Psychological Science

24(6) 981 –990

© The Author(s) 2013

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DOI: 10.1177/0956797612465439

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Research Article

A large body of work has demonstrated that visual long-

we demonstrated that after seeing thousands of objects,

observers succeeded at subtle object-exemplar discrimi-

nations (e.g., which of two chocolate cakes was seen)

and object-state discriminations (e.g., whether the cake

was half eaten or two-thirds eaten). But the information

observers had to store to make these discriminations is

difficult to quantify and compare across time scales and

items. Therefore, several fundamental questions remain

unanswered: Just how detailed is visual long-term mem-

ory? And how does its precision compare with the preci-

Determining the precision of long-term memory

fidelity-dependent retrieval limits), as opposed to system-

specific limitations (e.g., the number of “slots” or amount

of “resources” available to working memory; Wilken &

Ma, 2004; Zhang & Luck, 2008). Thus, comparing work-

ing memory and long-term memory can not only help

elucidate the underlying memory representation of visual

Kirkland St., Cambridge, MA 02138

E-mail: [email protected]

Visual Long-Term Memory Has the Same

Limit on Fidelity as Visual Working

Memory

representations, and how can one quantify this fidelity? Using the property of color as a case study, we estimated the

precision of visual information in long-term memory, and compared this with the precision of the same information

in working memory. Observers were shown real-world objects in random colors and were asked to recall the colors

after a delay. We quantified two parameters of performance: the variability of internal representations of color (fidelity)

and the probability of forgetting an object’s color altogether. Surprisingly, the fidelity of color information in long-

term memory was comparable to the asymptotic precision of working memory. These results suggest that long-term

memory and working memory may be constrained by a common limit, such as a bound on the fidelity required to

retrieve a memory representation.

visual memory, long-term memory, short-term memory

2006; Nairne, 2002).

In previous attempts to quantify the fidelity of long-

term memory representations, researchers used simple

stimuli, such as oriented gratings (Magnussen & Dyrnes,

1994; Magnussen, Greenlee, Aslaksen, & Kildebo, 2003).

However, performance in such cases may depend

on memory for decision criteria rather than on perceptual

features of the objects to be remembered (Lages &

Paul, 2006; Lages & Treisman, 1998; Magnussen, 2009).

In addition, although oriented gratings define a well-

objects can be.

In the study reported here, we took a psychophysical

approach to quantify the fidelity of visual long-term

memory for objects. We used color as a case study

because the color of objects can be manipulated in a

continuous space, which allowed us to extend the con-

tinuous-report paradigm used in visual working memory

(Wilken & Ma, 2004) to long-term memory. Furthermore,

there are metrics that allow separable, independent mea-

surements of the fidelity of color memory and of guess-

accurately observers remembered a feature of a given

object after seeing hundreds of objects, and how likely

observers were to completely fail to retrieve a feature.

We found that from perception to working memory,

observers lose significant precision in their representa-

tion of objects’ color. As more items are added to work-

ing memory, the fidelity of these memory representations

reaches an asymptotic limit, and, surprisingly, this limit is

almost identical to the fidelity of representations in long-

term memory. These results suggest that a common limit

memory may reflect a more general upper bound on

how noisy a memory representation can be before it is

unable to be retrieved.

In Experiment 1, observers performed a continuous-

report task involving pictures of real-world objects.

Observers were shown objects with randomly selected

hues and asked to choose from a color wheel what hues

the objects were. Such continuous-report methods have

been used to investigate working memory for simple

observers had to match the color of a visible object. In

the working memory condition, observers were given 3 s

to encode three objects and then had to report the color

of each object after a 1-s delay. We used three objects per

trial to match the set size at which working memory fidel-

ity reaches asymptote (Anderson et al., 2011; Zhang &

Luck, 2008). In the long-term memory condition, observ-

ers viewed hundreds of objects, presented one at a time,

and then were asked to report the color of every single

object, one at a time. In Experiment 1a, observers had

per object in this condition matched the display time per

object in the working memory condition. Observers saw

different objects in each of the three conditions.

Participants. Fourteen observers (age range = 18–25

years) participated in Experiment 1: 5 in Experiment 1a

and 9 in Experiment 1b. They gave informed consent and

had normal color vision (assessed using Ishihara’s, 1936,

test for color deficiencies). All participants completed all

three conditions, with the order randomized across

Twenty-six images in the study stream appeared twice in

a row, and participants pushed the space bar when they

noticed a repeat. Participants were given feedback only

when they responded; a red fixation cross indicated an

incorrect response, and a green fixation cross indicated a

correctly detected repeat. No feedback was given for

misses or correct rejections.

Immediately after the study block, we tested the fidel-

ity with which participants remembered the color of the

objects. Items that were repeated in the study stream

the center of the item. When the participant moved the

mouse, the test item appeared in color. The angle

between the mouse and the center of the test item deter-

mined the item’s hue, and a dot presented along an

adjustment ring surrounding the item indicated the cur-

rent angular position of the mouse. When participants

decided that the current color was correct, they clicked

the mouse. The angular error was taken as a measure of

accuracy. The color wheel was randomly rotated across

trials.

Data analysis. On any given trial, we measured error

in degrees, between 0° (perfect memory) and ±180°

(poor memory). In the continuous-report paradigm, the

histogram of errors over trials typically shows that

responses are centered around 0°, but that across all

responses, there are errors distributed across the entire

range. The error histograms we obtained for the three

conditions (see Fig. 2) were well fit by a mixture of two

distributions: (a) a Gaussian-like distribution (defined on

a circular space as a von Mises distribution), taken to

The fidelity (precision) of memory representation was

estimated as the standard deviation of the von Mises

distribution. Maximum likelihood estimation was used to

estimate these two parameters for each condition.

Figure 2 shows the distribution of errors in the percep-

tion, working memory, and long-term memory condi-

tions, combined across Experiment 1a and Experiment

1b. The fidelity and guessing parameters for each experi-

ment are summarized in Figure 3.

had a tight distribution centered on the correct color.

Results in the working memory condition were in line

with Zhang and Luck’s (2008) findings. Observers’ preci-

sion was 19.0° (SEM = 1.3), and their probability of guess-

ing was .09 (SEM = .02). Thus, there was a major change

in fidelity from perception to working memory: The stan-

dard deviation increased by 183%, a serious cost in mem-

ory fidelity for having to hold the items in mind for

several seconds, t(4) = 10.5, p < .0001.

In the long-term memory condition (3 s/item), observ-

fidelity observed for 3 items at a time in working mem-

ory, t(4) = −0.81, p = .46. Note that the estimated preci-

sion of working memory in this experiment is similar to

the precision observed in several working memory

experiments that tested memory for color patches at set

sizes of 3 and greater (Zhang & Luck, 2008, 2011), even

though we used real-world objects.

Experiment 1b. In this experiment, observers had only

1 s to encode the color of each item in the long-term

were .006 (SEM = .002), .08 (SEM = .01), and .63 (SEM =

.05), respectively. As before, the fidelity of working

Fig. 2. Results pooled across all observers in Experiments 1a and 1b. The histograms rep-

resent the distribution of the magnitude of error in observers’ responses in the (a) percep-

tion, (b) working memory, and (c) long-term memory conditions. The black curves show

the model fits from a mixture model that combines a uniform guessing distribution with a

Gaussian-like distribution of correct responses. The pink solid lines show the width of the

Gaussian at 1 standard deviation and are flanked by illustrations showing the corresponding

term memory (~20°). This was true both when long-term

memory encoding time matched the total encoding time

in the working memory condition (Experiment 1a) and

when long-term memory encoding time matched the

per-item encoding time in the working memory condi-

tion (Experiment 1b). The results showed that nearly all

of the information loss from working memory to long-

term memory is accounted for by an increased chance of

entirely losing an item’s color from memory (increased

guess rate).

ity of working memory (when three items were held in

mind) and the fidelity of long-term memory were nearly

tative forced-choice comparisons (Brady et al., 2008;

Hollingworth, 2004).

It is possible that long-term memory and working mem-

ory have the same fidelity because long-term memory

representations inherit their fidelity directly from working

memory. For example, if items have to enter working

memory to be encoded into long-term memory, and if

there is no further degradation of representations once

they are encoded, then long-term memory representa-

the fidelity of working memory for a single item. Results

from Experiment 1 cannot directly address this predic-

tion, because multiple items were presented simultane-

ously in the working memory task.

To test this inherited-precision hypothesis, we matched

the encoding conditions in the working memory and

long-term memory tasks in Experiment 2. To preview the

results, we found that observers can in fact remember a

single item with better precision in working memory

than in long-term memory, which is inconsistent with the

gave informed consent, were between the ages of 18

and 25, and had normal color vision (assessed using

Ishihara’s test for color deficiencies).

ment 1.

Procedure. The procedure was identical to that of

Experiment 1a, except that the working memory condi-

tion was modified to consist of 180 trials with only a

single item presented on each trial. Each object was pre-

sented for 3 s and then tested after a 1-s delay.

Results for the perception condition (fidelity = 5.6°, SEM =

1.1; probability of guessing = .01, SEM = .01) and the long-

term memory condition (fidelity = 20.5°, SEM = 7.0; prob-

fidelity of working memory for one item was significantly

better than the fidelity of working memory for three

items—comparison with Experiment 1a: t(9) = 2.45, p =

.03; comparison with Experiment 1b: t(13) = 2.06, p = .06.

These results show that the memory precision of color

information of real-world object stimuli is not fixed at

encoding; it is possible for the fidelity of working mem-

ory to be better than the fidelity of long-term memory.

The results of Experiment 2 show that when a single real-

reduces the measured precision of retrieved items to 20°.

Intriguingly, the data across all experiments show that

the level at which the fidelity of working memory pla-

teaus is identical to the fidelity observed in long-term

memory (Fig. 4). To bolster this finding, we conducted

several control experiments (see also the Supplemental

Material available online).

First, we tested working memory using displays with

five items (Control Experiment 1), to more clearly dem-

onstrate the plateau in the fidelity of working memory

and the fidelity of the remembered items remained at

about 20° (Control Experiment 2). Finally, we examined

whether long-term memory precision could be more pre-

cise than this limit—which would still be consistent with

a limit on the fidelity of the memory representations.

However, surprisingly, we found that even when the

memory set consisted of only 20 items (Control

Experiment 3), precision was similar; although there was

a benefit in overall performance relative to when the

memory set included 180 or 360 items, this benefit was

culty levels in the long-term memory task, with guess

rates ranging from .26 to .73, we found that fidelity

remained constant at a standard deviation of 19° to 20°.

Any representation more variable than this limit seems to

be lost entirely to guessing, in both working memory and

long-term memory.

hundreds of representations encoded and then retrieved

from long-term memory. Thus, long-term memory fidelity

is significantly higher than previously believed, even when

quantified using psychophysical methods.

However, our finding that long-term memory shares a

similar limit suggests an alternative model. Rather than

reflecting an intrinsic property of the working memory

system, this asymptotic fidelity limit may instead reflect a

The broader working memory literature—particularly the

empirical results highlight that working memory tasks do

not isolate working memory mechanisms independently

of long-term mechanisms. For example, performance on

any given working memory trial is influenced by previous

trials, an influence that includes systematically induced

biases and proactive interference (Hartshorne, 2008;

Huang & Sekuler, 2010; Makovski & Jiang, 2008). These

findings suggest an obligatory influence of long-term stor-

age on working memory (Brady et al., 2011; see also

Olson, Moore, Stark, & Chatterjee, 2006, for evidence from

bound on memory fidelity. Recalled items are never nois-

ier than a fixed limit; after that limit, an item is lost, per-

haps irretrievable via conscious access because it no

to the right and left represent colors 1 standard deviation above and below the studied color (±6°

in perception, ±19° in working memory for three items, ±20° in long-term memory).