Attractive serial dependence refers to peculiar biases in the representation of visual stimuli based on prior information, whereby current stimuli appear more simi-lar to previous ones. This effect has been initially docu-mented in orientation reproduction tasks, where the reproduced orientation of a test stimulus is systemati-cally biased toward the orientation of stimuli seen in previous trials (Fischer & Whitney, 2014). Serial depen-dence has been linked to the processes of visual stabil-ity and perceptual continuity, as a reflection of a “continuity field” integrating stimuli over space and time to smooth out noise from neural signals (Burr & Cicchini, 2014; Fischer & Whitney, 2014). In other stud-ies, researchers have also reported this effect in the context of numerosity perception (Cicchini, Anobile, & Burr, 2014; Corbett, Fischer, & Whitney, 2011), face identity (Liberman, Fischer, & Whitney, 2014), and even face attractiveness (Xia, Leib, & Whitney, 2016), sug-gesting that serial dependence is a generalized phe-nomenon concerning several domains of visual perception. However, in recent studies (Alais, Leung, & Van der Burg, 2017; Fritsche, Mostert, & de Lange, 2017), researchers have challenged this idea by
proposing that attractive effects might instead reflect the signature of a decision process that biases working memory representations—an interpretation that pre-cludes any significant role in visual stability itself. Spe-cifically, Fritsche and colleagues (2017) proposed that while attractive biases more easily emerge in slow and demanding tasks such as orientation reproduction, where a decision process may distort working memory representations, more perceptual tasks such as orienta-tion discrimination are instead affected in a repulsive way by recent stimuli (i.e., current stimuli appearing to be more different from previous ones), as in the case of perceptual adaptation (e.g., Kohn, 2007).
Because these different views have radically different implications, disentangling them is crucial for under-standing the mechanisms underlying perceptual stabil-ity and continuity. Here, we characterized a neural signature of serial dependence independently from a
737385 PSSXXX10.1177/0956797617737385Fornaciai, ParkSerial Dependence as a Perceptual Phenomenonresearch-article2018
Corresponding Author:Michele Fornaciai, Department of Psychological and Brain Sciences, University of Massachusetts Amherst, 135 Hicks Way, Amherst, MA 01003 E-mail: [email protected]
Attractive Serial Dependence in the Absence of an Explicit Task
Michele Fornaciai1 and Joonkoo Park1,2
1Department of Psychological and Brain Sciences and 2Commonwealth Honors College, University of Massachusetts Amherst
AbstractAttractive serial dependence refers to an adaptive change in the representation of sensory information, whereby a current stimulus appears to be similar to a previous one. The nature of this phenomenon is controversial, however, as serial dependence could arise from biased perceptual representations or from biased traces of working memory representation at a decisional stage. Here, we demonstrated a neural signature of serial dependence in numerosity perception emerging early in the visual processing stream even in the absence of an explicit task. Furthermore, a psychophysical experiment revealed that numerosity perception is biased by a previously presented stimulus in an attractive way, not by repulsive adaptation. These results suggest that serial dependence is a perceptual phenomenon starting from early levels of visual processing and occurring independently from a decision process, which is consistent with the view that these biases smooth out noise from neural signals to establish perceptual continuity.
decision process using a passive-viewing paradigm in the context of numerosity perception. Additionally, we followed up with a psychophysical experiment using numerosity stimuli, which demonstrated the attractive nature of serial dependence.
Method
Participants
Thirty-three participants (25 females; age range: 19–26 years) participated in the electroencephalography (EEG) experiment and were compensated for their time with course credits. A new group of 10 participants (6 females; age range: 20–37 years; including M. Fornaciai) participated in the behavioral experiment and were rewarded with monetary compensation ($10/hr). All participants had normal or corrected-to-normal vision and provided written informed consent before taking part in the study. Except for M. Fornaciai, all participants were naive to the purpose of the study. In the EEG experiment, nothing in the instructions or the recruit-ment materials indicated the central dimension of inter-est (i.e., magnitude) in the experiment. Note that the EEG data set was collected as part of a previously pub-lished study, which addressed a different research ques-tion (Fornaciai & Park, 2017). In that study, the sample size was determined on the basis of the strong effect size (Cohen’s d ~1.0) in an earlier work, which showed the modulation of visual-evoked potentials (VEPs) by numerosity (Park, Dewind, Woldorff, & Brannon, 2016). Here, we used all the available data from this previous data set in addressing the present research question. The sample size of the behavioral (psychophysical) experiment was determined on the basis of the original article on serial dependence that showed robust effects with 3 to 4 participants (Fischer & Whitney, 2014). Experimental procedures were approved by the Univer-sity of Massachusetts Institutional Review Board and were in line with the Declaration of Helsinki.
Apparatus and stimuli
Stimuli were generated using the Psychophysics Tool-box (Brainard, 1997; Kleiner et al., 2007; Pelli, 1997) for MATLAB (Version r2013b; The MathWorks, Natick, MA) and displayed on a monitor screen (ASUS VG248QE) encompassing 34° × 19° of visual angle from a viewing distance of about 90 cm, with a resolution of 1,920 × 1,080 pixels and running at 144 Hz. This experimental setup was the same for both the EEG and behavioral experiments.
Stimuli were arrays of white dots presented on a black background (EEG experiment) or black dots presented
on a gray background (behavioral experiment). In the EEG part of the study, arrays comprised either 100, 200, or 400 dots and were systematically constructed to range equally in three orthogonal dimensions: numer-osity, size, and spacing (DeWind, Adams, Platt, & Brannon, 2015; Fornaciai, Brannon, Woldorff, & Park, 2017; Park et al., 2016). However, the original analysis carried out by Fornaciai and Park (2017) demonstrated that variability in the neural responses was mainly driven by numerosity, so here we considered only that dimension. More information about the specific con-struction of the stimuli can be found in Fornaciai and Park (2017). Stimuli were defined by the following parameters. The individual dot area ranged from 0.0009 degrees2, corresponding to a diameter of 0.02 degrees, to 0.004 degrees2, corresponding to a diameter of 0.07 degrees. Field area (the total circular area within which the dots were presented) ranged from 7.6 degrees2, encompassing 1.5 degrees in diameter, to 30 degrees2, encompassing 6.2 degrees in diameter. In the behav-ioral part of the study, the individual area of the dots was 0.03 degrees2, corresponding to a diameter of 0.2 degrees, whereas the field area of the stimuli was 113.1 degrees2, encompassing 12 degrees in diameter. In all cases, the individual item area of the dots was homo-geneous within each array, and the minimum distance between any two dots was set to be no smaller than the radius of the dots.
Task and procedure
The experiment was performed in a quiet room. In the EEG experiment, participants completed six blocks of 400 trials each. Participants were instructed to keep their gaze on a central fixation, which was presented at the start of the experiment and during interstimulus intervals (ISIs). Each dot-array stimulus, randomly cho-sen from a set of 2,700 pregenerated stimuli, was pre-sented centrally for 200 ms. Successive presentations were separated by a variable ISI (500–700 ms). Partici-pants were required to perform a color-oddball detec-tion task to ensure that they pay attention to the stimuli: The dot array was occasionally displayed in red, and when this happened, participants were required to press a button on a joypad as fast as they could (Fig. 1a). Twenty oddball stimuli were presented during each block, separated by at least 9 and at most 19 standard trials. All oddball stimuli were excluded from data anal-ysis. No other instructions were provided, and the par-ticipants’ verbal reports at debriefing confirmed their naivety to the central dimension of interest (i.e., mag-nitude) of the study. Average hit rate (± SD) in the color-oddball task was 94.0% ± 17.7%, while the aver-age response time was 441 ± 50 ms.
Serial Dependence as a Perceptual Phenomenon 3
In the behavioral experiment, participants first com-pleted a baseline numerosity discrimination condition in which a sequence of two dot arrays was centrally presented. The first (reference) stimulus always com-prised 200 dots, whereas the second (probe) stimulus
comprised a variable number of dots (80–400 dots, with each numerosity tested an equal number of times). Participants were asked to report at the end of each trial which stimulus contained more dots. Each dot-array stimulus was presented on the screen for 250 ms,
Stimulus Presentation200 ms
Fixation Point
Stimulus Presentation200 ms
Catch Trial200 ms
EEG Experimenta
Behavioral Experimentb
Inducer(100 or 400 dots)250 ms
Inducer-ReferenceInterval (500–1500 ms)
Interstimulus Interval
(500–700 ms)
Reference-Probe Interval (550–650 ms)
Reference Stimulus(200 dots)250 ms
Probe Stimulus(80–400 dots)250 ms Response
∞
Fixation Point
Fig. 1. Procedure of the electroencephalogram (EEG) and psychophysical experiments. In the EEG experiment (a), participants were simply asked to view images presented on the screen and press a button when an image was in red. The images were dot arrays containing 100, 200, or 400 dots. On each trial of the psychophysical experiment (b), a series of three dot arrays was pre-sented sequentially: first, an inducer containing either 100 or 400 dots, followed by a reference containing 200 dots, and finally a probe containing a variable (80–400) number of dots. Participants were instructed to ignore the inducer array and indicate whether the reference or the probe contained more dots. Stimuli are not depicted to scale.
4 Fornaciai, Park
and the two stimuli were separated by a variable ISI of 550 to 650 ms. Responses were collected by means of a standard keyboard. After the response, the next trial started automatically after 550 ms. Participants were asked to keep their gaze on a central fixation point, displayed before each trial and during the ISI (Fig. 1b).
After this baseline condition, participants completed another condition that induced serial dependence. This condition was identical to the baseline condition, except that a task-irrelevant inducer stimulus with either 100 or 400 dots (randomly intermixed within each block) was presented for 250 ms prior to the reference. The duration interval between the inducer and the reference was 500 to 1,500 ms. Participants were instructed to ignore this first array in the sequence on each trial. Par-ticipants completed two blocks of 63 trials in the base-line condition and eight blocks of 54 trials in the subsequent condition, taking frequent breaks during the experiment. Each block took about 4 min, and the entire behavioral experimental session took about 50 min.
Electrophysiological recording and analysis
EEG data were recorded for the entire duration of the EEG experiment using a 64-channel, extended cover-age, triangulated equidistance cap (M10, EasyCap, Herrsching, Germany), with a sampling frequency of 1000 Hz, and low-pass filtered on-line at 100 Hz (actiCAP, Brain Products, Munich, Germany). Initially, all the channels were referenced to the vertex (Cz) during recording. The electrooculogram (EOG; one electrode below the left eye and two at the left and right canthi) was monitored to avoid artifacts resulting from eye movement and blinks. Impedance was kept below 15 kΩ most of the time, but occasionally channel imped-ances up to 35 kΩ were tolerated. Data were analyzed off-line in MATLAB (Version R2013b), using the EEGLAB software package (Delorme & Makeig, 2004) and the associated ERPLAB toolbox (Lopez-Calderon & Luck, 2014). First, the EEG data were rereferenced to the average value of all 64 channels, and a high-pass filter (0.1 Hz) was applied. The continuous data were then segmented in 700-ms-long epochs, time-locked to the onset of the stimulus (from −200 ms prestimulus to 500 ms after stimulus onset), with the prestimulus interval used as a baseline. A steplike artifact rejection (pro-vided in ERPLAB) was applied to discard epochs con-taining eye-movement artifacts (threshold = 30 µV, window width = 400 ms, window step = 20 ms), leading to an average rejection rate of 25.9%. VEPs were created by selectively averaging the epochs corresponding to either different numerosities (100, 200, 400 dots), irre-spective of the previous trial, or different combinations of stimuli in the previous and current trial, after which
a low-pass filter at 30 Hz was applied. Hereafter, we use the expression “previous trial condition → current trial condition” to indicate the sequential combination of stimuli. For example, 200 dots preceded by 100 dots is expressed as 100 → 200.
Multivariate pattern analysis
To characterize the influence of serial-dependence effects on the pattern of brain activity, we used a multi-variate pattern analysis in the time domain (King & Dehaene, 2014), using the Neural Decoding Toolbox (Meyers, 2013). To assess the differences in brain activity due to previous stimuli, we analyzed the neural responses to the dot-array stimuli as a function of the stimulus presented on the previous trial. Namely, we either com-pared the responses to the same numerosity preceded by two different numerosities (e.g., 100 → 200 vs. 400 → 200; Figs. 2c and 2d) or compared the responses to one numerosity preceded by the same numerosity (e.g., 100 → 100) with the responses to that numerosity pre-ceded by different ones (e.g., 200 → 100 or 400 → 100; see Fig. S1 in the Supplemental Material available online). A support-vector-machine pattern classifier was trained to classify patterns for two conditions (e.g., 100 → 200 vs. 400 → 200) and tested on a subset of trials not used in the training (leave-one-trial-out cross-validation). As suggested by Grootswagers, Wardle, and Carlson (2017), bins of multiple trials (five) were averaged together into “pseudo trials” to improve the signal-to-noise ratio, and at least five pseudo trials were included for each class. This decoding procedure was performed separately for each participant and repeated 40 times, using different random subsets of data for training and testing. The final estimate of decoding performance was calculated as the average of all the runs. Classification accuracies obtained by training and testing at the same time were tested against the null hypothesis of chance-level classification performance (i.e., 50% probability) with one-sample t tests at each time point, controlling for multiple com-parisons with false discovery rate (FDR; q = .01) and considering a time point to be significant only if at least two consecutive time points were significant at q = .01. Classification accuracies obtained by training at one time point and testing at all other time points (temporal gen-eralization analysis) were similarly tested against a null hypothesis of chance-level accuracy (50% probability), which was corrected for multiple comparisons using FDR (q = .01; Fig. S2 in the Supplemental Material).
Behavioral data analysis
The proportion of responses as a function of the probe numerosity was modeled with a cumulative Gaussian function, fitted according to the maximum-likelihood
method (Watson, 1979), and included a finger-error correction to account for mistakes in key pressing and guessing due to lapses of attention (finger-error rate = 2%). As a measure of accuracy in the different condi-tions of the behavioral task, we took the point of sub-jective equality (PSE), defined as the median of the best-fitting cumulative Gaussian curve to all the data of
a given condition. PSEs represent the probe numerosity perceptually matching (i.e., indistinguishable from) the reference stimulus. As a measure of precision, we took the Weber fraction (w), calculated as the PSE normal-ized by the minimum discriminable increment (just noticeable difference [ JND]; the standard deviation of the underlying Gaussian function).
2
Time From Stimulus Onset (ms)
0.50
0.60
Acc
urac
y
p = .034
Discriminability Betweenvs. vs.
b
d
Am
plitu
de (µ
V)
a
c
––
–
–
– –
–
––
–
–
Fig. 2. Event-related potentials and neural decoding results. Visual-evoked potentials (VEPs) corresponding to different numerosities at channel Oz (a) are shown for each dot array. VEPs evoked by 200 dots are shown (b) as a function of different preceding numerosities. The combinations of stimuli are indicated as “previous trial condition → current trial condition.” For instance, 200 dots preceded by 100 dots is indicated as “100 → 200.” The shaded area indicates the 50-ms time window used to test for the differences in VEP amplitudes. Results of the neural decoding analysis obtained by training and testing a support-vector-machine classifier at the same time point are shown in (c). The thick lines at the bottom of the graph indicate the statistically significant time windows. The shaded region represents the standard error of the mean. Results of the neural decoding analysis obtained by training and testing the classifier at one time point and testing it across all the latency windows, yielding a temporal generalization plot, are shown in (d).
6 Fornaciai, Park
Results
We first analyzed the VEPs elicited by numerosities irrespective of previous stimuli. As shown in Figure 2a, the VEPs in response to the dot arrays were strongly modulated by numerosity; greater numerical magnitude resulted in greater VEP amplitude around 100 ms (in the negative direction) and 200 ms (in the positive direction) after stimulus onset. This pattern is consistent with results of a recent study showing a strong modula-tion of early visual cortical activity by numerical mag-nitude (Park et al., 2016). Then, to test the effect of serial dependence in this neural signature, we sorted the VEPs in response to 200 dots as a function of the stimulus presented in the previous trial (i.e., 100, 200, or 400 dots). The brain waves to the same 200 dots showed different trajectories conditional on the stimu-lus presented in the previous trial (Fig. 2b). This differ-ence was pronounced at the positive deflection around 200 ms after stimulus onset, with a statistically signifi-cant difference in the VEP amplitudes at the peak latency (216 ms) taken from the neutral 200 → 200 condition (average amplitude in a 50-ms time window around the peak = 4.31 ± 0.876 µV and 4.77 ± 0.835 µV, respectively, for the 100 → 200 and 400 → 200 condi-tions); paired-samples t test, t(32) = 2.21, p = .034. The direction of this modulation was attractive, so a smaller numerosity presented in the previous trial resulted in a smaller VEP amplitude in the current trial, and vice versa. Importantly, such differences could not be explained by a decision process because participants were not making any judgment on numerosity, and, in fact, they were completely naive to the central dimen-sion of interest in this experiment.
To achieve a more sensitive measure of serial-dependence effects, we used a neural decoding analysis to quantify differences in the pattern of brain activity. We contrasted the two cases that were giving rise to opposite predictions (i.e., 100 → 200 vs. 400 → 200), which in a similar way to the VEP modulations should result in opposite biases (see Fig. S1 in the Supplemental Material for other comparisons). In this contrast (Fig. 2c), we found a robust pattern of classification accuracy, starting early in the visual stream and persisting throughout the analyzed epoch (three main clusters of above-chance classification accuracy: 55–85 ms, 105–225 ms, and 245–475 ms; FDR-adjusted ps ranged from .0001 to .006), with a peak at 375 ms (peak accuracy = 0.616 ± 0.127). Moreover, the pattern of temporal generalization shown in Figure 2d suggests that two stages of relatively sus-tained activity are involved in the observed effect: an early one spanning approximately 55 to 245 ms after stimulus onset and a later, much stronger one spanning 255 to 475 ms after stimulus onset (see also Fig. S2 in the Supplemental Material, which shows the significant
time windows of the temporal generalization plot). These findings suggest that the recent history of stimula-tion leaves a strong signature on the pattern of brain activity. It is important to note that although the decod-ing analysis did not provide information about the direc-tion of the effect, the pattern of VEPs as a function of the previous numerosity (Fig. 2b) provided a prelimi-nary hint that the current stimulus was biased toward the previous stimulus in an attractive fashion.
To acquire a clearer sense of the direction of the serial-dependence effect, we tested in a behavioral paradigm how a task-irrelevant dot array influences the perception of task-relevant dot arrays to follow (Fig. 1b). If the perceived numerical magnitude of dot arrays in a numerosity discrimination task is affected by previ-ous stimuli according to perceptual adaptation, as pro-posed by Fritsche et al. (2017), current task-relevant stimuli are expected to be biased in a repulsive way. Namely, adapting to low numerosities would make sub-sequent stimuli appear more numerous, and vice versa (e.g., Burr & Ross, 2008). On the other hand, an oppo-site outcome should be expected from attractive serial dependencies, with subsequent stimuli appearing more similar to previous ones. Baseline measurements (Fig. 3a) first showed that participants can reliably discrimi-nate the two sequentially presented dot arrays with relatively high precision (Weber fraction, w = 0.13 ± 0.015), although the 200-dot reference appeared to be slightly underestimated (average PSE = 184.9 ± 0.63), possibly because of time-order errors induced by the fixed order of the stimuli (Hellström, 1985). More important, when we presented a task-irrelevant inducer array before the reference array, we found a pattern of effects clearly consistent with attractive serial depen-dence (Figs. 3b and 3c), with the two inducer conditions yielding significantly different measures of perceived numerosity (Fig. 3b; average PSE difference = 22.8 ± 2.8 dots); two-tailed paired-samples t test, t(9) = 8.6, p < .0001, Cohen’s d = 1.69, although with comparable preci-sion of numerical discrimination (100-dot inducer: w = 0.12 ± 0.015; 400-dot inducer: w = 0.11 ± 0.006), t(9) = 0.55, p = .59, which was not different from the baseline condition (p > .28). Namely, while a less numerous inducer (100 dots) biased the perceived numerosity of the reference array (200 dots), causing a relative under-estimation, a more numerous inducer (400 dots) resulted in the opposite effect, causing a relative overestimation of the reference array. This effect was evident in all the participants tested (Fig. 3c).
Discussion
Attractive serial dependence has been initially proposed to reflect the results of brain processes aimed to ensure visual stability and continuity in the face of noise and
“Probe More Numerous”Response (proportion) PSE (dots)
Subj
ect 2
Subj
ect 3
Subj
ect 1
(M. F
.)
Subj
ect 4
Subj
ect 5
Subj
ect 6
Subj
ect 7
Subj
ect 8
Subj
ect 9
Subj
ect 1
0
Fig
. 3.
Beh
avio
ral
resu
lts.
The
aver
age
psy
chom
etri
c cu
rve
in t
he
bas
elin
e co
nditio
n f
or
“pro
be
more
num
erous”
res
ponse
s (a
) is
show
n a
s a
funct
ion o
f pro
be
num
erosi
ty.
The
aver
age
poin
t of
subje
ctiv
e eq
ual
ity
(PSE
; b)
is s
how
n f
or
each
induce
r co
nditio
n. Err
or
bar
s re
pre
sent st
andar
d e
rrors
of
the
mea
n. A
ster
isks
indic
ate
sign
ific
ant diffe
rence
s bet
wee
n c
onditio
ns
(***
p < .00
1). Psy
chom
etri
c cu
rves
are
show
n s
epar
atel
y fo
r ea
ch o
f th
e 10
par
tici
pan
ts in the
beh
avio
ral ex
per
imen
t, c
orr
espondin
g to
the
two induce
r co
ndi-
tions,
in (
c). The
curv
e fo
r “p
robe
more
num
erous”
res
ponse
s is
show
n a
s a
funct
ion o
f pro
be
num
erosi
ty. Par
tici
pan
ts’ psy
chom
etri
c cu
rves
show
that
the
two induce
rs r
esulted
in
mar
ked
ly d
iffe
rent
per
form
ance
s, w
ith P
SEs
shifte
d a
ccord
ing
to t
he
induce
r m
agnitude,
dem
onst
rating
that
the
per
ceiv
ed n
um
erosi
ty o
f th
e re
fere
nce
arr
ay r
efle
cts
attr
active
se
rial
dep
enden
ce, not
repuls
ive
adap
tation. A
rrow
s in
dic
ate
the
valu
es o
n t
he
x-a
xis
corr
espondin
g to
the
poin
t of
subje
ct e
qual
ity.
8 Fornaciai, Park
discontinuities in sensory input. Recently, however, the nature of this phenomenon has been subject to debate: In one view, serial dependence occurs at the perceptual level before sensory signals are turned into a conscious percept, hence biasing the phenomenological appear-ance of visual stimuli (Burr & Cicchini, 2014; Fischer & Whitney, 2014; St. John-Saaltink, Kok, Lau, & de Lange, 2016). In another view, attractive serial dependence emerges from a decision process that biases visual rep-resentations stored in working memory, resulting in behavioral effects but without any impact at the phe-nomenological level (Alais et al., 2017; Fritsche et al., 2017). In the present study, we aimed to disentangle these two possibilities by characterizing the neural sig-nature of serial dependence independently from a deci-sion process.
The analysis of VEPs corresponding to different dot-array stimuli show that numerosity-sensitive responses to currently viewed stimuli are systematically biased by the numerical magnitude of the stimulus in the previous trial in an attractive way, even in the absence of an explicit task or any behavioral relevance for the numer-osity dimension. Furthermore, the results of the decod-ing analysis more clearly highlight the temporal dynamics of serial dependence, demonstrating a robust neural signature of serial dependence on approximate numerical representations. As our paradigm did not involve any explicit judgments on the magnitude of the dot-array stimuli, this effect could not be explained as arising from a decision process. Thus, serial-dependence effects in the present study are more easily explained by biases at the perceptual level, likely directly altering the appearance of the visual stimuli as a function of the recent history of stimulation. The temporal dynam-ics highlighted by the decoding analysis further sup-ports this interpretation. Indeed, the early portion of the effect (55–245 ms; Fig. 2c) suggests that serial dependence arises at the initial feed-forward processing stage, very early after stimulus onset and with a latency compatible with the earliest stages of cortical visual processing for numerosity (Fornaciai et al., 2017). This observation, although in striking contrast with an account exclusively based on high-level decision pro-cesses (Fritsche et al., 2017), is consistent with a recent functional MRI study showing serial-dependence effects in visual area V1 (St. John-Saaltink et al., 2016). The current results further extend that previous finding by providing timing information implying that such activity in early visual areas reflects feed-forward sensory sig-nals rather than later feedback signals. This early effect is followed by a later peak of classification accuracy around 255 to 475 ms, showing that the bias persists in further processing stages. This two-stage dynamic is also suggested by the temporal generalization plot (Fig.
2d), where two relatively sustained patterns are evident at around 50 to 250 ms and 250 to 475 ms (see also Fig. S2 in the Supplemental Material, which shows the sig-nificant time windows of the temporal generalization plot). Collectively, the early onset of decoding effects suggests that serial dependence emerges from early visual areas in their feed-forward processes, establish-ing a perceptual representation, while the later decod-ing effects might reflect the amplified perceptual representation reaching multiple brain systems in a more global manner, as proposed by a recent theoreti-cal framework of conscious perception (Dehaene, Changeux, Naccache, Sackur, & Sergent, 2006; Dehaene & Naccache, 2001). Consistent with this idea, our results showed that across participants, decoding accuracy in the relatively early time window after stimulus onset (55–245 ms) was robustly correlated with decoding accuracy at the later time window (255–475 ms; r = .51, p = .0024), suggesting that the two stages are linked, occurring interdependently and possibly in a cascade fashion.
One may still argue that the current EEG results may have been driven by some implicit decision process on memorized representation of numerosities. However, this explanation could be ruled out for several reasons. First, since the EEG paradigm involved a detection task, it is unlikely that participants maintained a memorized representation of the stimuli. Second, even if partici-pants maintained a memorized representation of the stimuli, they made a decision on color, so it is unlikely that numerosity as a task-irrelevant dimension would have been represented in working memory (see LaRocque, Riggall, Emrich, & Postle, 2017; Lewis-Peacock, Drysdale, Oberauer, & Postle, 2012; Yu & Shim, 2017). Third, even if participants kept a memorized represen-tation of the magnitude aspect of the stimuli, there is no clear reason for participants to make memorized representations of numerosity (as opposed to other nonnumerical dimensions), as dot arrays are inherently multidimensional. Fourth, even if participants made a memorized representation of numerosity, it is unclear what kind of implicit decisions they would make. Thus, it is unlikely for a decision process on memorized rep-resentation of numerosity to occur in our EEG para-digm. Moreover, to reiterate, the emergence of neural signatures for serial dependence as early as 50 to 100 ms reflects initial feed-forward processes across early visual areas, consistent with the idea that serial depen-dence starts at the perceptual level (see Kiyonaga, Scimeca, Bliss, & Whitney, 2017).
One remaining question from the neural decoding results is whether the difference in brain patterns actu-ally reflects attractive serial dependence or repulsive adaptation, because classification accuracies do not
indicate the direction of the effect. Our behavioral results show that numerical representations are affected by previous stimuli in an attractive way, as shown by the systematic shift of the individual psychometric curves as a function of the numerical magnitude of the inducer, with little influence on the precision of numeri-cal discriminability (Fig. 3c). These serially dependent attractive biases, which distort the true nature of the stimuli, are thus distinct from priming, which enhances performance after repeated stimulus presentation.
It should be noted that this behavioral paradigm, which obviously necessitates a decision process, leaves some alternative possibilities open. Indeed, the observed attractive effect could arise from a biased perceptual representation of the reference stimulus, a biased working memory representation of the reference stimulus during the decision process, or a combination of both. Nevertheless, these results can be interpreted in the context of the EEG results, which demonstrate the neural signature of serial dependence in the absence of any explicit decision requirements (Fig. 2), which leads us to argue that biased perceptual representation is, at least in part, responsible for the observed attrac-tive serial dependence.
Finally, it is also worth noting that the size of the serial-dependence effect observed in the present behav-ioral experiment is fairly similar to that of orientation perception (Fischer & Whitney, 2014). Considering the magnitude of the effect (average difference between PSEs in the two inducer conditions = 22.8 dots) and the numerical distance between inducer and reference stimuli in terms of JNDs (average JND in the baseline condition = 23.6 dots), the extent of the bias in numeri-cal estimates was around 1 JND. Although this effect seems smaller compared with Fischer and Whitney’s (2014) results (effect around 3 JNDs in the two-alternative forced-choice task reported in Experiment 3), this is easily explained by the fact that the stimuli used in the present task did not represent an optimal range to induce attractive effects. Indeed, the inducer-reference numerical distance in the present study was around 7 JNDs, whereas Fischer and Whitney (2014) found a peak of the attractive effect when the difference in orientation between successive stimuli was around 5 JNDs—peak effect at 27.78 degrees (from Experiment 1), with an average JND of 5.39 degrees (from Experi-ment 3).
In sum, the current results demonstrate that serial dependence occurs in the absence of an explicit task—hence independently from a decision process—and differences in stimulus representation due to past stim-uli can be decoded from brain signals starting early in the visual stream. These results thus suggest that attrac-tive serial dependence has a clear perceptual nature,
and they support the idea that serial dependence serves as a mechanism for perceptual continuity and visual stability.
Action Editor
Edward S. Awh served as the action editor for this article.
Author Contributions
M. Fornaciai conceived the study. M. Fornaciai and J. Park devised the experiments. M. Fornaciai collected and analyzed the data. M. Fornaciai and J. Park wrote and revised the manuscript.
We thank Brynn Boutin, Nancy Cai, and Samuel Casler for their assistance with data collection. We appreciate Guido Marco Cicchini, Zach Salander, and Adrian Staub for insightful comments on the manuscript.
Declaration of Conflicting Interests
The author(s) declared that there were no conflicts of interest with respect to the authorship or the publication of this article.
Funding
This work was supported by National Science Foundation CAREER Award BCS1654089 to J. Park.
Supplemental Material
Additional supporting information can be found at http://journals.sagepub.com/doi/suppl/10.1177/0956797617737385
References
Alais, D., Leung, J., & Van der Burg, E. (2017). Linear sum-mation of repulsive and attractive serial dependencies: Orientation and motion dependencies sum in motion perception. The Journal of Neuroscience, 37, 4381–4390. doi:10.1523/JNEUROSCI.4601-15.2017
Brainard, D. H. (1997). The Psychophysics Toolbox. Spatial Vision, 10, 433–436. doi:10.1163/156856897X00357
Burr, D., & Cicchini, G. M. (2014). Vision: Efficient adaptive coding. Current Biology, 24, R1096–R1098. doi:10.1016/j .cub.2014.10.002
Burr, D., & Ross, J. (2008). A visual sense of number. Current Biology, 18, 425–428. doi:10.1016/j.cub.2008.02.052
Cicchini, G. M., Anobile, G., & Burr, D. C. (2014). Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform. Proceedings of the National Academy of Sciences, USA, 111, 7867–7872. doi:10.1073/pnas.1402785111
Corbett, J. E., Fischer, J., & Whitney, D. (2011). Facilitating stable representations: Serial dependence in vision. PLOS
Dehaene, S., Changeux, J. P., Naccache, L., Sackur, J., & Sergent, C. (2006). Conscious, preconscious, and subliminal processing: A testable taxonomy. Trends in Cognitive Sciences, 10, 204–211. doi:10.1016/j.tics.2006.03.007
Dehaene, S., & Naccache, L. (2001). Towards a cognitive neuroscience of consciousness: Basic evidence and a workspace framework. Cognition, 79, 1–37. doi:10.1016/S0010-0277(00)00123-2
Delorme, A., & Makeig, S. (2004). EEGLAB: An open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. Journal of Neuroscience Methods, 134, 9–21. doi:10.1016/j.jneumeth.2003.10.009
DeWind, N. K., Adams, G. K., Platt, M. L., & Brannon, E. M. (2015). Modeling the approximate number system to quan-tify the contribution of visual stimulus features. Cognition, 142, 247–265. doi:10.1016/j.cognition.2015.05.016
Fischer, J., & Whitney, D. (2014). Serial dependence in visual perception. Nature Neuroscience, 17, 738–743. doi:10.1038/nn.3689
Fornaciai, M., Brannon, E. M., Woldorff, M. G., & Park, J. (2017). Numerosity processing in early visual cortex. NeuroImage, 157, 429–438. doi:10.1016/j.neuroimage .2017.05.069
Fornaciai, M., & Park, J. (2017). Distinct neural signatures for very small and very large numerosities. Frontiers in Human Neuroscience, 11, Article 21. doi:10.3389/fnhum.2017.00021
Fritsche, M., Mostert, P., & de Lange, F. P. (2017). Opposite effects of recent history on perception and deci-sion. Current Biology, 27, 590–595. doi:10.1016/j.cub .2017.01.006
Grootswagers, T., Wardle, S. G., & Carlson, T. A. (2017). Decoding dynamic brain patterns from evoked responses: A tutorial on multivariate pattern analysis applied to time series neuroimaging data. Journal of Cognitive Neuroscience, 29, 677–697. doi:10.1162/jocn_a_01068
Hellström, Å. (1985). The time-order error and its relatives: Mirrors of cognitive processes in comparing. Psychological Bulletin, 97, 35–61. doi:10.1037/0033-2909.97.1.35
King, J.-R., & Dehaene, S. (2014). Characterizing the dynam-ics of mental representations: The temporal generaliza-tion method. Trends in Cognitive Sciences, 18, 203–210. doi:10.1016/j.tics.2014.01.002
Kiyonaga, A., Scimeca, J. M., Bliss, D. P., & Whitney, D. (2017). Serial dependence across perception, attention,
and memory. Trends in Cognitive Sciences, 21, 493–497. doi:10.1016/j.tics.2017.04.011
Kleiner, M., Brainard, D., Pelli, D., Ingling, A., Murray, R., & Broussard, C. (2007). What’s new in Psychtoolbox-3? Perception, 36, 1–16. doi:10.1068/v070821
Kohn, A. (2007). Visual adaptation: Physiology, mechanisms, and functional benefits. Journal of Neurophysiology, 97, 3155–3164. doi:10.1152/jn.00086.2007
LaRocque, J. J., Riggall, A. C., Emrich, S. M., & Postle, B. R. (2017). Within-category decoding of information in dif-ferent attentional states in short-term memory. Cerebral Cortex, 27, 4881–4890. doi:10.1093/cercor/bhw283
Lewis-Peacock, J. A., Drysdale, A. T., Oberauer, K., & Postle, B. R. (2012). Neural evidence for a distinction between short-term memory and the focus of attention. Journal of Cognitive Neuroscience, 24, 61–79. doi:10.1162/jocn_a_00140
Liberman, A., Fischer, J., & Whitney, D. (2014). Serial depen-dence in the perception of faces. Current Biology, 24, 2569–2574. doi:10.1016/j.cub.2014.09.025
Lopez-Calderon, J., & Luck, S. J. (2014). ERPLAB: An open-source toolbox for the analysis of event-related poten-tials. Frontiers in Human Neuroscience, 8, Article 213. doi:10.3389/fnhum.2014.00213
Meyers, E. M. (2013). The neural decoding toolbox. Frontiers in Neuroinformatics, 7, Article 8. doi:10.3389/fninf.2013.00008
Park, J., Dewind, N. K., Woldorff, M. G., & Brannon, E. M. (2016). Rapid and direct encoding of numerosity in the visual stream. Cerebral Cortex, 26, 748–763. doi:10.1093/cercor/bhv017
Pelli, D. G. (1997). The VideoToolbox software for visual psy-chophysics: Transforming numbers into movies. Spatial Vision, 10, 437–442. doi:10.1163/156856897X00366
St. John-Saaltink, E., Kok, P., Lau, H. C., & de Lange, F. P. (2016). Serial dependence in perceptual decisions is reflected in activity patterns in primary visual cortex. The Journal of Neuroscience, 36, 6186–6192. doi:10.1523/JNEUROSCI.4390-15.2016
Watson, A. B. (1979). Probability summation over time. Vision Research, 19, 515–522. doi:10.1016/0042-6989(79)90136-6
Xia, Y., Leib, A. Y., & Whitney, D. (2016). Serial dependence in the perception of attractiveness. Journal of Vision, 16(15), Article 28. doi:10.1167/16.15.28
Yu, Q., & Shim, W. M. (2017). Occipital, parietal, and frontal cortices selectively maintain task-relevant features of multi-feature objects in visual working memory. NeuroImage, 157, 97–107. doi:10.1016/j.neuroimage.2017.05.055
![OFF-LINE ARABIC HANDWRITTEN WORDS SEGMENTATION … · complicated the task [6]. This is task seems simple, but it isn't. Even for human beings when the absence of full context [7].](https://static.documents.pub/doc/80x56/60a3096f6812f250186c748c/off-line-arabic-handwritten-words-segmentation-complicated-the-task-6-this-is.jpg)
