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\begin{document}

\title{Statistics Learning of Target Regularities in a Pop-out Search:
Behavioral Performance and Neural Mechanisms}



\author[1]{Guang Zhao}%
\author[1]{Yuhao Duan}%
\author[1]{Jiahuan Chen}%
\author[2]{Dongwei Li}%
\author[1]{Shiyi Li}%
\author[1]{Qiang Wang}%
\author[3]{Hongjin Sun}%
\affil[1]{Tianjin Normal University}%
\affil[2]{Beijing Normal University}%
\affil[3]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 12, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
The study examined human performance and related neural mechanisms in a
pop-out search with different probabilities of target location and the
relation between the target location and feature. In a search array, we
introduced the binding relation between two target features and two
kinds of location probability. Moreover, in the second half of the
experiment, such a probability pattern for location/feature binding was
reversed. Behavioral results revealed successful statistical learning of
probability for both absolute target location and target's
location-feature binding indicated by faster RTs in the high-probability
conditions for both location and location-feature binding. Moreover, the
learning benefit for the probability of location-feature binding
acquired during 1st (training) phase was still expressed in the 2nd
(reversal) phase despite the actual binding probability was reversed.
ERP results suggested that both the attentional selection and response
selection process were affected by such learning revealed in the
difference in N2pc and LRP amplitudes between the two conditions with
different binding probability in the reversal phase. An expectation to
the high probability for location-feature binding was also suggested
from time-frequency analysis and Multi-Variate Pattern Classification
(MVPC) indicated by larger alpha ERD magnitude and lower decoding
accuracy, respectively, when the target appeared at the high-binding
location in the training phase instead of the reversal phase. Overall,
we have demonstrated behavioral evidence and 4 EEG markers for the
associative learning of the probability of relation between location and
feature of target in a pop-out search.%
\end{abstract}%



\sloppy


\textbf{Statistics Learning of Target Regularities in a Pop-out Search:
Behavioral Performance and Neural Mechanisms}

Guang Zhao\textsuperscript{1*\#}, Yuhao Duan\textsuperscript{1\#},
Jiahuan Chen\textsuperscript{1}, Dongwei Li\textsuperscript{2, 3}, Shiyi
Li\textsuperscript{1}, Qiang Wang\textsuperscript{1}, Hong-jin
Sun\textsuperscript{4}

\textsuperscript{1} Faculty of Psychology, Tianjin Normal University,
Tianjin 300387, China

\textsuperscript{2} State Key Laboratory of Cognitive Neuroscience and
Learning \& IDG/McGovern Institute for Brain Research, Beijing Normal
University, Beijing, China

\textsuperscript{3} Centre for Human Brain Health, University of
Birmingham, Birmingham, UK

\textsuperscript{4} Department of Psychology, Neuroscience and
Behaviour, McMaster University, Hamilton, Ontario, Canada

\textsuperscript{\#} These authors contributed equally

\textsuperscript{*} Correspondence should be sent to

Dr. Zhao Guang

Faculty of Psychology, Tianjin Normal University, Tianjin 300387, China

Email: zhaoguang721@163.com



\textbf{ABSTRACT}

The study examined human performance and related neural mechanisms in a
pop-out search with different probabilities of target location and the
relation between the target location and feature. In a search array, we
introduced the binding relation between two target features and two
kinds of location probability. Moreover, in the second half of the
experiment, such a probability pattern for location/feature binding was
reversed. Behavioral results revealed successful statistical learning of
probability for both absolute target location and target's
location-feature binding indicated by faster RTs in the high-probability
conditions for both location and location-feature binding. Moreover, the
learning benefit for the probability of location-feature binding
acquired during 1\textsuperscript{st} (training) phase was still
expressed in the 2\textsuperscript{nd} (reversal) phase despite the
actual binding probability was reversed. ERP results suggested that both
the attentional selection and response selection process were affected
by such learning revealed in the difference in N2pc and LRP amplitudes
between the two conditions with different binding probability in the
reversal phase. An expectation to the high probability for
location-feature binding was also suggested from time-frequency analysis
and Multi-Variate Pattern Classification (MVPC) indicated by larger
alpha ERD magnitude and lower decoding accuracy, respectively, when the
target appeared at the high-binding location in the training phase
instead of the reversal phase. Overall, we have demonstrated behavioral
evidence and 4 EEG markers for the associative learning of the
probability of relation between location and feature of target in a
pop-out search.

\textbf{Key Words} : Selection history, Probability; Flexibility;
Attention; Decoding; EEG



\textbf{Introduction}

Humans possess the capacity to extract regularities in their
surroundings. This cognitive process is commonly known as statistical
learning (SL) (Frost et al., 2019; Turk-Browne et al., 2005; Zhao et
al., 2013). Visual statistical learning (VSL) involves various types of
regularities, including probability for spatial location of objects
(Geng \& Behrmann, 2005; Wang \& Theeuwes, 2018a) and relation between
objects (Chun \& Jiang, 1998).

Humans' cognitive resources are limited, necessitating the allocation of
these resources to the most relevant information in the environment.
This allocation is accomplished through the function of attention. VSL
is believed to modulate attention to enhance behavioral performance. For
instance, in probabilistic cuing or location probability learning, a
process related to learning of the spatial regularity of object,
participants are typically instructed to search for a target 'T' among
distractors 'L's (Geng \& Behrmann, 2005; Gim\selectlanguage{ngerman}énez-Fernández et al.,
2021; Jiang et al., 2013, 2014). Unbeknownst to them, the target appears
more frequently in one region than in the others. It was found that
search responses are faster when the target appears in the more frequent
region.

It was observed that targets appearing in high-probability locations
elicited a larger N2pc, a negative ERP component associated with
attentional selection (Duncan et al., 2023). In addition, eye-tracking
research demonstrated that the probability of first saccade directed to
high-probability location was greater than that for the low-probability
location (Jiang et al., 2014). To offer more direct evidence of the
nature of the VSL, Huang et al. (2023), by combining a search task with
a probe task, discovered that more cognitive resource was allocated to
the high-probability region compared to the low-probability
region\emph{before} the stimulus onset. This suggests a proactive
attention bias was developed through target location probability
learning.

Due to the importance of VSL, it is crucial to determine the conditions
and mechanisms under which the learning can take place. Previous studies
have typically employed either a serial search task (e.g., searching for
a `T' among `L's) or an additional singleton task (e.g., searching for a
unique shape among a set of homogeneous shapes while ignoring a salient
color singleton, Theeuwes, 1991; 1992). It remains unclear whether
location probability learning would still benefit the search when the
target is a \emph{pop-out stimulus in a homogeneous distractor array}and
the search process is expected to be efficient already.

While location probability learning typically focuses on only location
regularities, it has been discovered that individuals can also learn the
corresponding relationship between spatial regularities and other
factors (e.g., context, time). For example, in Hong et al (2020), the
location probability of the target varied based on different contexts,
wherein each context predicted distinct high-probability target
locations. The results showed that context-specific spatial biases
emerged when the contextual information was relevant to the task. In Xu
et al (2023), the target high-probability location was associated with
interval of fixation. And it was found that participants prioritized
high-probability locations based on where the target was most likely to
appear there. Furthermore, in the task-irrelevant singleton paradigm,
successful learning of the relationship between distractor features and
the spatial regularity of distractors has been confirmed (Failing et
al., 2019). However, it remains to be examined whether VSL of the
relationship between the feature and the spatial regularity of
the\emph{target} is also possible.

In the case of target location probability learning, a certain level of
rigidity has been observed. Jiang et al. (2013) discovered that
following learning in the training phase, when the regularity was
removed in the testing phase, the difference in response times between
trials where the target appeared at previously high-probability
locations and trials where it appeared at previously low-probability
locations did not decrease compared to that in the training phase. The
study also demonstrated that the learning effect could persist for at
least a week. In a recent study by Golan and Lamy (2023),
target-location probability cueing was found to reduce search slopes
both during the learning phase and the testing phase, indicating a
long-lasting and inflexible nature of the learned attentional bias. The
meta-analysis by Giménez-Fernández and colleagues (2022) determined that
the effect size of target location probability learning decreased by
half in the testing phase. Overall, research suggests that the effect of
target location probability learning tend to be persistent and long
lasting. However, it remains unclear how flexible VSL is in the context
of new regularities in the environment.

Although it could be beneficial that VSL is long lasting, the extent to
which observers benefit from VSL can also rely on their capacity to
adapt flexibly to \emph{changes} of the regularity in the environment.
Failure to update previously learned regularities can impair behavioral
performance, if the old regularities conflict with the new regularity in
the altered environment. The flexibility of VSL can be investigated
through a two-phase approach (Hong et al., 2022). The initial learning
takes place during the first training phase, followed by a subsequent
phase where the regularity is changed by introducing new ones.
Flexibility is evaluated by examining how quickly participants adjust
their performance to track the updated statistical regularity. In Hong
et al. (2022), it was found that people could successfully learn the
changed spatial regularity which was reflected by the faster RTs for
target in the new high-probability region compared to low-probability
region which had never served as the high-probability region.
Nevertheless, the RTs was still fast for target in the previous
high-probability region compared to other low-probability regions and
the RTs between trials in which targets appeared at previous and new
high-probability region didn't differ, showing that previously learned
attention bias persist even when the regularity had changed.

The present study aimed to investigate the characteristics of VSL for
learning of probability of both single attribute and association of two
attributes. To this end, in a visual search task, we manipulated
probability of both target location and target location-feature binding.
We selected pop-out search as a paradigm, as one would assume that in
pop-out search, observers can easily ignore other search items. Yet it
has been shown that pop-out search can be affected by inter-trial
priming, on pop-out performance has been well studied (Maljkovic and
Nakayama, 1994). Here, we intended to examine another form of selection
history (Anderson et al., 2021; Awh et al., 2012; Theeuwes, 2019)
involving statistical regularity of target in a pop-out task. A previous
study (Wang and Theeuwes, 2018c) has examined shape search in the
present of elements of different shapes and task-irrelavant singleton
and found statistical regularities affected search performance.

We implemented two high-probability locations. The target appeared in
one of two high-probability locations more frequently than in other
low-probability locations. In addition, one target feature was presented
more frequently in one high-probability location, and the other feature
was presented more frequently in the other high-probability location. In
the reversal phase, we reversed the relationships between locations and
features in the two high-probability locations. Moreover, we also
examined whether new learning could occur if the probability of target
location-feature binding were changed after initial learning. Our
experiment thus consisted of training and reversal phases.

Using EEG with high temporal resolution, we focused on the temporal
dynamics of event related potentials (ERP) by analyzing two components:
N2pc and LRP. First, N2pc component is a lateralized component that
typically occurs around 200-300ms, reflecting allocation of attention to
the task-relevant stimulus (Luck \& Hillyard, 1994; Sawaki \& Luck,
2013). Second, LRP component reflects the efficiency of response
selection, that is, the process of determining which response is
appropriate after the target have been found (Smulders et al., 2012).

Third, post-stimuli alpha-band oscillatory activities was also proposed
to be modulated by expectation (Rungratsameetaweemana et al., 2018; Zhou
et al., 2020). We thus conducted the time frequency analysis to reveal
the role of expectation in VSL of relation between the target feature
and the spatial regularity and how the expectation was changed by
updated regularity. Fourth, it has been found that expectation of
following stimuli can influence the feature decoding accuracy of the
stimuli that actually appear (Kok \& De Lange, 2012; Kumar et al., 2017;
Richter et al., 2018). Multivariate pattern analysis (MVPA) leverage
pattern information that would normally be averaged out in univariate
analyses. This makes it more sensitive to effects based on distributed
patterns of neural activity (Hall-McMaster et al., 2019). Therefore, we
employed the MVPA to provide more robust evidence about the function of
expectation in such learning.

For behavioural performance, our hypotheses consisted of two parts.
First, we expected better performance (higher accuracy and/or faster
reaction time, RT) (1) when the target appeared in high-probability
locations than low-probability locations and (2) when target feature was
consistent with the feature with high-probability of location-feature
binding compared to the feature with low-probability of location-feature
binding. Second, given we reversed the probability of location-feature
binding following training phase, we hypothesized that, if the learning
is long lasting and not flexible, the pattern of results in the reversal
phase should reversed from that of training phase when comparing
conditions with high vs low binding probability. In contrast, if
observers could quickly learn the new regularities, we would expect to
observe similar results between training and reversal phase.

For the EEG measures, if learning took place, we would see a difference
between high vs low probability for location-feature binding in N2pc or
LRP respectively. In the two conditions with high vs low probabilities
for location-feature binding, the stimulus-driven (from pop-out
singleton target) or goal-driven (task instruction to search for color
or shape singleton) factors were identical, any magnitude difference in
ERP between the two binding conditions (found in either training or
reversal phase, or both) would reflect the effect of statistical
learning. In addition, the general learning effect (expectation) would
also be seen in post-stimuli alpha-band oscillatory activities and MVPA.

For the condition for low location probability, there was equal
probability for either of the two target features. This is different
from the conditions for high location probability where the feature is
location contingent. Thus, our design would not allow isolation of the
contribution of probability learning for target location. The comparison
of results from high vs low location probability should be treated with
caution.

\textbf{Method}

\textbf{Participant}

Thirty-two participants from Tianjin Normal University in China
participated in this experiment. The sample size was determined
according to a recent EEG study investigating a similar question as the
current study (van Moorselaar et al., 2021). Out of the original sample,
three participants were excluded due to bad segments in ERP in more than
40\% of all segments. Participants were paid approximately 60 RMB per
hour. All participants had normal visual acuity or corrected visual
acuity. They were provided with written informed consent before the
experiment. The research was approved by the committee for research
ethics from the local institution.

\textbf{Equipment and stimulation}

The experiment was carried out in an EEG shielded room. Participants
were seated approximately 80 cm from the monitor. The control of the
experimental procedure was achieved through the E-prime 3.0 software.
The stimuli were presented on a 19-inch LED monitor (1024 × 768 pixels,
75 Hz). Participants were told to keep their heads still during the
completion of the task to minimize artifacts and were encouraged to
relax during breaks.

The search display contained 8 outline shapes including 7 gray circles
(approximately 1.2×1.2°, RGB: 165/165/165) plus one target item that was
either colored in green (approximately 1.2×1.2°, RGB: 0/123/0) or
colored in gray but in rectangular shape (approximately 1.2×1.2°, RGB:
165/165/165). The shapes were presented on an imaginary circle at equal
distance (4.2° visual degrees radius). Inside all stimuli were gray bars
(approximately 0.7×0.2°, RGB: 165/165/165), with the gray bar either
tilted 30° to the left or 30° to the right. All stimuli were presented
on a black background (see Figure 1A).

\textbf{Design and procedure}

We manipulated target probability in both location and location-feature
binding. We generated three probability conditions termed
``low-location'', ``high-binding'' and ``low-binding''. Low-location
condition referred to the condition where target appeared in the 6 low
probability (5\%) locations and the probability of the two features was
equal (2.5\%). The two targets' high probability locations were always
placed on the opposite sides of an imaginary circle with a maximum
distance between each other. High-binding and low-binding conditions are
the two conditions with high location probability (35\%) and the
probability of a given feature was high (30\%) and low (5\%)
respectively.

Figure 1B shows an example of one high location probability condition
with two possible target features appearing in upper right and bottom
left locations respectively (note that in actual experiment, only one
singleton target would be displayed). For a given participant, a target
could appear in upper right location with 30\% probability being green
circle and 5\% gray square or a target could also appear in bottom left
location with 5\% probability being green circle and 30\% gray square.
Thus, the likelihood of the two target features appearing at one
high-probability location was different from the other but equal for the
two high probability locations combined.

To obtain optimal lateralized electrophysiological activities, the high
probability locations would only be located on the diagonal of the
imaginary circle avoiding top and bottom locations. The locations of
high location probability conditions and their binding relationships
with target features were counterbalanced between participants.

In the second half of the experiment, the relationship between location
and feature were reversed. For example, the green circle, which had
previously often appeared in upper right location, now often appeared in
bottom left location, while the gray square, previously often appeared
in bottom left location, now often appeared in upper right location.

Each trial began with a display of a fixation point lasting for a
duration randomized between 0.9s to 1.2s, then the search display
appeared on the screen. Participants was asked to find the target that
was unique in either color or shape and respond to the orientation of
the bar within the target by pressing the 'j' key with the right hand if
the bar was oriented to the right, or the 'f' key with the left hand if
the bar was oriented to the left. The search display vanished once
participants provided a response or with a maximum duration of 1.5s.
Subsequently, a blank screen was presented for 0.3s inter-trial
interval. Participants were not informed of the existence of regularity
of targets' spatial distribution or the relationship between the
high-probability locations and target features. A graphical
representation of the single-trial procedure is shown in Figure 1A.

Participants had to complete 32 practice trials until they had
completely understood the task. No single-trial feedback was provided in
the formal experiment, but feedback was provided at the end of each
block on the accuracy and average RT of the current block to promote
participants' engagement to the task. The formal experiment consisted of
12 blocks of 120 trials, and at the end of each block there was a
resting period during which participants could proceed to the next block
on their own. Overall, all 1440 trials took approximately 60 minutes to
complete.

\textbf{INSERT FIGURE 1 HERE}

\textbf{EEG Recording and preprocessing}

EEG data were collected through a Neuroscan EEG acquisition device at a
sampling rate of 1000 Hz, with electrodes arranged and placed according
to the international 10-20 system. All electrode signals were amplified
with a 0.01-450 Hz amplifier. Electrode impedance was kept below 10k\selectlanguage{greek}Ω
\selectlanguage{english}during the experiment.

Offline preprocessing was performed via EEGlab. The data were initially
subjected to high-pass filtering at 0.1 Hz, followed by low-pass
filtering at 30 Hz, and finally band-stop filtering at 48-52 Hz. The
data were then segmented. Bad segments that were severely contaminated
by noise were manually inspected and removed, and the bad electrodes
were spherically interpolated. Artifacts caused by blinks were
subsequently corrected using independent component analysis (ICA). If
the voltages of any electrode at any time during the segment exceeded
\selectlanguage{ngerman}±80 \selectlanguage{english}?V, that segment was eliminated from further analyses. The data of
three out of all thirty-two participants were removed due to having bad
segments more than 40\% of all segments. Both their EEG and behavioral
data were excluded from subsequent analyses.

\textbf{Statistical Analysis}

\textbf{Behavioral data}

Trials with incorrect responses or RT exceeded +-2.5 standard deviations
from the mean RT were excluded from subsequent analyses for both
behavioral and EEG data. To exclude the individual difference in
reaction time, we Z-transformed the remaining data (and arbitrarily
added 5 to avoid showing negative values). A two-way repeated-measures
ANOVA with within-subject factors of phase (training phase vs. reversal
phase) and target probability (low-location, high-binding and
low-binding) was conducted. In addition to the analyzing entire eligible
data set, we also analyzed the remaining data set after excluding trials
where the target was at the same location as the proceeding trials. This
was intended to minimize the contribution of the effect of priming of
pop-out (Maljkovic and Nakayama, 1994). Greenhouse-Geisser correction
was performed for cases that did not meet the test of sphericity.

\textbf{Event-related potentials}

For the N2pc component and the s-LRP (stimulus-locked LRP) component,
electrophysiological data were divided into segments from \selectlanguage{english}-200 to 800ms
relative to search display onset. The parieto-occipital electrodes (PO7
and PO8) were chosen to analyze the N2pc component with a 220ms-300ms
time window after stimulus onset. The electrodes C3 and C4 were selected
for analyzing the s-LRP component with a 300ms-500ms time window
following stimulus onset. For the amplitudes of ERP components, we
performed the cluster-based permutation test within the corresponding
time window. This method involves estimating the t-statistic across
participants for a contrast of interest at each time point, defining
observed clusters of consecutive above-threshold time points, and
calculating the cluster mass (by summing all t values in an
above-threshold cluster). Next, condition labels were randomly shuffled
within participants (sign-flip for contrasts against zero), and the
largest cluster mass produced by chance was extracted. This permutation
step was performed 10,00 times to estimate the null distribution. The
probability of the observed group-level cluster against chance was then
derived as the rank order of the observed cluster relative to the null
distribution (Maris \& Oostenveld, 2007; Myers et al., 2014; Noonan et
al., 2023). The approach of cluster-based permutation test effectively
preserves the dynamical information within the designated time window,
while simultaneously mitigating the issue of increased Type I error
probability resulting from multiple comparisons (Maris \& Oostenveld,
2007). This approach has been employed to examine the outcomes of
time-series signals in recent studies (Cheng et al.,2023; Hassall et
al., 2022). We employed the approach to analyze the results of ERP.

Note that in this study we used stimulus-locked LRP to quantify the
contrition of response selection in the task. It has been shown that
stimulus-locked LRP, just like response-locked LRP, could be accepted as
reflecting the efficiency of making a response and was widely applied in
EEG researches (e.g., Schankin \& Schubo, 2009; Vaskevich et al., 2021).

\textbf{Time-frequency analysis}

To explore the role of expectation in statistical learning in the
`pop-out' search task, we calculate Event-related spectral perturbation
maps (ERSPs), which was completed by utilizing the newtimef() function
of EEGLAB and applying the fast Fourier transform with Hanning window
tapering. To obtain nonphase-locked spectral power, phase-locked ERPs
were removed before any spectral measures were calculated to avoid
oscillatory activities contaminated by ERPs (Wang and Ding, 2011). The
time-frequency analysis was conducted over a frequency range of 2-30 Hz
with a specific time window which spanned from -1 s to 0.8 s around the
onset of the search scene. We removed 0.25 s at the edges (the beginning
and the end), leaving an epoch between \selectlanguage{english}- 0.75 to 0.55 s. The data
outside of this time window were trimmed off. The resulting data was
baseline-corrected between --0.75s and --0.25s and transformed into Log
space. The alpha power (8--12 Hz) was estimated in the parieto-occipital
electrodes (P3/4, PO3/4, PO5/6, P7/8, PO7/8, O1/2, Pz, Oz) according to
previous literature (Li et al., 2023). Non-parametric cluster-based
permutation test was used following the same approach as described
above. Also, the averaged posterior alpha power (8--12 Hz) between
300-500ms was averaged for statistics. which was calculated separately
for high-binding and low-binding condition in both the training phase
and reversal phase. The paired sample t-test between the high-binding
and low-binding condition was conducted in the training phase and
reversal phase respectively.

\textbf{Multivariate Pattern Classification}

To further confirm the existence of expectation in the statistical
learning of the relationship between the target feature and location, we
performed the MVPC on EEG data. Specifically, this analysis was employed
to decode the orientation of targets, which was conducted in
high-binding and low-binding conditions respectively during both the
training phase and reversal phase. Each segment for decoding analysis
was from -600ms to 800ms from the onset of the stimulus, and was down
sampled to 100 Hz to improve the stability of decoding by averaging
several adjacent time points. Segments with the same label were assigned
to 5 bins to improve the signal-to-noise ratio. The classifier was based
on a linear support vector machine (SVM). For each participant, for each
moment point, data from all 62 electrodes were used to train the
classifier, a process that was implemented using MATLAB's fitcsvm()
function. For each data point, different data sets were used for
training and testing. A five-fold cross-validation and one hundred
iterations procedure was applied at each data point to minimize the
fortuity caused by the trial assignments and to yield a more stable
outcome. The decoding accuracy is calculated by comparing whether the
actual labels of the orientation were same as the predicted labels.
Non-parametric cluster-based permutation test was used following the
same approach as described above.

If the learning of the binding relationship between the target feature
and location occurs during training phase rather than during reversal
phase. The targets in the high-binding condition were supposed to be
distinguished from those in the low-binding condition only in training
phase. To further uncover the different pattern of neural activities in
distinguishing the high and low binding conditions between the training
phase and the reversal phase, we also decode the high and low binding
conditions in the training phase and reversal phase respectively using
the similar approach described above. Then the decoding accuracy was
averaged between 200-500ms. The averaged decoding accuracy in training
phase and in reversal phase was compared using the paired sample t-test.

\textbf{Result}

Behavioral data

\textbf{INSERT FIGURE 2 HERE}

\textbf{Accuracy}

The overall mean rate of accuracy was 0.96. The mean rate of accuracy
for each condition is shown in Figure 2A. The results of the
repeated-measures ANOVA with factors of phase and target location
indicated that none of the main effects of phase, target location, or
the interaction between the two were significant, all F's
\textless{}2.67, all \emph{p's} \textgreater{}0.07.

\textbf{RT}

The mean RTs as a function of phase and target location was shown in
Figure 2B. The repeated measure ANOVA with within-subject factors of
phase (training phase vs. reversal phase) and target location
(low-location, high-binding, low-binding) showed a significant main
effect of phase, F(1, 28)=68.071,\emph{p}
\textless{}.001,\selectlanguage{english}\emph{?\textsuperscript{2}\textsubscript{p}} =0.375,
target location, F(2, 28) = 114.968,
p\textless{}.001,\selectlanguage{english}\emph{?\textsuperscript{2}\textsubscript{p}} =0.298 ,
and a significant interaction between phase and target location, F(1,
28)=8.876, \emph{p} =.002,\selectlanguage{english}\emph{?\textsuperscript{2}\textsubscript{p}}
=0.024.

For the training phase, post hoc t tests revealed that RTs were
significantly slower in low-location condition compared to both
high-binding, t=11.231, p\textless{}0.001, d=2.119, and low-binding,
t=7.165, p\textless{}.001, d=1.402, conditions (low-location:
5.342+-0.134; high-binding: 5.015+-0.11; low-binding: 5.133+-0.167). RTs
were significantly faster in the high-binding than low-binding
condition, t=4.066, p\textless{}.01, d=0.645, suggesting that
participants not only learned the regularity regarding to the spatial
location of the targets, but also acquired probability of location and
feature binding.

In reversal phase where the regularity updated, RTs for targets
appearing at low-probability locations was likewise significantly slower
than targets appearing at both the high-binding, t=8.14,
p\textless{}.001, d=1.997 and low-binding, t=10.085, p\textless{}.001,
d=1.716 (low-location: 5.057+-0.124; high-binding: 4.82+-0.096;
low-binding: 4.763+-0.146). However, the difference of RTs between the
high- and low-binding failed to be evident, t=1.945, p=.813, d=0.362.
This suggests that, following the reversal of regularities, even with
the same duration as in the initial learning, the acquisition of new
binding relationships was not successful, indicating the inflexibility
of learning of binding regularities.

\textbf{Learning effect following exclusion of inter-trial priming
effect}

To rule out the influence of inter-trial priming effects, we eliminated
trials in which the targets appeared at the same location as their
previous trial and conducted the repeated-measures ANOVA of phase
(training phase vs. reversal phase) and target location (low-location,
high-binding, and low-binding) (see Figure 2C). The pattern of results
was generally consistent with that of the entire eligible data. There
were significant main effects of phase, F=71.473,
p\textless{}0.001,\selectlanguage{english}\emph{?\textsuperscript{2}\textsubscript{p}} =0.446),
and target location, F=45.927,
p\textless{}.001,\selectlanguage{english}\emph{?\textsuperscript{2}\textsubscript{p}} =0.146,
and significant interaction between them, F=14.729,
p\textless{}.001,\selectlanguage{english}\emph{?\textsuperscript{2}\textsubscript{p}} =0.05.
Interestingly, the RTs were significantly faster low-binding condition
(4.703+-0.151) than in the high-binding condition (4.85+-0.093) after the
rule reversed, t=4.624, p\textless{}.001, d=0.955, suggesting that the
learning acquired during training phase was still expressed in the
reversal phase despite the actual statistics was already reversed.

\textbf{Electrophysiological data}

\textbf{N2pc}

The three left panels of Figure 3 illustrate the ERP waveforms elicited
by search displays from electrodes PO7/PO8 contralateral and ipsilateral
to the target. Employing the cluster-based permutation test, we observed
more negative voltages contralateral relative to ipsilateral to the
lateralized targets in both the training phase (high-binding condition,
0.22 - 0.3s, summed t=263.68, clustered p\textless{}.001; low-binding
condition, 0.22s - 0.3s, summed t=196.17, clustered p\textless{}.001;
low-location condition, 0.22s - 0.3s, summed t=201.83, clustered
p\textless{}.001) and the reversal phase (high-binding: 0.22s - 0.3s,
summed t=218,88, clustered p\textless{}.001; low-binding: 0.22s - 0.3s,
summed t=288.78, clustered p\textless{}.001; low-location condition,
0.22s - 0.3s, summed t=179.13, clustered p\textless{}.001). The results
demonstrated that a robust N2pc was triggered by lateralized targets.

The corresponding contralateral-ipsilateral difference waveforms for
high-binding and low-binding conditions are shown in rightmost panel of
Figure 3. Although it appeared that N2pc amplitude was slightly lower
for low-binding than high-binding condition, the difference was not
significant.

In the reversal phase, a reversed trend was evident as we found that the
N2pc amplitude was significantly greater in the low-binding than
high-binding condition (0.22 - 0.234s, summed t=21.48, clustered
p\textless{}0.001; 0.274 - 0.298s, summed t=32.89, clustered
p\textless{}.001). N2pc amplitude was also significantly greater in the
low-binding than low-location condition (0.278 - 0.296s, summed t=28.82,
clustered p\textless{}0.001).

\textbf{INSERT FIGURE 3 HERE}

\textbf{s-LRP}

The left panel of Figure 4 shows the ERP waveforms elicited by search
displays from electrodes C3/C4 contralateral and ipsilateral to the side
of reacting hand. The s-LRP were triggered by lateralized targets which
was evidenced by the more negative voltages contralateral relative to
ipsilateral to the response hand in both the training phase
(high-binding condition, 0.302 - 0.5s, summed t=452.54, clustered
p\textless{}0.001; the low-binding condition, 0.358 - 0.5s, summed
t=268.2, clustered p\textless{}0.001; low-location condition,
0.336-0.5s, summed t=434.84, clustered p\textless{}0.001) and the
reversal phase (high-binding condition: 0.3 - 0.488s, summed t=408.67,
clustered p\textless{}0.001; low-binding condition: 0.3s - 0.306s,summed
t=8.91, clustered p\textless{}0.001 and 0.312s -0.478s, summed t=297.38,
clustered p\textless{}0.001, low-location condition, 0.31-0.5s, summed
t=354.98, clustered p\textless{}0.001). The s-LRP difference waves were
shown in right panel of Figure 4. No difference in s-LRP amplitudes
among the high-binding, low-binding conditions and low-location
condition was found in the training phase. This suggests that the
facilitated behavior performance could not be attributed to improved
response selection process. However, in the reversal phase, the s-LRP
triggered by targets in low-binding condition was significantly larger
than that in high-binding condition (0.344s - 0.372s, summed t=36.5,
clustered p\textless{}0.001). And the s-LRP triggered by targets in the
low-binding condition was also significantly larger than that in the
low-location condition (0.34s - 0.374s, summed t=54.72, clustered
p\textless{}0.001). The targets in low-location condition triggered a
larger s-LRP compared the high-binding condition (0.466s - 0.5s, summed
t=58.89, clustered p\textless{}0.001).

\textbf{INSERT FIGURE 4 HERE}

\textbf{Time-frequency analysis}

To reveal the role of expectation in statistical learning of the
relation between location and feature, we calculated ERD in alpha band
(8-12 Hz) oscillatory activities.

Figure 5A illustrated time-frequency representations in the high-binding
and low-binding conditions during the training phase and the reversal
phase. As illustrated in Figure 5B, a lateralized alpha ERD was observed
in both the training phase (high-binding condition, 0.266s - 0.53s,
summed t=494.01, clustered p\textless{}0.001; low-binding condition:
0.27s - 0.462s, summed t=247.05, clustered p\textless{}0.001) and the
reversal phase (high-binding: 0.318s - 0.492s, summed t=263.46,
clustered p\textless{}0.001; low-binding: 0.29s - 0.498s,summed
t=308.46, clustered p\textless{}0.001). We further compared the averaged
lateralized alpha ERD during 0.3 - 0.5s after stimulus onset between the
high-binding and low-binding conditions. The Paired sample t-test
demonstrated a significantly larger lateralized alpha ERD was evoked in
the high-binding condition than low-binding condition in the training
phase, t=2.816, p\textless{}0.01, d=0.523. However, the difference
between the high-binding and low-binding conditions was only marginally
significant in the reversal phase, t=1.909, p=.067, d=0.354.

\textbf{INSERT FIGURE 5 HERE}

\textbf{Multivariate pattern classification}

We decoded the orientations of targets in high-binding and low-binding
conditions respectively to examine the expectation formed in learning
(see Figure 6A). The orientation of targets could be decoded after
stimulus onset in both the training phase (high-binding condition: 0.3 -
0.79s, summed t=247.98, clustered p\textless{}0.001; low-binding
condition: 0.37 - 0.79s, summed t=186.93, clustered p\textless{}0.001)
and the reversal phasev(high-binding condition: 0.34 - 0.79s, summed
t=247.98, clustered p\textless{}0.001; low-binding condition: 0.37 -
0.79s, summed t=186.93, clustered p\textless{}0.001). Crucially, the
decoding accuracy was higher for targets in low-binding than
high-binding condition in the training phase (0.49s-0.54s, summed
t=14.45, clustered p\textless{}0.001 and 0.67s-0.69s, summed t=6.57,
clustered p \textless{}0.01). Recall that the decoding accuracy was
related to the expectation for target. The results suggested that an
expectation for target feature for high-binding condition was formed
through learning and the unexpected targets were represented more
accurately than expected targets, highlighting the role of expectation
in initial learning. However, the difference in feature decoding
accuracy between the high-binding and low-binding conditions disappeared
in the reversal phase, which indicates that the neural representation of
targets in the two conditions became comparable, and participants failed
to establish a stable expectation.

To further reveal the different pattern of neural activities in
distinguishing the high-binding and low-binding condition between the
training phase and the reversal phase. We decode the high-binding and
low-binding conditions (see Figure 6B). The results revealed a
successful decoding was observed only in the training phase (0.09 --
0.46s, summed t=117.53, cluster p\textless{}0.001 and 0.5 -- 0.51s,
summed t=4.22, cluster p\textless{}0.05). And the decoding accuracy was
significantly higher in the training phase than in the reversal phase
(0.15s - 0.21s, summed t=15.24, cluster p\textless{}0.001 and 0.29s -
0.38s, summed t=26.55, cluster p\textless{}0.001), indicating that the
high-binding and low-binding conditions were more distinguishable from
neural activities in the training phase than in the reversal phase. The
paired sample t-test of averaged decoding accuracy during 300 -- 500 ms
between the training phase and the reversal phase also showed a
significantly larger decoding accuracy in the training phase, t=2.575,
p\textless{}.05, d=0.478. These outcomes provided further support for
the effect of expectation in the initial learning instead of the
reversal phase.

\textbf{INSERT FIGURE 6 HERE}

\textbf{General Discussion}

The current study investigated whether statistical learning of the
relation between the target location and feature occurs in a `pop-out'
search task and also examined the flexibility of such learning. On top
of the regularity for target location, we varied the probability of
relation between the target location and feature with a given feature
appeared more frequently at one high-probability location than the other
high-probability location. In addition, following initial learning we
also examined search performance when the relation between location and
feature was reversed. Utilizing the EEG technology, we further explore
its related neural mechanisms.

In the training phase, the behavioral results demonstrated a successful
learning of not only the spatial regularities but also the relation
between the target feature and the high-probability location, which was
evident in the faster reaction times when the target appeared in the two
high-probability locations than that in the low-probability location and
the faster reaction times for targets in high-binding condition than in
low-binding condition. From electrophysiological recording, N2pc and LRP
amplitudes were also affected by the relation between the target feature
and high-probability location, although that was more evident in the
reversal phase. More importantly our results suggest that an expectation
to target feature appearing at high-binding locations was developed,
which was indicated by the larger lateralized alpha ERD. The results of
decoding also support that participants expect the target to appear at
its high-binding location rather at its low-binding location. This is
evident in the decreased feature decoding accuracy for target in
high-binding condition than in low-binding condition and the successful
decoding of the two conditions.

In the reversal phase, the lack of learning of the reversed relationship
between the target feature and the high-probability location supports
the inflexibility of statistical learning. First, RTs for the
high-binding condition and low-binding condition were comparable when
the entire data set were factored in. Second, when the contribution of
inter-trial priming was removed, faster RTs were found for the
low-binding than high-binding condition suggesting that the learning
acquired during training phase was still expressed in the reversal phase
despite the actual statistics was already reversed. It appears that VSL
for location-feature binding is long lasting and, once established, is
resistant from learning any new regularities.

N2pc and LRP amplitudes reached significant difference between
low-binding and high-binding conditions only during reversal phase.
Although the absolute amplitude of these components could be affected by
the stimulus-driven (from pop-out singleton target) or goal-driven (task
instruction to search for color or shape singleton) factors, the
difference between two binding conditions would only be contributed by
VSL. Although the exact nature of the difference in the reversal phase
is an open question, the difference between two binding conditions can
only be attributed to statistical learning of location-feature binding
probability.

Contrary to the training phase, the lateralized alpha ERD triggered by
targets in high-binding condition and low-binding condition did not
demonstrate a significant difference, indicating a reduction or even
disappearance of expectation. Lastly, the difference in feature decoding
accuracy between target in high-binding condition and low-binding
condition didn't exist, and the high-binding condition was not
distinguishable from the low-binding condition according to the neural
activities. Both results of the two decoding analyses showed different
patterns with those in the reversal phase.

The statistical learning in current study occurred in a `pop-out' search
task where the search efficiency was supposed to be optimal. The results
in the training phase showed that even in a very efficient search task,
observers could still extract complex regularities to promote even more
efficient behavior performance, demonstrating robust statistical
learning even when the benefit of the learning would be limited.

What is the cognitive mechanism of statistical learning in efficient
search task? Previous studies typically suggest the role of modulated
attention priority in statistical learning. However, it may not be fully
expressed in N2pc amplitude as it was not significantly affected by the
binding probability between the target feature and high-probability
location in training phase. Recently, Wang and colleagues (2023) found
that learning of the frequency of target was arisen by the influence
from the response selection process. However, LRP in our study was also
unaffected by the regularities in the training phase. Nevertheless, our
results suggest that an expectation to target in high-binding condition
was developed during the training phase, which was reflected by the
larger lateralized alpha ERD and decreased feature decoding accuracy.
This meant that the expectation to location and feature of task-relevant
before stimuli onset doesn't necessarily modulate post-stimuli
attentional selection.

Previous studies have generally observed the effect of expectation in
statistical learning involving spatial regularity as evidenced by
proactive attentional bias when the regularity was employed in
task-relevant target or proactive attentional suppression when the
regularity was employed in task-relevant distractor (Jiang et al, 2014;
Wang \& Theeuwes, 2018a; 2018b; 2018c). We expand upon these findings by
demonstrating that through statistical learning of the relationship
between the target location and feature, participants formed an
expectation not only for the locations where the targets were likely to
appear but also for the probable feature associated with those
locations. We observed a larger lateralized alpha ERD in high-binding
condition compared to the low-binding condition during the training
phase. This finding is consistent with Noonan et al. (2023), where they
observed lateralized alpha ERD for both expected and unexpected targets,
although a direct comparison between them was not conducted in their
research. Thus, our findings provide additional evidence highlighting
the relationship between lateralized alpha power and the expectation
with larger post-stimuli lateralized alpha ERD meaning larger
expectation. It is worth noting that Noonan et al. (2023) also found
that expected distractors elicited a lateralized alpha ERD, while
unexpected distractors did not. This may suggest that the modulation of
alpha power by expectation is similar for targets and distractors.
Empirical evidence supporting the exact relationship between the
post-stimuli lateralized alpha ERD and the expectation is still limited.
Further studies should investigate the relationship between alpha power
and expectation to gain deeper insights.

In the current study, the impact of expectation was also evident in the
higher feature decoding accuracy for targets in the low-binding
condition compared to the high-binding condition during the training
phase, which suggested that the unexpected targets were represented more
accurately. Similar results were also reported by Kumar et al (2017) and
Richter et al (2018). The sharped neural representation to unexpected
stimulus was consistent with the predictive processing models, which
propose that the brain constantly attempting to match incoming sensory
inputs with top-down expectations or predictions and what matters is the
prediction error. Errors in predicting lower-level inputs cause the
higher-level models to adapt so as to reduce the discrepancy. Thus, the
novel/unexpected information will

undergo enhanced encoding (Clark, 2013; Barron et al., 2020). But in Kok
\& De Lange (2012), the opposite result was observed. In their study,
the auditory cue predicted orientation of the subsequent grating stimuli
with 75\% validity and the decoding performance for the expected stimuli
was superior compared to the unexpected stimuli. It should be noted that
the overall probability of different orientations appearing was equal in
their study. And the expectation was formed on a trial-by-trial basis.
However, in our study, the expectation was formed on a larger time
scale. This discrepancy may explain the different patterns observed in
Kok \& De Lange (2012).

It is possible that the observed learning of the relationship between
the target feature and the spatial regularity was affected by the
inter-trial priming effect (van Moorselaar et al., 2021; Qiu et al.,
2023), as the high-binding condition leads to more frequent repetitions
of target color in a given location than low-binding condition. However,
the fact that the pattern of results remained largely immutable after
excluding trials with the same target location as the previous trial
contradicts this possibility. The RT difference between the high-binding
and low-binding condition was still observed in training phase,
suggesting that the learning effect primarily reflect long-term effect,
rather than short-living inter-trial priming effect.

Another question arises regarding the dimension of feature-based
processing. Previous studies have demonstrated the learning of
relationship between two distractor features and two distractor
high-probability locations. However, it appears that the condition for
the learning to occur is that the two features should be defined in
different dimensions. For instance, in the study by Liesefel \& Muller
(2021), participants were instructed to search for an
orientation-defined target uniformly distributed in space. Two
distractor features were introduced: one defined in the same dimension
as the target (an orientation-based singleton) and the other defined in
a different dimension from the target (a luminance-based singleton).
Importantly, only one distractor feature exhibited spatial regularity,
while the other did not. The results showed that feature-specific
spatial attentional suppression only occurred in the condition where the
distractor with regularity was defined in the same dimension as the
target. The critical role of dimensions aligns with the dimension
weighting account, which posits that the human visual system dynamically
adjusts the weighting of saliency signals from different feature
dimensions based on task goals and prior experience (Liesefeld \&
Muller, 2019). In line with previous literature, the two target features
in our current study were defined in different dimensions (shape and
color). However, in Failing and colleagues (2019), regardless of whether
the two types of distractors were defined in the same (color) or
different dimensions (color and shape), participants successfully
learned the spatial and feature-based dual regularities. The different
results by Failing and colleagues (2019) can be explained by the
specialized mechanisms in color processing (Liesefeld \& Muller, 2019).
It has been suggested that color may be better considered as comprising
multiple dimensions (Liesefeld \& Muller, 2019). Future studies should
investigate whether dimension manipulation is necessary for learning of
the relationship between the feature and its spatial regularity.

In summary, we provide evidence for the successful learning of not only
the overall spatial regularity but also the binding relationship between
the target feature and the spatial regularity in a `pop-out' search task
where the search is supposed to be optimal. Our results suggest that
attentional selection, response selection and, more importantly,
expectation could be related to the learning. Furthermore, evidence from
behavioural and EEG data demonstrated the inflexibility nature of
statistical learning of binding relation between location and feature.

\textbf{References}

Anderson, B. A., Kim, H., Kim, A. J., Liao, M. R., Mrkonja, L., Clement,
A., \& Gregoire, L. (2021). The past, present, and future of selection
history. Neuroscience \& Biobehavioral Reviews, 130, 326-350.

Awh, E., Belopolsky, A. V., \& Theeuwes, J. (2012). Top-down versus
bottom-up attentional control: A failed theoretical dichotomy. Trends in
Cognitive Sciences, 16(8), 437--443.
https://doi.org/10.1016/j.tics.2012.06.010.

Barron, H. C., Auksztulewicz, R., \& Friston, K. (2020). Prediction and
memory: A predictive coding account. Progress in neurobiology, 192,
101821.Clark, A. (2013). Whatever next? Predictive brains, situated
agents, and the future of cognitive science. Behavioral and brain
sciences, 36(3), 181-204.

Cheng, S., Ding, Z., Chen, C., Sun, W., Jiang, T., Liu, X., \& Zhang, M.
(2023). The effect of choice on memory: The role of theta oscillations.
Psychophysiology, e14390.

Chun, M. M., \& Jiang, Y. (1998). Contextual cueing: Implicit learning
and memory of visual context guides spatial attention. Cognitive
psychology, 36(1), 28-71.

Duncan, D. H., van Moorselaar, D., \& Theeuwes, J. (2023). The
Electrophysiological Markers of Statistically Learned Attentional
Enhancement: Evidence for a Saliency Based Mechanism. bioRxiv, 2023-03.

Failing, M., Feldmann-Wustefeld, T., Wang, B., Olivers, C., \& Theeuwes,
J. (2019). Statistical regularities induce spatial as well as
feature-specific suppression. Journal of experimental psychology: human
perception and performance, 45(10), 1291.

Frost, R., Armstrong, B. C., \& Christiansen, M. H. (2019). Statistical
learning research: A critical review and possible new directions.
Psychological Bulletin, 145(12), 1128.

Geng, J. J., \& Behrmann, M. (2005). Spatial probability as an
attentional cue in visual search. Perception \& psychophysics, 67(7),
1252-1268.

Gimenez-Fernandez, T., Luque, D., Shanks, D. R., \& Vadillo, M. A.
(2022). Is probabilistic cuing of visual search an inflexible
attentional habit? A meta-analytic review. Psychonomic Bulletin \&
Review, 1-9.

Golan, A., \& Lamy, D. (2023). Attentional guidance by target-location
probability cueing is largely inflexible, long-lasting, and distinct
from inter-trial priming. Journal of Experimental Psychology: Learning,
Memory, and Cognition.

Hall-McMaster, S., Muhle-Karbe, P. S., Myers, N. E., \& Stokes, M. G.
(2019). Reward boosts neural coding of task rules to optimize cognitive
flexibility. Journal of Neuroscience, 39(43), 8549-8561.

Hassall, C. D., Yan, Y., \& Hunt, L. T. (2022). The Neural Correlates of
Continuous Feedback Processing. bioRxiv, 2022-10.

Hong, I., Jeong, S. K., \& Kim, M. S. (2020). Context affects implicit
learning of spatial bias depending on task relevance. Attention,
Perception, \& Psychophysics, 82, 1728-1743.

Hong, I., \& Kim, M. S. (2022). Habit-like attentional bias is unlike
goal-driven attentional bias against spatial updating. Cognitive
research: principles and implications, 7(1), 50.

Huang, C., Donk, M., \& Theeuwes, J. (2022). Proactive enhancement and
suppression elicited by statistical regularities in visual search.
Journal of Experimental Psychology: Human Perception and Performance,
48(5), 443.

Jiang, Y. V., Swallow, K. M., Rosenbaum, G. M., \& Herzig, C. (2013).
Rapid acquisition but slow extinction of an attentional bias in space.
Journal of Experimental Psychology: Human Perception and Performance,
39(1), 87.

Jiang, Y. V., Won, B. Y., \& Swallow, K. M. (2014). First saccadic eye
movement reveals persistent attentional guidance by implicit learning.
Journal of Experimental Psychology: Human Perception and Performance,
40(3), 1161.

Kok, P., Jehee, J. F., \& De Lange, F. P. (2012). Less is more:
expectation sharpens representations in the primary visual cortex.
Neuron, 75(2), 265-270.

Kumar, S., Kaposvari, P., \& Vogels, R. (2017). Encoding of predictable
and unpredictable stimuli by inferior temporal cortical neurons. Journal
of Cognitive Neuroscience, 29(8), 1445-1454.

Li, D., Hu, Y., Qi, M., Zhao, C., Jensen, O., Huang, J., \& Song, Y.
(2023). Prioritizing flexible working memory representations through
retrospective attentional strengthening. NeuroImage, 269, 119902.

Liesefeld, H. R., \& Muller, H. J. (2019). Distractor handling via
dimension weighting. Current opinion in psychology, 29, 160-167.

Liesefeld, H. R., \& Muller, H. J. (2021). Modulations of saliency
signals at two hierarchical levels of priority computation revealed by
spatial statistical distractor learning. Journal of Experimental
Psychology: General, 150(4), 710.

Luck, S. J., \& Hillyard, S. A. (1994). Spatial filtering during visual
search: evidence from human electrophysiology. Journal of Experimental
Psychology: Human Perception and Performance, 20(5), 1000.

Maljkovic, V., \& Nakayama, K. (1994). Priming of pop-out: I. Role of
features. Memory \& Cognition, 22(6), 657--672.

Maris, E., \& Oostenveld, R. (2007). Nonparametric statistical testing
of EEG-and MEG-data. Journal of neuroscience methods, 164(1), 177-190.

Myers, N. E., Stokes, M. G., Walther, L., \& Nobre, A. C. (2014).
Oscillatory brain state predicts variability in working memory. Journal
of Neuroscience, 34(23), 7735--7743.

Noonan, M. P., Von Lautz, A. H., Bauer, Y., Summerfield, C., \& Stokes,
M. S. (2023). Differential modulation of visual responses by distractor
or target expectations. Attention, Perception, \& Psychophysics, 85(3),
845-862.

Qiu, N., Zhang, B., Allenmark, F., Nasemann, J., Tsai, S. Y., Muller, H.
J., \& Shi, Z. (2023). Long\selectlanguage{english}-term (statistically learnt) and short\selectlanguage{english}-term
(inter\selectlanguage{english}-trial) distractor\selectlanguage{english}-location effects arise at different pre\selectlanguage{english}-and
post\selectlanguage{english}-selective processing stages. Psychophysiology, e14351.

Richter, D., Ekman, M., \& de Lange, F. P. (2018). Suppressed sensory
response to predictable object stimuli throughout the ventral visual
stream. Journal of Neuroscience, 38(34), 7452-7461.

Rungratsameetaweemana, N., Itthipuripat, S., Salazar, A., \& Serences,
J. T. (2018). Expectations do not alter early sensory processing during
perceptual decision-making. Journal of Neuroscience, 38(24), 5632-5648.

Sawaki, R., \& Luck, S. J. (2013). Active suppression after involuntary
capture of attention. Psychonomic bulletin \& review, 20, 296-301.

Smulders, F. T., Miller, J. O., \& Luck, S. J. (2012). The lateralized
readiness potential. New York, NY: Oxford University Press.

Theeuwes, J. (2019). Goal-driven, stimulus-driven, and history-driven
selection. Current opinion in psychology, 29, 97-101.

Theeuwes, J. (1991). Exogenous and endogenous control of attention: The
effect of visual onsets and offsets. Perception \& Psychophysics, 49(1),
83--90.

Theeuwes, J. (1992). Perceptual selectivity for color and form.
Perception \& Psychophysics, 51(6), 599--606.

Turk-Browne, N. B., Junge, J. A., \& Scholl, B. J. (2005). The
automaticity of visual statistical learning. Journal of Experimental
Psychology: General, 134(4), 552.

van Moorselaar, D., Daneshtalab, N., \& Slagter, H. A. (2021). Neural
mechanisms underlying distractor inhibition on the basis of feature
and/or spatial expectations. Cortex, 137, 232-250.

Vaskevich, A., Nishry, A., Smilansky, Y., \& Luria, R. (2021). Neural
evidence suggests both interference and facilitation from embedding
regularity into visual search. Journal of Cognitive Neuroscience, 33(4),
622-634.

Wang, B., \& Theeuwes, J. (2018a). Statistical regularities modulate
attentional capture. Journal of Experimental Psychology: Human
Perception and Performance, 44(1), 13.

Wang, B., \& Theeuwes, J. (2018b). How to inhibit a distractor location?
Statistical learning versus active, top-down suppression. Attention,
Perception, \& Psychophysics, 80, 860-870.

Wang, B., \& Theeuwes, J. (2018c). Statistical regularities modulate
attentional capture independent of search strategy. Attention,
Perception, \& Psychophysics, 80, 1763-1774.

Wang, S., Cong, S. H., \& Woodman, G. F. (2023). Statistical learning
speeds visual search: More efficient selection, or faster response?.
Journal of Experimental Psychology: General.

Wang, X., \& Ding, M. (2011). Relation between P300 and event-related
theta-band synchronization: a single-trial analysis. Clinical
Neurophysiology, 122(5), 916-924.

Xu, Z., Theeuwes, J., \& Los, S. A. (2023). Statistical learning of
spatiotemporal regularities dynamically guides visual attention across
space. Attention, Perception, \& Psychophysics, 85(4), 1054-1072.

Zhao, J., Al-Aidroos, N., \& Turk-Browne, N. B. (2013). Attention is
spontaneously biased toward regularities. Psychological science, 24(5),
667-677.

Zhou, Y. J., Perez-Bellido, A., Haegens, S., \& de Lange, F. P. (2020).
Perceptual expectations modulate low-frequency activity: a statistical
learning magnetoencephalography study. Journal of Cognitive
Neuroscience, 32(4), 691-702.

\textbf{Figure Caption}

\emph{Figure 1}\textbf{.} Task and procedure. (A) Trial sequences of the
search task. (B) Diagram illustrating an example of the spatial and
feature-based regularities of the targets (solid shapes are shown for
illustration purpose only). For the two high-location probability items,
the top right item often appeared as a green circle and the bottom left
item often appeared as a gray square. The gray circles represent the
low-probability locations. The percentages at each location indicate the
probabilities of each target feature appearing in that specific
location. (C) Time sequence during experiment illustrating most likely
target feature during the learning and reversal phase.

\emph{Figure 2.} Behavior data across three target probability
conditions. (A) Mean error rate by the phase and the target location.
(B) Mean response time by the phase and the target location. (C) Mean
response time after excluding trials where the target was at the same
location as their previous trials. \selectlanguage{english}*p \textless{} 0.05; \selectlanguage{english}*\selectlanguage{english}*p \textless{}
0.01; \selectlanguage{english}*\selectlanguage{english}*\selectlanguage{english}*p \textless{} 0.001.

\emph{Figure 3.} N2pc results. The three panels on the left: Waveforms
of electrodes (PO7/PO8) contralateral and ipsilateral to the target
hemifield for targets in the high-binding (leftmost), low-binding
(2\textsuperscript{nd} column) and low-location
(3\textsuperscript{rd}column) conditions during the training phase (top)
and the reversal phase (bottom), respectively. The dashed vertical line
indicates the search arrays onset. The gray areas represent the interest
time window (220-300ms) for N2pc analysis. The horizontal bars indicate
time clusters for significant difference between the contralateral and
ipsilateral signals. The right panel: The N2pc difference waves. The
horizontal bars indicate time clusters with significant difference in
N2pc amplitude between the high-binding and low-binding conditions (thin
line) and between the low-binding and low-location conditions (thick
line).

\emph{Figure 4.} LRP results. The three panels on the left: waveforms of
electrodes (C3/C4) contralateral and ipsilateral to the reacting hand in
the high-binding (1\textsuperscript{st} column), low-binding
(2\textsuperscript{nd} column), and low-location (3\textsuperscript{rd}
column) conditions during the training phase (top) and the reversal
(bottom) phase, respectively. The dashed vertical line indicates the
search arrays onset. The gray area represents the interest time window
(300-500ms) for LRP analysis. Horizontal bars indicated time clusters
for significant difference between the contralateral and ipsilateral
signals. The right panel: The LRP difference waves. The colored
horizontal bars indicate time clusters with significant difference
between the low-binding and high-binding conditions (thin line) and
between the low-binding and low-location conditions (empty bar) and
between high-binding and low-location conditions (thick line).

\textbf{Figure 5.} Oscillatory results. (A) Time-frequency
representations in the high-binding and low-binding conditions during
the training phase and the reversal phase, respectively. White squares
represent alpha power (8--12 Hz) between 300 and 500ms. (b) The
lateralized alpha ERD was observed in both probability conditions in
both phases. The gray area represents the time interval (300--500ms)
used to calculate the averaged alpha power. Lines composed by *
indicated significant time clusters for lateralized alpha ERD. (C)
Averaged alpha power between the high-binding and low-binding conditions
showed a significant difference in the training phase but not in the
reversal phase. \selectlanguage{english}*p \textless{} 0.05; ns represents p\textgreater{}0.05.

\textbf{Figure 6.} Orientation and condition classification. (A)
Temporal dynamics of the decoding accuracy for orientation
classification in the high-binding and low-binding conditions during the
training phase and the reversal phase, respectively. (B) Temporal
dynamics of the \textbf{decoding} accuracy for condition of high-binding
and low-binding during the training phase and the reversal phase,
respectively. The gray area represents the interval (200--500 ms) used
to calculate the averaged condition decoding accuracy. (C) Averaged
decoding accuracy for condition of high-binding and low-binding between
the 200--500ms interval after stimulus onset showed a significant
difference. \selectlanguage{english}*p \textless{} 0.05.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/condition/condition}

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\end{figure}\selectlanguage{english}
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\includegraphics[width=0.70\columnwidth]{figures/2behavior/2behavior}

\end{center}
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\textbf{Hosted file}

\verb`3N2pc_new.eps`  available at \url{https://authorea.com/users/673397/articles/672200-statistics-learning-of-target-regularities-in-a-pop-out-search-behavioral-performance-and-neural-mechanisms}

\textbf{Hosted file}

\verb`4LRP_new.eps`  available at \url{https://authorea.com/users/673397/articles/672200-statistics-learning-of-target-regularities-in-a-pop-out-search-behavioral-performance-and-neural-mechanisms}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/5Alpja-new/5Alpja-new}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/6decoding-new/6decoding-new}

\end{center}
\end{figure}

\selectlanguage{english}
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