Examples of mean firing rate (dashed lines)
and activity on a single trial (points) in neural populations responding to
the stimuli in a. Neurons are ordered by preferred orientation. At set size 2,
gain (population amplitude) per item is reduced compared with set size 1.
(c) Error distributions obtained by optimally decoding spike patterns such
as those in b. Errors arise because of stochasticity in spike generation.
Precision declines with decreasing gain62,63, leading to wider distributions
for more memory items. In this context, the limited resource is the gain of
the population activity.
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35 2 VOLUME 17 | NUMBER 3 | MARCH 2014 nature neuroscience
stored, that is, an item limit (Fig. 2b,c). The plateau in SDnormal was
interpreted as indicating just such a limit on the number of items
stored. However, interpretation of the parameters of the normal +
uniform mixture critically depends on the validity of the mixture fit.
Careful comparison with data suggests the normal + uniform mixture
provides a relatively poor fit to experimental error distributions15,16,70
and SDnormal may therefore systematically underestimate the true
variability in memory (Fig. 5).
Variable precision. The most recently proposed continuous-resource
model postulates that precision is itself variable across items and trials,
even when set size is kept fixed15,16 (Fig. 2d), and should therefore
be modeled as being drawn from a probability distribution. In this
model, the noisy memory of a stimulus would not follow a normal
distribution with a fixed precision, but an infinite mixture of normal
distributions of different precisions, including ver y low ones.
Many sources could potentially contribute to variability in precision,
including stimulus differences71, waxing and waning of alertness,
covert attention shifts25, grouping and other configural effects72 ,
and variability arising during maintenance16,61. One proposal is that
deviations from normality in the distribution of working memory
errors may arise from the same source of stochasticity as the errors
themselves, namely Poisson variability in neural spiking73.
Error distributions in delayed estimation are predicted consider-
ably better by a variable-precision model than by alternative models,
including the discrete-representation model15,16,70. In particular, the
model accounts for the increase in the ‘guessing rate’ with increasing
set size: when a normal + uniform mixture is fitted to recall errors,
low-precision trials will be absorbed into the uniform component,
even though they might not represent true guesses. Thus, an increase
in guessing rate with set size simply reflects an increasing prevalence
of low-precision representations. The variable-precision model also
provides a good quantitative account for both actual standard devia-
tion and SDnorma l as a function of set size15 (Fig. 5c). These findings
further call into question the interpretation of the uniform compo-
nent in the normal-uniform mixture as being a result of an item limit.
More generally, it is important to keep in mind that summary statistics
computed using a descriptive model, such as capacity K when using a
classic slot model or the guessing rate when using a normal + uniform
mixture, are only as good as the model itself. They can be misleading
when the model is a poor description of the data. Conclusions from
formal model comparison based on individual-trial data are always
more reliable than conclusions from summary statistics69.
Figure 5 Interpreting the shape and width of
working memory error distributions. (a) A crucial
area of debate concerns how to model the
distribution of recall errors (gray histogram, color
estimation data from ref. 15, averaged over all
subjects and set sizes). A popular analysis method
attempts to do this with a mixture of a circular
normal distribution (intended to correspond to
items in memory) plus a uniform distribution
(intended to correspond to items that are not
stored)19. The red line depicts this fit, also
averaged over all subjects and set sizes.
Note that the circular standard deviation of the normal component in the mixture, SDnormal (average value given) is much lower than that of the raw data
(compare actual standard deviation (actual SD) with SDnormal). The mixture does not fit human recall data well, and the interpretation of the two mixture
components has therefore been called into question15,16. (b) Actual SD and SDnormal as a function of set size. SDnormal substantially underestimates the level
of noise in memory, which, if all items are stored, is simply the actual SD. An apparent plateau in SDnormal (red symbols) at higher set sizes has been used to
argue for slot models19,21, but such a plateau is not present in the raw data (black symbols). Data are from ref. 15. Error bars represent s.e.m. (c) A resource
model in which all items are stored with variable precision accurately accounts for both actual SD and SDnormal. Thus, SDnormal by itself cannot serve to
distinguish between slot and resource models69. Adapted from ref. 15; shaded areas are s.e.m. of model fits.
Other findings also point to variability in precision: when subjects
are asked on some trials to recall the item they remembered best,
performance on those trials was substantially better than on ones on
which a random item was probed16. Furthermore, when participants
report the confidence of their estimate, their ratings have a wide
distribution and correlate strongly with performance, consistent with
variable precision20; indeed, the variable-precision model fits these
data well. However, further work is needed to determine the origins
of variability in precision, a basis for the particular distributions over
precision that fit human data, and how variable precision relates to
neural coding of working memory.
Binding errors. Although delayed estimation (Fig. 1) provides advan-
tages over classification tasks such as change detection, the error
distributions obtained using delayed estimation are not determined
solely by memory quality for the reported feature. This is because
observers are required to report a feature of just one of the objects in
working memory, uniquely identified by its value on some second-
ary feature dimension (Fig. 1a,d). In multiple-item arrays, observers
must not only hold in memory the features to be reported, but also
the features that will identify the relevant object and, crucially, the
‘binding’ information that pairs the two features together (Fig. 6).
Errors in storing or maintaining these latter classes of information
may result in incorrect retrieval of one of the other items in working
memory at test. In other words, memory recall might be systemati-
cally corrupted by reporting of features belonging to items retained
in working memory other than the probed item.
In delayed estimation, such non-target or swap errors may be
mistaken for random guesses if responses are compared only with
the feature value of the probed item9. However, in a comparison
with all array objects, non-target errors have been directly observed
as a clustering of responses around feature values of non-probed
items9,26,35,49,74. Such non-target errors grow in prevalence as working
memory object load is increased9,10,26, consistent with the resource
principle of a graded decline in representational quality (Fig. 5a–c).
Both non-target errors and deviations from normality in target
recall (of the kind predicted by variable precision) could account for
responses previously attributed to guessing.
There is emerging evidence that failures of binding properties that
belong to an object in working memory may have a specific role in
forgetting over brief time periods10,28 and be a crucial component of
deficits associated with old age, dementia and medial temporal lobe
lesions28,75–78. Although the principles of neural coding of basic visual
Actual SD = 21.3°
SDnormal = 13.8°
Weightnormal = 0.83
Estimation error (color wheel degrees)
cResource model fit
npg © 2014 Nature America, Inc. All rights reserved.
nature neuroscience VOLUME 17 | NUMBER 3 | MARCH 2014 353
features are well established, current neural models of binding remain
largely hypothetical. Investigation of the factors that determine
binding failure might help constrain neural mechanisms of object
representation in working memory.
Computing with working memories: probabilistic inference
in change detection
The models described thus far are all concerned with encoding and
maintenance: how sensory stimuli are internally represented during a
delay period. In many natural and experimental situations, however,
working memories are subsequently retrieved and used. For exam-
ple, in change detection, the memory of a first display is compared
with a second one to determine whether a change occurred (Fig. 7a).
Because of encoding noise, change detection decisions must be made
without exact knowledge of the stimuli in the first display and are
therefore a form of inference. In the classic slot model, inference is
ignored and decrease of performance with increasing set size is attrib-
uted to a limited number of items being held in working memory5,79.
This approach is typically justified by stating that the changes used
in the experiments are large. However, how large a change is percep-
tually depends on the noise level: even seemingly large changes will
be difficult to detect when precision is low. In fact, performance in
detecting a change between supposedly highly distinct colors strongly
depends on the specific colors23.
Resource models attribute the majority, if not all, of change detec-
tion errors to the consequences of noise (Fig. 7b). This idea has been
formalized in signal detection theory and Bayesian models of change
detection8,13,25,80, change discrimination11,60 and change localiza-
tion15,23. Bayesian models are signal detection theory models in which
observers make the best possible decision based on the noisy evidence
on each trial. These models, which are computationally very similar
to models of non-memory tasks such as visual search81,82, account for
many observations that are inconsistent with the slot model.
First, in change detection, false alarm rate increases with set size8,13.
Although the slot model predicts no relationship, resource models do:
noise causes the internal representation of an individual item to differ
between the two displays, even if no physical change occurred (Fig. 7c),
and more so when precision is lower. Furthermore, resource mod-
els explain the dependence of working memory capacity estimates
on stimulus category12, and the higher difficulty of within-category
Figure 6 Modes of failure in working memory
retrieval. (a) The working memory representation
of a colored square can be decomposed into the
location of the object in an internal representation
of physical space (for example, in posterior
parietal cortex; green), the location of the object’s
color in an internal ‘color space’ (for example,
in area V4; blue), and ‘binding’ information that
associates the position and color (illustrated here
by a spring). (b,c) Increasing working memory
load may degrade the quality with which each of
the three classes of information is maintained:
increasing variability in both color and space
representations and making binding information
more fragile. (d) To report the color in memory
belonging to a given position, the relevant location in internal position space is interrogated, leading via binding information to the corresponding
representation in color space. This process can fail in at least three ways. First, variability in position space may cause the wrong position representation to be
selected, leading to incorrect report of the color of one of the other objects in memory. Second, binding failure may prevent access to the corresponding color;
in this case, a forced response may lead to a random guess from any of the colors in memory. Third, variability in color space may lead to incorrect report of
a similar, neighboring color in the internal space. (e) In human data, incorrect reports of non-target objects as a result of the first or second possible sources
of failure will produce responses that appear randomly (uniformly) distributed when plotted relative to the target feature value. (f) However, such incorrect
reports can be directly observed as a central peak when responses are plotted relative to non-target feature values: if errors were solely a result of variability
in the reported feature, this distribution would be flat (data replotted from ref. 9).
compared to between-category change detection83: the signal-to-noise
ratio will depend on the perceptual space associated with a category
and is expected to be lower within a category than between categories.
Finally, receiver operating characteristics obtained using a confidence
rating procedure follow the predictions of continuous-resource
models across a range of set sizes and numbers of changing items8.
Surprisingly, researchers have only recently started to systematically
vary the magnitude of change in multiple-item change detection13,25,80
and change localization15. Manipulating the magnitude of change in
addition to set size produces a much richer data set, consisting of a
full psychometric curve at each set size, rather than a single hit rate
and a single false-alarm rate. The psychometric curves show a gradual
increase of performance with magnitude of change (Fig. 7d). This
is consistent with resource models, which predict that performance
increases continuously with signal-to-noise ratio. When these change
detection and change localization data were analyzed using the clas-
sic slot model, estimates of K were consistent with earlier studies,
but the full psychometric curves revealed that the slot model was
inadequate13. Instead, a variable-precision model augmented with a
Bayesian decision rule provided an accurate account of these data13
(Fig. 7d,e). In contrast, a different study concluded that receiver-
operating characteristics in a change detection task are consistent with
a slot model84, but neither variable precision nor a Bayesian decision
rule were considered in this work.
A change detection study in which stimulus reliability was unpre-
dictably varied on a trial-to-trial and item-to-item basis found that
observers possess knowledge of these variations and take them into
account near-optimally during the decision stage80. This raises the
possibility that not only feature information, but also the correspond-
ing precision (or certainty level), gets stored in working memory
on every trial.
Context and ensemble effects. Probabilistic inference may also be
involved in delayed estimation. Further computation could consist
of combining the sensory measurement at the probed location with
summary statistics of the memory display. There is evidence that this
happens: for example, a circle is remembered as being slightly bigger
than its true size when other circles of the same color were bigger85.
This illustrates a broader phenomenon, namely that the recalled value
of a stimulus might be influenced by the features and positions of
npg © 2014 Nature America, Inc. All rights reserved.
35 4 VOLUME 17 | NUMBER 3 | MARCH 2014 nature neuroscience
other items in the display. A shortcoming of all of the working mem-
ory models discussed thus far is that they assume that all items are
encoded independently. A recent focus has been on the effect of con-
text on how well we remember72,85,86. One proposal is that observers
store summary statistics, or the ‘gist’, of a scene, such as how correlated
the colors of neighboring elements tend to be, in addition to individual
items72. If working memory resources can be flexibly deployed, stimuli
that fit the gist could be safely stored with lower precision, reserving
high-precision memory for informative outliers.
Taken together, behavioral evidence from multiple tasks supports a
continuous-resource account of human working memory and does
not support the notion that it is limited by a fixed number of slots that
can hold items. However, resources may not be infinitely divisible, and
even if they are, outside of laboratory experiments there will always
be variations in the salience or importance of environment stimuli
that make even allocation over large numbers of objects undesirable.
Furthermore, if the quality of item representations in working mem-
ory is limited by noise, in practical terms there might be limits to how
well a limited working memory resource can be allocated, or thinly
spread, over a very large number of items. One direction of future
research could be to examine the optimal distribution of resources in
situations in which items have unequal probabilities of being tested
or are rewarded differentially.
Another direction would be to combine ingredients from existing
models in new ways, such as a continuous-resource model with a
maximum number of items that can be stored or models in which the
number of items stored varies across trials87,88. However, such models
should ideally be informed by biological plausibility and neural data.
A recent paper, comparing 32 models in a three-factor space, found
that the most successful models incorporated both continuous, vari-
able precision and spatial binding errors, with additional evidence for
variability in the number of items stored70.
In the slots framework, a long-running debate askes whether slots
hold individual features or entire objects5,48,89,90. In resource models,
Figure 7 Changing concepts of change detection.
(a) Trial procedure in an orientation change
detection task13. In contrast with previous
studies, the magnitude of the change was varied
on a continuum, producing a richer data set.
(b) Resource model for change detection.
Stimuli in both displays are internally measured
in a noisy manner, and an observer applies a
decision rule to these measurements to reach a
judgment. To maximize accuracy, the decision
rule should be based on probabilistic inference.
(c) Probabilistic inference in change detection
at set size 1 in a resource model, for a circular
stimulus variable. The change measured by the
observer follows a bell-shaped distribution
centered at the true magnitude of change.
The observer applies a criterion (green) to
decide whether to report a change. At small
magnitudes of change, ∆, the miss rate
(red shading) might exceed 50%. Both the width
of the distribution and the value of the criterion
will depend on noise level and thus on set size.
At higher N, the measured changes at different locations are combined nonlinearly before a criterion is applied. (d) Proportion of ‘change’ reports as a
function of the magnitude of change, for each set size. Circles and error bars represent data and shaded areas represent variable-precision model with
probabilistic inference. In traditional change detection studies, magnitude of change is not varied systematically and these psychometric curves cannot
be plotted. (e) Probability distributions over precision in the variable-precision model, as estimated from one subject in a change detection experiment.
In the equal-resource model (Fig. 2b), these distributions would be infinitely sharp. All panels except for c are adapted from ref. 13.
this question has to be rephrased: do different feature dimensions
(for example, colors and orientations) compete for the same resource
pool? Present evidence indicates that recall variability depends pri-
marily on the number of competing features in each dimension and
that errors arise independently for different features of the same
Generalizations of resource models to more real-world situations
remain underexplored. Alphanumeric characters, shapes and line
drawings have all been used in previous working memory experiments.
In principle, resource models can also be applied to such stimuli.
However, the space in which these complex objects are perceptually
represented, and how noise corrupts measurements in this space, is
not as well understood as for basic visual features. In addition, each
such stimulus is part of a large, high-level category of objects, which
might affect encoding. Resource models might have an advantage over
slot models when dealing with natural or crowded scenes. An ‘item’ is
often relatively easy to define in laboratory experiments, but this is not
necessarily the case in real scenes. In an image of a bike, for example,
is the entire bike the item, or are its wheels or its spokes items? Slot models
cannot avoid this question, as the definition of the item determines
what goes into a slot. In resource models, resource is easily conceptual-
ized as being allocated to groups of features or spatial locations, rather
than to items. However, it remains to be seen how well behavioral data
from natural scenes can be described by resource models.
Continuous-resource models might also be extendable beyond
visual working memory, to visual long-term memory94, other sensory
domains95 or other multiple-object tasks. Multiple-object tracking,
for example, is often considered to be limited by a four-item limit,
but this conclusion is being challenged60,96,97. A similar reexamina-
tion may be necessary for subitizing limits98. Finally, resource model
approaches have now begun to be applied to a range of issues in neu-
roscience, such as working memory development9 9, aging77,100 and
pathology78, where changes in memory quality may have a vital and
previously overlooked role.
Recent work that has explored decoding of working memories from
neural activity51–55 opens the door to directly test, at a neural level, the
Proportion reports ‘change’
0 10 50
N = 2
N = 4
N = 6
N = 8
N = 2
N = 4
N = 6
N = 8
20 30 40
Magnitude of change (°)
Respond ‘no change’
Probability of measured
Change of ∆
0 30 60 90
npg © 2014 Nature America, Inc. All rights reserved.
nature neuroscience VOLUME 17 | NUMBER 3 | MARCH 2014 355
predictions that the various models make for the dependence of preci-
sion on set size. Although it is challenging to probe the contents of
working memory of all items in a display simultaneously in behavioral
experiments, this might be possible when decoding neural signals,
thereby providing more power to distinguish between competing
models. Moreover, neural data offers the opportunity to study in detail
the modulation of working memory when attention is directed to a
subset of stored items.
Recent years have seen a resurgence of interest in the nature and
limits of short-term storage in the brain, driven by methodologi-
cal advances in measuring and interpreting recall errors, as well as
improved techniques for probing neural representations of memory.
In this review, we have presented some of the growing body of
evidence from behavior and neurophysiology that suggest that consid-
ering only the quantity of representations and ignoring their quality
provides an incomplete description of working memory.
An important consequence is that the common practice of char-
acterizing memory ability using a capacity estimate K is increasingly
difficult to sustain. Although many researchers use K as a convenient
summary statistic, it is important to realize that such an approach
is not model free: using K implies committing to a particular slot
model5,6 that has been superseded by both resource models11,15 and
newer slot models19. A model-agnostic approach would be to simply
report the standard deviation of recall errors as a function of set size
(Fig. 5) and compare this entire function, for example, between two
subject populations. An even better approach would be to fit both slot
and resource models, compare their goodness of fit and report the
parameters of the best-fitting model.
Clearly, the concept of a limited memory resource has become cen-
tral to present debates, providing a consistent and intuitive account
for both the decline in precision associated with increasing working
memory load and the precision gains (and costs) observed for stimuli
of differing salience. However, many details in this framework con-
tinue to be debated, particularly the extent to which resources are
divisible and the degree to which different features tap independent
resource pools. Regardless of theoretical position on these issues,
the growing sophistication of behavioral analyses combined with an
expansion in the range of neurophysiological approaches can only
lead to a deeper understanding of how and why individuals remember
We thank R. van den Berg for useful discussions and assistance with Figure 5.
W.J.M. is supported by award number R01EY020958 from the National Eye
Institute and award number W911NF-12-1-0262 from the Army Research Office.
P.M.B. and M.H. are supported by the Wellcome Trust.
COMPETING FINANCIAL INTERESTS
The authors declare no competing financial interests.
Reprints and permissions information is available online at http://www.nature.com/
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