Confidence is predicted by pre- and post-choice decision signal dynamics

约翰·P. Grogana,乙, Wouter Rysa, Simon P. Kellyc, Redmond G. O’Connella,乙

aSchool of Psychology, Trinity College Dublin, 都柏林, 爱尔兰.

bTrinity College Institute of Neuroscience, Trinity College Dublin, 都柏林, 爱尔兰.

cSchool of Electrical and Electronic Engineering and UCD Centre for Biomedical Engineering, University College Dublin, 都柏林, 爱尔兰.

通讯作者: 约翰·P. Grogan (john.grogan@tcd.ie)

抽象的
It is well established that one’s confidence in a choice can be influenced by new evidence encountered after commit-
ment has been reached, but the processes through which post-choice evidence is sampled remain unclear. To inves-
tigate this, we traced the pre- and post-choice dynamics of electrophysiological signatures of evidence accumulation
(Centro-parietal Positivity, CPP) and motor preparation (mu/beta band) to determine their sensitivity to participants’
confidence in their perceptual discriminations. Pre-choice CPP amplitudes scaled with confidence both when confi-
dence was reported simultaneously with choice, and when reported 1 second after the initial direction decision with
no intervening evidence. When additional evidence was presented during the post-choice delay period, the CPP
exhibited sustained activation after the initial choice, with a more prolonged build-up on trials with lower certainty in
the alternative that was finally endorsed, irrespective of whether this entailed a change-of-mind from the initial choice
或不. Further investigation established that this pattern was accompanied by later lateralisation of motor preparation
signals toward the ultimately chosen response and slower confidence reports when participants indicated low cer-
tainty in this response. These observations are consistent with certainty-dependent stopping theories according to
which post-choice evidence accumulation ceases when a criterion level of certainty in a choice alternative has been
reached, but continues otherwise. Our findings have implications for current models of choice confidence, and pre-
dictions they may make about EEG signatures.

关键词: 决策, confidence, ERP, CPP, meta-cognition

介绍

Mathematical modelling and neurophysiological investiga-
tions of perceptual decision making suggest that choice
confidence evolves over the course of deliberation, 并且是
informed by several factors, including the strength of evi-
dence favouring the chosen alternative (Bang & Fleming,
2018), the difference in evidence between the available
选项 (李 & Ma, 2020), and the time taken to decide (Kiani
等人。, 2014). Confidence judgements can also be updated
after a decision has been made, taking account of evi-
dence accumulated while the decision-reporting action is
still being executed (Resulaj et al., 2009) and/or new evi-
dence encountered after response completion (Fleming

等人。, 2018; Moran et al., 2015; van den Berg et al., 2016;
Yu et al., 2015). What form such post-commitment accu-
mulation processes take remains unclear, and several
alternative possibilities have been proposed.

According to some models, confidence levels are
updated by a continuation of the same evidence accu-
mulation process that informed the initial choice (Moran
等人。, 2015; Pleskac & Busemeyer, 2010; Yu et al., 2015)
but other accounts invoke a distinct metacog nitive pro-
cess that evaluates the accuracy of the preceding choice
(Desender, 里德林克霍夫, et al., 2021; Fleming & Daw,
2017). Another key point of distinction between existing
models of confidence in perceptual decisions is whether

已收到: 13 六月 2023 公认: 16 六月 2023 Available Online: 19 七月 2023

Imaging Neuroscience, 体积 1, 2023
https://doi.org/10.1162/imag_a_00005

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they assume that post-choice evidence accumulation
operates until confidence is probed (Yu et al., 2015), or is
terminated when a criterion level of confidence (Pleskac
& Busemeyer, 2010) or elapsed time (Desender, 唐纳,
et al., 2021) has been reached (“optional stopping”).
Adjudicating among these accounts has been difficult as
post-choice evidence accumulation has rarely been
observed or probed in the brain with sufficient temporal
precision. Electrophysiological research
in monkeys
using opt-out paradigms has established that choice
confidence can be read-out jointly from the pre-choice
firing rate of decision-variable encoding neurons and
deliberation time (Kiani & 沙德伦, 2009), but this work
has not yet examined the neural underpinnings of post-
choice confidence reports.

One promising signal for probing post-choice confi-
dence representations in humans is the Centro-parietal
Positivity (CPP), which tracks sensory evidence accumu-
lation during decision formation (O’Connell & 凯莉, 2021).
Whereas effector-selective decision signals previously
reported in humans and other species reach a stereo-
typed amplitude immediately prior to response execu-
的, the CPP’s amplitude varies with several factors
known to influence choice confidence, 例如, hav-
ing greater amplitudes on correct trials and reduced
amplitudes for trials with longer RTs (Kelly et al., 2021;
Steinemann et al., 2018). 到目前为止, only a few studies
have directly investigated the CPP’s relationship with
confidence, and mainly using stimulus-locked CPPs
which are potentially confounded by faster RTs for higher
confidence responses. Most of these studies reported
that CPP reaches a higher amplitude after evidence onset
on trials rated highly confident (Davidson et al., 2021;
Gherman & Philiastides, 2015, 2018; Herding et al., 2019;
Tagliabue et al., 2019) apart from one study which found
no such link (Rausch et al., 2020). 此外, one study
that used response-locked CPPs also found no confi-
dence effect (Feuerriegel et al., 2022).

Elsewhere, it has been reported that a post-choice cen-
tro-parietal signal with identical topography to the CPP,
but traditionally labelled as the Error Positivity (Pe), 还
scales with choice confidence but in the opposite direction
to that reported for the pre-choice CPP. The Pe is seen
after erroneous choices that are explicitly reported to be
不正确 (Falkenstein, 1990; Nieuwenhuis et al., 2001;
Steinhauser & Yeung, 2010), and its amplitude increases
the more confident participants are that they have made
an error (Boldt & Yeung, 2015; Feuerriegel et al., 2022). 这
Pe has also been shown to exhibit a build-to-threshold
relationship with error signalling reports (Murphy et al.,

2015), and to predict subsequent post-error slowing and
post-choice information-seeking (Desender, Boldt, et al.,
2019; Desender, 墨菲, 等人。, 2019).

While the Pe literature seems to suggest an “error accu-
模拟” process that selectively gathers evidence indi-
cating that a preceding choice should be reversed (Boldt &
Yeung, 2015; Desender, 唐纳, 等人。, 2021), much of this
research involved studies with no post-choice evidence
可用的 (Boldt & Yeung, 2015; Desender, 唐纳, 等人。,
2021) or where participants only responded when errors
were detected (Murphy et al., 2015). 此外, 最近的
work has highlighted that the use of baseline correction to
an interval just before the initial response may have caused
pre-choice amplitude differences to be transferred to post-
choice amplitude measurements (Feuerriegel et al., 2022).
最后, some studies modelling delayed confidence
responses have assumed that people accumulate during
the entire post-choice evidence presentation (Pleskac &
Busemeyer, 2010; Yu et al., 2015), while other models
propose a time- or confidence-dependent stopping rule
(Desender, 唐纳, et al., 2021; Moran et al., 2015). 经过
allowing accumulation to be traced while post-choice evi-
dence remains available, EEG offers a means of testing for
early stopping during the delay period between choice and
confidence reports. To our knowledge, there has not been
a direct comparison of the post-commitment dynamics of
neural evidence accumulation signals with versus without
post-choice evidence presentation.

We present two experiments investigating the relation-
ship between CPP and confidence. 实验 1 用过的
simultaneous confidence and choice reports to investi-
gate whether previous confidence effects on the stimu-
lus-locked CPP would be found in the response-locked
signal. It also served as a benchmark for Experiment 2, 在
which participants withheld their confidence reports for a
1-second post-commitment delay, and randomly varied
across trials whether the physical evidence remained on
screen or was extinguished. Pouget et al. (2016) distin-
guish between the related concepts of certainty and con-
fidence, where certainty derives from the perceived
probability distribution of stimulus variables irrespective
of choice, while confidence is the probability that a
choice—whether overtly completed or still covertly evolv-
ing—is correct. In tasks with a single choice between two
stimulus alternatives, as in Experiment 1, these cannot
be distinguished (Bang & Fleming, 2018); 然而, 什么时候
confidence is reported after the initial choice and allows
for changes of mind, as in Experiment 2, we can cast that
report in two alternative ways to aid our analyses: 作为
“confidence in initial choice,” whose lowest value is

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attained when certain that an error was made, or as “final
肯定,” which ranges from “maybe” to “certain”
regarding current perception irrespective of the initial
选择. Our results across these two experiments indi-
cate that when there is no further evidence provided, 这
CPP amplitude at the time of initial choice scales with the
confidence in that choice. 然而, when physical evi-
dence remains available during the interval between the
choice and confidence reports, post-choice accumula-
tion of this evidence terminates early when participants
achieve high final certainty, irrespective of whether or not
this entails a reversal of their initial choice.

2. 方法

2.1. 伦理

The study was approved by Trinity College Dublin ethics
committee and carried out in accordance with the Decla-
ration of Helsinki, and EU GDPR. Written informed con-
sent was given before the start of the first session.

2.2. 参加者

Participants were between 18 和 32 years old, with nor-
mal or corrected-to-normal vision, no history of neuro-
logical or psychiatric disorders, epilepsy, or unexplained
fainting. 实验 1 recruited 27 参与者 (13 女性,
14 males), with two excluded following artefact rejection
(N = 25, 见下文). 实验 2 recruited a different
group of 30 参与者 (18 女性, 12 males), five of
whom were excluded due to insufficient data retained after
artefact rejection (N= 25). Participants were paid for their
时间 (€35 in Experiment 1, €45 in Experiment 2), plus a
bonus depending on their performance (实验 1: 向上
to €6.50, mean = €4.40, SD = 1.10; 实验 2: up to
€16, mean = €8.50, 标准差= 1.50).

2.3. 实验设计

2.3.1. Experiment 1—simultaneous choice and confidence reports

实验 1 was a random dot-motion direction dis-
crimination task in which participants simultaneously
reported the direction of coherent motion and their choice
confidence (如图. 1). The task was programmed in MATLAB
(R2013b) and Psychtoolbox-3 (Kleiner et al., 2007). Test-
ing took place in a dark, sound-attenuated room, 和
participants seated 57 cm from a CRT monitor (51 厘米,
65.2 cd/m2 luminance, 75 Hz refresh rate, 1024 X 768 res-
olution), with their head on a chin rest.

Trial onsets were self-paced, beginning when partici-
pants pressed the space button. A white central fixation
cross was presented for 400 多发性硬化症, followed by the random
dot kinematogram composed of 75 white dots (0.16°
diameter) in an aperture (8° diameter) on a grey back-
地面 (fixation cross remained on-screen until feedback).
The dots moved with zero coherence for an initial lead-in
period of 1500 ms to prevent visual-evoked potentials elic-
ited by stimulus onset from overlapping with choice-re-
lated signals. A proportion of the dots began moving
coherently after this 1500 ms lead-in, with the proportion
individually titrated to achieve a criterion discrimination
accuracy level (见下文). Dot positions were updated on
every frame, with a proportion (matching the coherence)
randomly selected to move either left or right on each trial
(equal probability) by 0.2° relative to their location three
frames earlier, to give an overall motion speed of 15°s-1.
The remaining dots were moved to a random new location
every frame, and the coherent dots were re-selected every
frame to prevent people tracking individual dots. 这
coherent motion was presented for 350 多发性硬化症, 500 多发性硬化症, 或者
750 多发性硬化症 (equal probability), and was followed by the
appearance of a 6-point response scale. 参加者
rested the first three fingers of each hand on the response
keys of a keyboard and were instructed to click the “s,”
“d,” or “f” key with their left hand to indicate “certain left,”
“probably left,” or “maybe left,” respectively, and clicking
“j,” “k,” “l” with their right hand to report “maybe right,”
“probably right,” “certain right,” respectively. 参加者
were instructed to withhold reporting their choices until the
appearance of the confidence scale, and only responses
之内 0-1500 ms of scale onset were recorded. Visual
feedback was then provided for 500 ms in the form of
“correct,” “error,” “too fast” (RT < 0 ms), or “too slow” (RT > 1500 多发性硬化症). Participants were shown their mean accu-
racy and response time at the end of each block and were
informed of their bonus winnings at the end of the experi-
蒙特 (see scoring rule in Experiment 2 部分).

Participants completed two consecutive days of test-
英, with training on the behavioural task and task difficulty
titration taking place on day 1. Training started with 50 tri-
als at high coherence, until participants performed close to
100% accuracy on the direction decision and were com-
fortable rating their confidence simultaneously. The coher-
ence was then titrated in blocks of 30 trials to achieve
大约 75% discrimination accuracy using a stair-
case procedure that increased the coherence 1% 后
every error and decreased it by 1% after three consecutive
correct responses (average titrated coherence 11.19%,
标准差= 4.66). The EEG testing session took place on day 2

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如图. 1. Task designs for experiments 1 和 2. 实验 1 was a dot motion direction discrimination task, 和
simultaneous direction and confidence reporting. Each trial started with an initial 1500 ms lead-in of incoherent motion to
allow visual-evoked potentials associated with stimulus onset to resolve, offering a clear view on choice-related signals.
Participants withheld reporting their choice and confidence until the appearance of a 6-point confidence scale following
stimulus offset (350/500/750 ms stimulus duration). In Experiment 2, participants were presented with overlaid gratings
and reported whether the grating tilted to the left or right was higher in contrast. 再次, trials started with an initial zero-
evidence lead-in period during which the gratings appeared at equal contrast. Initial left/right choices had to be reported
在一个 1500 ms deadline. Participants were then probed to report their choice confidence using the same scale as in
实验 1 after a post-choice delay of 1000 多发性硬化症. During the delay period, the evidence either remained on screen (作为
shown in the figure) or was extinguished with equal probability. Note that stimulus sizes in all panels are not to scale.

and consisted of 8 blocks of 72 trials with a short rest
break in between blocks. Only the data from day 2 是
included in the analyses reported below.

2.3.2. Experiment 2—delayed confidence reports with or without
post-choice evidence

实验 2 (如图. 1) was a contrast discrimination task in
which participants made an initial speeded two-alternative
choice and were subsequently cued to report their final
choice confidence after a 1-second delay. In randomly
interleaved trials, evidence was either extinguished
immediately after the initial choice report or continued
throughout the delay period. The same physical set-up
was used as for Experiment 1, except the monitor was a
40.5 cm CRT monitor.

After pressing the space bar to begin the trial, partici-
pants saw a central fixation for 250 多发性硬化症, followed by two
overlaid gratings tilted at 45° from vertical in each direction
(spatial frequency = 2 cycles per degree) in an annulus

shape around a central fixation (inner radius = 1°, outer
radius = 6°; the fixation-cross remained on-screen until the
confidence-scale appeared). The two gratings were ini-
tially presented at 50% 对比. Evidence onset occurred
后 1000 多发性硬化症, with one grating increasing by a criterion
数量 (见下文) and the other grating decreasing by
the same amount. To allow reverse correlation analyses
(analyses not reported here), we introduced small frame-
to-frame variations in the contrast-difference between the
two stimuli with values drawn from a Gaussian noise distri-
bution (标准差= 1.5% which corresponds to around 10% 的
the mean evidence strength, maximum variation was
capped at 3 标清). Throughout the stimulus presentation,
the two gratings were flickered at 15 Hz in anti-phase,
which allowed us to recover a 15 Hz steady-state visual
evoked potential (SSVEP) driven by the contrast difference
between alternating gratings, whose phase indicated the
direction of the difference. 此外, activity at 30 赫兹
indexed the summed visual response to the two gratings,
offering a general index of engagement. Participants indi-

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cated which grating had the higher contrast with a button
press (“f” or “j” for left or right) as soon as they liked, 和
a deadline of 1500 多发性硬化症. Following the initial response, 这
evidence either Continued at the same mean strength or
was Extinguished and replaced with a fixation cross. 这些
trial types were randomly interleaved and occurred with
equal probability. 1000 ms after the initial response, 这
confidence rating scale was shown on the screen, 和
participants responded as in Experiment 1—importantly,
the scale still ran from “certain left” to “certain right.” Par-
ticipants were instructed to report their final choice confi-
dence in light of all the evidence they had viewed, 作为
opposed to retrospectively reporting on their confidence in
their initial choice. Feedback was given as in Experiment 1.
Participants completed 16 blocks of 80 trials while
undergoing EEG recordings, with half of the trials com-
pleted on the first day of testing, and half on the second
(consecutive) 天. These two days of data were combined
for the analyses. The first day also included training and
staircasing, using a two-down one-up staircase to reach
70% 准确性 (step-size starting at 6% and decreasing by
1% point each step until they reached 1%; mean con-
trast = 13.19%, 标准差= 4.61). A bonus was paid out based
on their accuracy and confidence in the main task,
based on a quadratic scoring rule (points = 100 * (1 – (这-
tial accuracy – confidence-in-initial-choice)2)), scaled to
€0-€16. Initial accuracy in this equation is coded as 1 为了
correct and 0 for incorrect, and confidence-in-initial-
choice is expressed relative to initial choice on each trial,
taking one of 6 equally spaced values ranging from 0, 科尔-
responding to “certain” in the initially unchosen option, 到
1, corresponding to “certain” in the initially chosen option.
Given there is no guarantee of additional evidence being
presented after the initial response, this scoring rule incen-
tivises initial accuracy as well as the accuracy of confi-
dence responses (Staël von Holstein, 1970). It also
orthogonalises confidence from expected reward; 更多的
points are given for high-confidence than low-confidence
initially correct responses, 尽管, 同时, 更多的
points are given for low-confidence than high-confidence
initially error responses. We checked that participants
understood this rule by asking them how many points they
would get if they incorrectly responded “left” and then
pressed “certain left” (the correct answer to which is zero).

2.4. EEG acquisition and pre-processing

EEG was recorded with a BioSemi ActiveTwo system
(BioSemi, 荷兰), 和 128 scalp electrodes at
512 赫兹. Vertical EOG was recorded from electrodes above

and below the left eye. Data were processed and analysed
using custom MATLAB scripts that drew on routines from
EEGlab (Delorme & Makeig, 2004). EEG data were linearly
detrended across each session, low-pass filtered at 40 赫兹
(FIR filter), and epoched in intervals of -1000:3000 ms rel-
ative to evidence onset. Trials were baseline-corrected to a
period after the initial zero-evidence stimulus appeared,
but before the evidence appeared (这 400 ms before
coherent motion onset in Experiment 1, 和 200 多发性硬化症
before the contrast-difference in Experiment 2). 相同
pre-evidence baseline was used for pre- and post-choice
CPP analyses in Experiment 2, except for the pre-response
baseline investigation which used the 100 ms before initial
RT (see Supplementary Materials). Channels with extreme
variance or high artefact counts were
interpolated
(mean = 4.48 channels, 标准差= 2.88, range = 0-12).

Epochs with any scalp electrode voltages over 100 µV,
or with bipolar VEOG voltages over 200 µV (250 µV in
实验 2) between the baseline and the response
onset (confidence cue onset in Experiment 2) 是
flagged as artefactual and removed. Participants with
more than half their trials removed were excluded from
the analysis (2 in Experiment 1, 5 in Experiment 2). Exper-
iment 1 had a mean of 490.56 在......之外 576 trials included
(标准差= 63.30, range = 337-567), and Experiment 2 had a
mean of 929.88 在......之外 1280 trials included (标准差= 151.65,
range = 653-1242). Response-aligned epochs were also
extracted from the evidence-aligned epochs, using the
间隔 -1000 多发性硬化症:500 ms relative to response in Experi-
蒙特 1, 和 -1000 多发性硬化症:1000 ms in Experiment 2. The volt-
ages were transformed into Current Source Density
(可持续发展委员会) using CSDToolbox (Kayser & Tenke, 2006) 与
default parameters (λ = 1 X 10-5, m-constant = 4; 看
Supplementary Materials for non-CSD key data).

2.5. 分析

For both experiments, trials with initial choice reaction
times less than 100 ms were excluded (实验 1:
mean = 10.12, SD = 12.69, range = 0-52; 实验 2:
mean = 2.04, 标准差= 3.31, range = 0-12). Because in Experi-
蒙特 2 participants were able to change their minds
between the initial choice and the final confidence report,
we scored their final reports in two different ways. Firstly, 到
test the hypothesis that the post-choice CPP reflects a dis-
tinct accumulation process selectively gathering evidence
calling for a revision of the initial choice, we compared
waveforms according to “confidence-in-initial-choice” as
defined above. This provides a directional measure of the

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participants’ finally reported confidence in their earlier
选择, allowing for changes-of-mind (CoM). 例如,
if the subject initially reported “right,” then a final report of
“certain right” corresponds to the highest level of confi-
dence-in-initial-choice (“certain no-CoM”), while “certain
left” corresponds to the lowest value (“certain CoM”) 和
the “maybe” reports lie in the middle. In later analyses, 我们
also tested whether the CPP scaled with the level of confi-
dence they had in their final choice, irrespective of whether
this involved a CoM or not, a factor we labelled “final cer-
tainty” to reflect its independence of the initial choice.

Data were analysed with trial-wise linear mixed models
(LMM), after z-scoring all variables. The regression coeffi-
cients from these models are standardised by the z-scor-
英, and the degrees of freedom represent the total number
of trials minus the degrees taken up by the factors included
in the model. Generalised LMM were used for logistic
regression when binary variables such as accuracy or
change-of-mind were the dependent variable. Reaction
次 (RT) were measured from stimulus offset in Experi-
蒙特 1 (to account for different stimulus durations), 和
from evidence onset in Experiment 2. 实验 2 final
RTs were measured from the confidence-scale onset.
实验 1 RTs and Experiment 2 final RTs were
log-transformed for statistical analysis (实验 2 最初的
RTs were approximately normal). For Experiment 1, Stimu-
lus Duration was included in the LMM. The main factors of
interest were initial accuracy and final certainty (或许,
probably or certain), and Experiment 2 also had Post-
choice Evidence Condition (Continued or Extinguished)
and Change-of-mind. We ran a model comparison to
select the best random-effects structure to use, 用一个
backward-selection likelihood ratio test method (αLRT = 0.2)
starting
from the maximal random-effects structure
(Matuschek et al., 2017). We ran this once, using the
pre-response CPP amplitude effect in Experiment 2, 和
fixed-effects of Post-choice Evidence Condition and final
肯定, and the best fitting model was one with only ran-
dom intercepts (see Supplementary Materials). 相当
than running this selection in each of the 36 main LMMs
and the >200 LMMs used when analysing the time-bins
across each waveform figure, we used this intercept-only
random-effect for all LMMs. This keeps the interpretation
of the models consistent across analyses.

“Maybe” responses were less common than the others,
especially when evidence was extinguished in Experiment
2, so a minimum number of 10 trials for each Final-Certain-
ty*Evidence combination was applied. This led to the
exclusion of “maybe” extinguished-evidence trials from 5
参与者 (35 trials in total; their other trials were kept in).

相似地, 7 participants in Experiment 1 had fewer than 10
trials for some Final-Certainty*Stimulus Duration combina-
系统蒸发散, so these trials were excluded (46 in total). Other trials
from these participants were kept in the analysis, 作为
LMM allows for missing data—excluding these partici-
pants entirely did not change the pattern of results.

The added stochastic contrast variation in Experi-
蒙特 2 intended for reverse correlation analyses was
unable to replicate previous effects of initial choice
准确性, indicating that the variance was too low, 和
so also had no detectable effects of confidence ratings,
so is not included here.

2.6. EEG signals

To identify appropriate electrodes for measuring the CPP,
we examined the grand-average ERP topographies (IE。,
averaged across all included trials, thus across all confi-
dence ratings) and covering the time range from -150:-
50 ms before the initial choice report. A cluster of 5
Centro-parietal channels centred on the focus of the CPP
topography were selected and, for each individual, 我们
identified the channel within this cluster that exhibited the
largest pre-choice amplitude in order to extract CPP mea-
surements. The pre-choice mean amplitude was taken
之内 -150:-50 ms before initial response in Experiment 1,
和 -140:-50 ms for Experiment 2 (in order to capture an
integer number of cycles of the SSVEP signal). We used
these same electrodes for the post-choice CPP, 和
examining this indicated that this signal dropped partially
toward baseline soon after the initial choice report before
undergoing a second build-up in advance of the presenta-
tion of the confidence cue, which differed between Contin-
ued and Extinguished Post-choice Evidence Conditions
towards the end of the delay (see Supplementary Fig. 1).
Based on this observation, we measured the amplitude of
the post-choice CPP in the window 700:1000 ms after the
initial choice. A 10 Hz low-pass filter is applied for figure
plotting only in order to remove the 15 Hz and 30 赫兹
SSVEP components. We additionally examined the effect
of a pre-response baseline (-100:0 ms before initial
response) on the post-choice CPP both in our time-win-
dow, and an earlier window (200:350 多发性硬化症) as reported in a
previous paper (Feuerriegel et al., 2022; see Supplemen-
tary Materials). In addition to the a priori mean amplitude
windows analysed, we analysed mean amplitude within
each 100 ms bin with LMM, across the 1000 ms before
initial-response and the 1000 ms between initial-response
and final response in Experiment 2. Effector-selective
motor preparation was analysed via mu/beta band

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(8-30 赫兹) 活动. Fast-Fourier transforms were performed
on the CSD data, with 256-sample windows (~500 ms)
moving in 8-sample steps (20 多发性硬化症). Clusters of three elec-
trodes in each hemisphere were chosen, centred on the
strongest ipsilateral minus contralateral pre-response
(-150:-50 多发性硬化症) amplitude in the grand-average topography.
Within these clusters, the channel with the largest differ-
ence in amplitude was chosen for each person. 意思是
amplitudes were calculated for the interval -250:-100 多发性硬化症
before initial choice in Experiment 1, 和 -300:0 ms in
实验 2, along with a post-choice measurement in
实验 2 从 700:1000 多发性硬化症 (IE。, -300:0 ms before
confidence cue appears).

In Experiment 2, the two gratings each flickered at
15 Hz in anti-phase generating distinct phase-tagged con-
trast-dependent SSVEP responses to each grating. 什么时候
both gratings are at equal contrast, the anti-phase ensures
that the signals for each grating will cancel out on the
scalp. When one grating has higher contrast, 这 15 赫兹
signal will be more strongly phase-aligned to that grating,
providing an index of the encoding of the sensory evidence
for this experiment (IE。, the differential contrast of the two
gratings). 这 15 Hz phase-tagged signals were calculated
by convolving the CSD data with a 15 Hz sinewave (171
samples length, 334 多发性硬化症, 5 cycles), and the phase was pro-
jected onto the mean phase 400 ms after the initial
response, when the 15 Hz signal was steady. The real
component of this projection reflects the strength of the
alignment with this phase, with negative values corre-
sponding to the opposite phase, which we term the differ-
ential SSVEP. Mean topographies were used to pick the
best channel from a cluster centred on Oz, per person. 我们
took the mean value of this differential SSVEP from
700:1000 ms after initial response. We could only analyse
the continued evidence condition, as there was no post-
choice visual stimulus when evidence was extinguished.

这 30 Hz SSVEP, reflecting overall stimulus engage-
ment to both stimuli, was taken from the same Fourier
transformed data described above, from the Oz elec-
trode, and normalised to the adjacent frequencies. 这
mean amplitude was taken -400:-200 ms before the initial
response, 和 700:1000 ms after it.

3. 结果

3.1. Pre-choice CPP predicts choice accuracy and simultaneously
reported confidence

In Experiment 1, participants made two-alternative forced
choice dot motion direction discrimination decisions and

simultaneously reported their confidence in that choice
(如图. 1). 正如预期的那样, Accuracy (β = 0.15, t (11765) = 6.75,
p < .0001) and Confidence (β = 0.06, t (11765) = 7.73, p < .0001) increased with Stimulus Duration, as shown in Figure 2a-d. RT relative to stimulus offset decreased with longer Stimulus Durations (β = -0.23, t (11759) = -33.32, p < .0001), and with greater Confidence (β = -0.11, t (11759) = -15.60, p < .0001), and was faster for correct responses (β = -0.33, t (11759) = -43.47, p < .0001). There were also interactions of Accuracy and Stimulus Duration (β = -0.03, t (11759) = -4.51, p < .0001), and Accuracy and Confidence (β = -0.03, t (11759) = -4.80, p < .0001), as the effects of Stimulus Duration and Confidence on RT were stronger on correct trials. As previously observed in studies of perceptual choice, the CPP exhibited a steady build-up during deliberation (Fig. 2e), reaching a peak just before response execution. The CPP reached a significantly higher amplitude prior to Correct responses compared to erroneous ones (β = 0.04, t (11759) = 3.93, p < .0001), and on trials with higher reported Confidence (β = 0.05, t (11759) = 4.88, p < .0001) with no significant interactions (p > .5). Post-hoc contrasts
indicated that CPP amplitude was significantly larger for
“certain” compared to “maybe” (F (1,11761) = 8.87,
p = .0029) and “probably” (F (1,11761) = 5.32, p = .0211)
confidence ratings, but did not differ reliably between
“maybe” and “probably” confidence ratings (F (1,11761) =
0.39, p = .53).

3.2. Pre-choice CPP only predicts delayed confidence reports
when evidence is extinguished following commitment

In Experiment 2, participants made two-alternative forced
choice contrast discriminations and reported their confi-
dence after a delay of 1000 多发性硬化症 (如图. 1), during which the
physical evidence either Continued on-screen or was
Extinguished. Discrimination accuracy increased from
initial-choice to final choice (β = 0.15, t (42494) = 11.90,
p < .0001, Fig. 3a) with a significant Response (initial vs final) by Post-choice Evidence (Continued vs Extin- guished) interaction (β = 0.05, t (42494) = 4.12, p < .0001), as accuracy increased more when evidence presentation Continued throughout the delay period. We first analysed the participants’ confidence-in-initial- response (i.e., whether their delayed confidence report showed a change-of-mind or not). Reported confidence-in- initial-choice was higher following a Correct initial choice (Fig. 3c; β = 0.45, t (21245) = 80.02, p < .0001), and lower when Evidence presentation Continued throughout the Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 7 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 Fig. 2. Pre-choice CPP predicts confidence reported simultaneously with direction in Experiment 1. (a) Mean accuracy increases with stimulus duration. (b) Mean accuracy is higher for trials rated higher confidence. (c) Mean confidence rating (1 = maybe, 2 = probably, 3 = certain) increases with stimulus duration only for correct responses. (d) Mean post-offset RT is quicker for longer stimulus durations, and for higher confidence ratings, but is slower for incorrect trials (dashed lines). (e) Mean pre-choice CPP traces in Experiment 1, leading up to response time, split by Confidence (within each stimulus duration and averaged across durations). Experiment 1 pre-choice CPP amplitude within the grey time-window is higher for “certain” responses (black bar = effect of Confidence, p < .05 within each 100 ms time-bin). The inset topography shows the mean activity within the time-window (red = positive, blue = negative) for the grand-mean over all confidence levels, with the black dots showing the electrodes used for CPP selection. Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 8 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 Fig. 3. Pre-choice CPP in Experiment 2 predicts delayed confidence-in-initial-choice only if evidence is extinguished after initial response. (a) Choice accuracy increases between initial and final responses, with a much greater increase if evidence continues. (b) Mean RT for initial responses is quicker for trials rated higher confidence-in-initial-choice (i.e., dependent on whether this involved a change-of-mind or not), slower for correct responses, with an interaction of the two. (c) Mean confidence-in-initial-choice (6 = certain no-CoM, 1 = certain CoM) is higher after correct responses, but slightly lower if evidence continues. (d) Changes-of-mind are far more common following errors, and continued evidence increases changes-of-mind, with greater effect on error trials. (e-f) To allow better comparison with Figure 2e, trials with changes-of-mind are excluded from the waveforms in panels (e) & (f) only (see Supplementary Fig. 2 for those trials). (e) Pre-choice CPP amplitude is greater on trials later rated as higher confidence-in-initial-choice, but only when the evidence is extinguished after the initial response (black bar shows significant effects of confidence on mean amplitude within 100 ms time-bins, p < .05). (f) If post-choice evidence instead continues, this disrupts the link between pre-choice CPP and the delayed confidence-in-initial-choice rating. The inset topography shows the grand-mean activity within the time-window across all trials (both evidence conditions, all no-CoM confidence ratings), with the black dots showing the electrodes used for CPP selection (same scale as inset in Fig. 2). Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 9 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 delay period (β = -0.13, t (21245) = -23.53, p < .0001), with an interaction of the two (β = 0.15, t(21245) = 26.29, p < .0001) as there was much greater confidence resolution (i.e., the difference between confidence to correct and error trials) when Evidence Continued (β = .57, t(12104) = 71.18, p < .0001) than was Extinguished (β = 0.29, t(9141) = 39.27, p < .0001). Investigating this trend further, we found that Contin- ued evidence led to a significant increase in change-of- mind rates (Fig. 3d; β = .54, t (16930) = 12.40, p < .0001) following correct initial response (β = .54, t (16930) = 12.40, p < .0001) as well as erroneous ones (β = .80, t (4315) = 20.88, p < .0001), although the effect was significantly greater for initial errors (Accuracy by Post-choice Evi- dence interaction (β = -0.10, t (21245) = -4.34, p < .0001). Thus, while post-choice evidence mainly causes cor- rective changes-of-mind leading to greater final accu- racy overall, it also causes a reduction in confidence ratings and increase in choice reversals following cor- rect initial responses (Fig. 3d). This observation likely stems from the fact that, based on confidence levels reported for correct trials in Experiment 1 and in the extinguished evidence condition of Experiment 2, par- ticipants were likely close to the maximum level of con- fidence that could be reported at the time of initial commitment, reducing the scope for any further mea- surable increases. Turning to the CPP, we first sought to test the relation- ship between the delayed confidence reports and its amplitude measured immediately prior to the initial choice. To allow direct comparison with the pre-choice CPP effects observed in Experiment 1 (where partici- pants rated confidence alongside their choice and there- fore could not report changes-of-mind), we examined pre-choice CPP amplitude as a function of confidence- in-initial-choice, but excluded any trials with changes-of- mind—thus, it reflects the confidence relative to the initial choice, but rated at the final response (similar effects were observed when changes-of-mind were included, see Supplementary Fig. 2 for statistics). Consistent with the results reported for Experiment 1, pre-choice CPP amplitude increased with confidence-in-initial-choice (β = 0.01, t (18512) = 2.06, p = .0394), although the effect of choice Accuracy did not reach significance (β = 0.01, t (18512) = 1.02, p = .31). There was also a Confidence-in- initial-choice*Post-choice Evidence interaction (β = -0.02, t (18512) = -2.24, p = .0251), and separate LMMs in each Post-choice Evidence Condition indicated that pre- choice CPP amplitude increased with confidence-in- initial-choice when evidence was Extinguished during the delay period (Fig. 3e; β = 0.04, t (8485) = 2.74, p = .0062), but not when Evidence Continued (p = .9699; Fig. 3f). This accords with the observation that post-choice evi- dence had a substantial influence on the confidence reports—if decision processes are updated during the post-choice interval, then this would naturally reduce the degree to which pre-choice CPP amplitudes would pre- dict the confidence level reached by the end of the trial, even if no change-of-mind occurred. 3.3. Post-choice CPP scales inversely with final choice certainty irrespective of change-of-mind Next, we looked at how the CPP evolves during the post-choice delay period in Experiment 2 (Fig. 4), includ- ing in change-of-mind trials. When evidence was Extin- guished, the grand-average CPP returned gradually back to baseline over the next 1000 ms (Supplementary Fig. 1) but, when evidence presentation continued, the CPP decayed at a markedly slower rate overall, and exhibited a positive build-up during the delay period on certain trial types. To match analyses conducted in previous studies of confidence-related modulations of post-choice ERP sig- nals (e.g., Boldt & Yeung, 2015; Feuerriegel et al., 2022), we first analysed post-choice CPP amplitudes (measured at the end of the delay period) as a function of confidence relative to the initially chosen option (“confidence-in- initial-choice”). Here, we observed an interaction of Post-choice Evidence and confidence-in-initial-choice (β = -0.02, t(21073) = -3.084, p = .0020), and separate LMM in each evidence condition showed this was driven by higher post-choice CPP amplitudes for lower confidence-ratings when evidence presentation Contin- ued during the delay period (β = -.03, t (12014) = -3.59, p = .0003), an effect that was absent when evidence was Extinguished (β = 0.00, t(9059) = 0.11, p = .91). The absence of any relationship with confidence on Extin- guished trials appears to be in direct disagreement with results reported by Boldt and Yeung (2015). However, that study used the interval immediately prior to the initial choice for its baseline correction which could cause pre- choice amplitude differences to be transferred to post- choice measurements. When we applied the same pre-choice baseline correction, we found the same pat- tern of results as Boldt and Yeung, with the post-choice CPP now decreasing with confidence-in-initial-choice in the Extinguished condition both in our measurement win- dow and in the one used by Boldt and Yeung (Supple- mentary Fig. 3). This last observation also indicates that, Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 10 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 Fig. 4. Post-choice CPP is sensitive to post-choice evidence and increases when participants have low final certainty. Post-choice CPP refers to the CPP time-course between the initial choice response and the final choice with accompanying confidence 1000 ms later in Experiment 2. (a) CPP waveforms as a function of the 6-point “confidence- in-initial-choice” rating, taking into account whether the trial included a change-of-mind (CoM) or not, indicating whether the participant believed the initial response was wrong or correct. The mean CPP (700:1000 ms) decreases after the initial choice if the evidence is Extinguished at that time, with no significant difference depending on confidence-in-initial-choice. (b) When Evidence Continued after the initial response, the post-choice CPP plateaued, and rose again on trials where subjects’ final ratings translated to their initial choice being “maybe” or “probably CoM.” The effect of confidence-in-initial- choice became significant from about 400 ms after the initial decision (solid black bars show p < .05 in 100 ms time- windows). (c) The same data as above, but with confidence-in-initial-choice binned in pairs to increase the trial-numbers within one waveform; again, Extinguished trials have no differences, but (d) Continued trials show a significant effect, which is non-linear, as the medium bin (maybe CoM & no-CoM) is highest. (e) Extinguished evidence trials did not differ by final certainty (i.e., maybe/probably/certain rating for the final option chosen, regardless of CoM or no-CoM) responses. (f) Continued-evidence trials had greater post-choice CPP amplitudes on trials rated “maybe” than “probably” or “certain.” The topography inset in panel (f) shows the mean amplitude within the grey window for the low final-certainty trials (red = positive, same scale as Figures 2 & 3, black dots are CPP electrodes), and the solid black bars along the bottom show which 100 ms time-windows have significant effects in the CPP waveforms (p < .05, none were significant for the Extinguished conditions). Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 11 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 while the present study used confidence scales that were mapped to the choice alternatives (left vs right) and Boldt and Yeung (2015) used a scale mapped to the accuracy of the initial choice (correct vs incorrect), these differ- ences did not alter the post-choice dynamics of the CPP qualitatively, at least in the Extinguished condition. Although there was an effect of confidence-in-initial- choice on CPP amplitude when evidence presentation continued, Figure 4b shows that CPP amplitudes were very similar for “certain CoM” and “certain no-CoM” trials where the difference in confidence-in-initial-choice is greatest (t(22) = 0.119, p = .907, BF01 = 4.543, indicating moderate evidence for the null). CPP amplitudes were also highly similar for “maybe CoM” compared to “maybe no-CoM” trials (t(24) = 0.140, p = .890, BF01 = 4.701, indi- cating moderate evidence for the null) with differences only apparent between “probably CoM” and “probably no-CoM” (t(23) = 2.247, p = .035, BF01 = 0.573 indicating anecdotal evidence for the alternative hypothesis). To investigate this pattern further, we grouped the confidence ratings such that trials were labelled accord- ing to the subjects’ confidence in the option they finally chose, regardless of whether this involved a CoM from their initial choice or not (termed “final certainty” to reflect its independence from the initial-choice). Here, we observed a Final-Certainty*Post-choice Evidence inter- action (β = -0.29, t (21073) = -4.22, p < .0001), driven by the fact that when Evidence Continued (Fig. 4b) higher final certainty was associated with a smaller post-choice CPP amplitude (β = -0.02, t (12014) = -2.27, p = .0231), while no such relationship was observed when evidence was extinguished (Fig. 4a; β = 0.01, t (9059) = 0.75, p = .45). BIC slightly favoured final certainty as a predic- tor of CPP amplitude over confidence-in-initial-choice (ΔBIC = -3). Taken together, these results suggest that the post- choice CPP scales with the participant’s final certainty, irrespective of whether or not the ultimately chosen alter- native differs from the initially chosen one. While the CPP scaled positively with the participants’ initial choice con- fidence, post-choice CPP amplitude was inversely related to final certainty in Experiment 2, with “maybe” trials now having the highest amplitude. One potential explanation for this pattern, inspired by a previously reported mathe- matical model (Pleskac & Busemeyer, 2010), is that the duration of post-choice evidence accumulation is cer- tainty-dependent, such that participants are more likely to terminate the accumulation process when highly cer- tain in a particular alternative, after which the CPP decays back to baseline as seen when evidence is Extinguished (Fig. 4a). Assuming the certainty-dependent stopping rule is stable across trials, it would result in lower ampli- tudes in our measurement window (which was toward the end of the delay period) for trials with high final certainty because of the earlier peak and decay of the CPP. An example of this kind of effect was reported in Twomey et al. (2016) where the CPP was found to peak and decay earlier on easier trials when participants were required to withhold reporting dot motion direction decisions until stimulus offset (see also Rogge et al., 2022; Tagliabue et al., 2019). This pattern resulted in larger average CPP amplitudes toward the end of the delay period for trials with weaker physical evidence. In other words, when CPP amplitude measurements are taken within a fixed time window within a delay period, they will scale with the proportion of trials on which evidence accumulation was still ongoing during that window (see Discussion for illus- tration). In the following sections, we report a number of analyses designed to test the hypothesis that partici- pants were reaching commitment earlier on trials with high final certainty. 3.4. Earlier post-choice CPP peak latency and confidence reports on trials with high final certainty We ran a post-hoc exploratory analysis on the peak latency of the post-choice CPP. The surface plots in Figure 5a highlight substantial cross-trial variability in post-choice CPP peak latency in the continued evidence condition. Post-choice CPP peak latencies were signifi- cantly later when Post-decision Evidence Continued (Fig. 5b, β = 0.28, t (21245) = 4.15, p < .0001), but earlier when final certainty was higher (β = -0.21, t(21245) = -2.71, p = .0067), with a significant interaction of the two (β = -0.24, t(21245) = -3.50, p = .0005). This was due to final certainty only having a significant association with peak latency when Evidence Continued (p = .0036), but not when it was Extinguished (p = 0.40). If commitment is being reached earlier on trials with high final certainty, then responses for the final report should be made more quickly. Analysis of final-response RTs confirmed this, with significantly faster final RTs when final certainty was higher (Fig. 5c; β = -0.22, t(21245) = -32.44, p < .0001). Final RTs were also significantly faster when evidence was Extinguished (β = 0.30, t(21245) = 50.07, p < .0001) and there was a significant final cer- tainty by Evidence interaction (β = -0.01, t(21245) = -2.17, p = .0298). Examining this interaction, there were signifi- cant effects of final certainty both when Evidence Contin- ued and was Extinguished (p < .0001), although the effect Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 12 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 Fig. 5. Post-choice CPP peak latency and final-response RT are quicker for high final-certainty responses. (a) Single- trial post-choice CPP surface plot, sorted by peak latency (curved black line) for the Continued Evidence trials (smoothed over 100 trials). The post-choice CPP decreased after the peak, rather than remaining elevated. (b) The mean post-choice CPP peak latency was earlier on trials rated higher final certainty, but only when Evidence Continued—giving the inverted U-shaped pattern when considering confidence-in-initial-choice. (c) Final-response RTs showed a similar pattern when Evidence Continued, with faster final RTs for higher final-certainty reports. Please note that final-response RTs were cued- responses after the 1000 ms delay, so did not occur around the same time as the peak latencies. was stronger when Evidence Continued (β = -0.23 vs -0.20). As Figure 5c shows, when Evidence Continued, the “certain CoM” and “certain no-CoM” had the fastest final-response RTs, and these were almost as fast as tri- als where the evidence was Extinguished (only 182 ms and 135 ms slower on “Certain CoM” and “Certain No-CoM” trials respectively, vs >290 ms all the other trial
类型). 合在一起, these results fit with the idea that
deliberation stopped earlier when highly certain in that
选择.

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3.5. Faster motor lateralisation on trials with high final certainty

We reasoned that, if a certainty-dependent stopping rule
were being implemented, then preparation of the final
response should emerge earlier in the delay period on
trials with higher final certainty. We first examined levels
of motor preparation in the same measurement window
used to analyse the post-choice CPP.

There was a significant effect of final certainty on mean
mu/beta lateralisation (700:1000 ms window; β = -0.07,
t(21018) = -10.16, p < .0001), which significantly inter- acted with Post-choice Evidence (β = -0.02, t(21018) = -3.43, p = .0006). This interaction was due to a stronger effect of final certainty when Evidence Continued (Fig. 6f; β = -0.09, p < .0001) than when Extinguished (Fig. 6e; β = -0.04, p < .0001). Motor lateralisation also varied significantly as a func- tion of confidence-in-initial-choice (mean within 700: 1000 ms; β = -0.04, t (21018) = -4.90, p < .0001), although without a significant interaction of Post-choice Evidence (p > .4). Figure 6b highlights a similar but inverted pattern
to that observed for the CPP, with lateralisation increas-
ing with final certainty in both CoM and no-CoM trials.
including confidence-in-initial-
Comparing the LMM
choice to that including final certainty, we found that the
latter again gave a better fit to the neural data (ΔBIC = -90).
因此, greater delay period motor preparation was
observed on trials with higher reported final certainty.
Although this is the opposite pattern to that seen for the
CPP, it is equally consistent with the certainty-dependent
stopping-rule account because whereas the CPP would
be expected to drop to baseline once the accumulation
has halted, lateralised motor preparation would be
expected to remain at its extreme near-threshold level
since the response has yet to be executed, as seen in
some delayed-response tasks (Rogge et al., 2022;
Twomey et al., 2016).

To further test the hypothesis that participants were
committing to and preparing their responses earlier on
high final-certainty trials, we measured mean β lateralisa-
tion slopes in 200 ms windows after the initial choice and
ran separate analyses on CoM and no-CoM trials (due to
the large inversion of lateralisation that occurs on CoM tri-
作为). In both CoM and no-CoM trials, trials with higher
final-certainty ratings had significantly stronger slopes
than lower final-certainty trials, and this effect was appar-
ent from 0-800 ms after initial choice in CoM trials and
200-600 ms in no-CoM trials (p < .05, see blue & red bars in Fig. 6b, respectively). This suggests an earlier build-up of motor lateralisation and accords with the final-RT results reported above, suggesting that motor preparation occurred earlier in the delay period on high final-certainty trials, which would fit with a certainty-dependent stopping. 3.6. Sensory evidence signals increase with confidence and track changes-of-mind We also examined the post-choice dynamics of the differ- ential SSVEP which indexes the encoding of the sensory evidence, i.e., the relative contrast of the two grating stim- uli. The differential SSVEP response following the initial choice was greater on trials with higher confidence-in- initial-choice (β = 0.08, t(12102) = 7.62, p < .0001), which interacted with initial accuracy (β = 0.04, t(12102) = 5.85, p < .0001), as the differential SSVEP was higher following correct responses subsequently rated as “certain no- CoM” (β = 0.11, t(9607) = 8.77, p < .0001), but lower fol- lowing errors subsequently rated as “certain no-CoM” (Fig. 7a-b; β = -0.03, t(2495) = -2.15, p = 0.0313). Unlike the CPP and mu/beta signals above, confidence had a monotonic effect; as the evidence always favoured the correct response, stronger evidence encoding was associ- ated with higher confidence in correct initial choices, and lower confidence in incorrect initial choices, i.e., greater confidence in the correct option. Final certainty was sig- nificantly associated with higher differential SSVEPs (β = 0.06, t(12102) = 7.08, p < .0001), but this had no sig- nificant interaction with initial accuracy (p = .42). BIC favoured confidence-in-initial-choice over final certainty as a predictor (ΔBIC = -18), in contrast to the post-choice CPP and motor preparation signals reported above. Whereas the differential 15 Hz SSVEP traced the sensory-level representation of the relative contrast of the two gratings (i.e., the evidence), the 30 Hz SSVEP offered a metric of the overall visual response to both stimuli combined. There was no significant relationship between the post-choice 30 Hz SSVEP and final certainty (p > .05), although there was a negative main effect of
confidence-in-initial-choice (β = -0.03, t(11979) = -2.09,
p = .0369), but this did not interact with initial accuracy
(p > .05) like the differential SSVEP did (Supplementary
如图. 4). BIC favoured the confidence-in-initial-choice pre-
dictor only very slightly (ΔBIC = -1). In order to interpret
this lack of initial-accuracy*confidence-in-initial-choice
effect in the 30 Hz signal, we directly compared it with the
differential 15 Hz SSVEP. A significant three-way interac-
tion was observed (p = .0013), indicating that the two
SSVEPs differed significantly in their sensitivity to the
combination of confidence and accuracy.

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如图. 6. Motor lateralisation signals invert with changes-of-mind, and scale with final certainty. Mu/beta power
lateralisation index relative to the hand used for the final response (therefore it is inverted at the time of the initial response
on trials where participants changed their minds). Topography in panel (d) shows the grand-mean motor lateralisation
index within the grey window, averaged across all conditions and trials (red = positive, black dots = selected channels).
The solid black bar shows the 200 ms time-bins with significant effects (p < .05) of that factor on the slopes of the lateralisation, while blue/red solid bars show the same for effects of final certainty on slopes within change-of-mind/ no-change in the top row. Mean mu/beta lateralisation (within the grey window, 700:1000 ms after initial RT) is stronger when people have greater confidence-in-initial-choice, whether evidence is extinguished (a) or continued (b), and the slopes are steeper for high-confidence responses from around soon after initial RT when evidence Continues (blue/red solid bars). When confidence-in-initial-choice is binned into adjacent pairs (c & d), it is clearer that the “maybe” trials have less motor preparation, especially when evidence Continues (d). Using this coding, the green line involves trials that do and do-not change responses, so the average is close to zero at the initial response time; however when evidence is Extinguished (c) this is also seen in the blue line, which is due to the “certain CoM” trials having slightly negative motor preparation in this time-period, perhaps reflecting motor execution errors. (e-f) Mu/beta lateralisation is stronger for trials with greater final certainty, and weakest for “maybe” trials, with the difference in slopes appearing around 400 ms after initial response. Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 15 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 Fig. 7. Sensory post-choice evidence signals show greater stimulus engagement with higher confidence and predict changes-of-mind. Differential SSVEP strength (arbitrary units) measures the difference in sensory signal strength for the target and non-target (i.e., the strength of sensory evidence encoding) to the post-choice continued evidence. The phase of the stimuli reset at initial RT, so the signal builds from zero then. The topography in panel (b) shows the grand-mean differential SSVEP within the grey window, averaged across all Continued Evidence trials (red = positive, black dots show electrodes used for selection). Black solid bars show which 100 ms time-bins have a significant effect of the factor for that initial-accuracy (p < .05). The mean differential SSVEP (within the grey time-window, 700:1000 ms) shows an interaction with confidence-in-initial-choice and initial accuracy as: (a) following an error response, the differential SSVEP is higher on trials where participants change their minds (blue lines), and lowest for trials in which they stick with their initial choice with high confidence (dark red); (b) following a correct response, the opposite pattern is seen, with a linear increase in differential SSVEP for trials with higher confidence-in-initial-choice. (c-d) When confidence-in-initial-choice is binned (to increase trial numbers for the rarer responses), the same pattern is seen. (e-f) When split by final certainty, there was no significant interaction between initial error and final certainty; there was a significant positive relationship following initial correct responses, and a non-significant positive relationship following initial errors. 4. DISCUSSION While the role of neural evidence accumulation processes in forming perceptual decisions is now well-established, the extent to which these same processes continue to operate after an initial choice to inform subsequent con- fidence judgements has remained an open question. The results of Experiment 1 demonstrate that when confi- dence is reported simultaneously with a perceptual choice, the pre-choice amplitude of a motor-independent EEG signature of evidence accumulation (CPP) increases monotonically with confidence (Fig. 2e), and this effect was replicated in a different sample and task in Experi- ment 2 in which confidence reports were delayed by Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 16 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 1000 ms with no intervening evidence (Fig. 3e). Experi- ment 2 also allowed us to examine the post-choice dynamics of the CPP, and whether they were influenced by the continued availability of physical evidence. Multiple elements of our data suggest that commit- ment to the final confidence report tended to be reached very soon after the initial choice in the Extinguished con- dition: compared to trials with continued evidence, par- ticipants had faster final RTs (Fig. 5c), and no positive build-up or confidence-dependent modulation in the trial averaged post-choice CPP (Fig. 4). Nevertheless, partic- ipants’ final reports were significantly more accurate than their initial choices on these trials (Fig. 3a) suggesting that some further accumulation did take place, poten- tially drawing on evidence still in the perceptual pipeline at the time of commitment (Resulaj et al., 2009). When the physical evidence remained on screen, the CPP did continue to exhibit confidence-dependence, but now its amplitude at the end of the delay period was bet- ter explained by final certainty than confidence-in-initial- choice (Fig. 4b & f), as there were little differences between CoM and no-CoM trials. It is perhaps not sur- prising that the upcoming (final) decision better explains the CPP than the earlier initial decision, but the sugges- tion that this is invariant to whether the final choice involves a CoM or not is novel, as previous studies find large effects of CoM, although these studies did not pres- ent evidence during the interval between choice and con- fidence report (Boldt & Yeung, 2015; Feuerriegel et al., 2022). Additionally, the CPP-confidence relationship has inverted, with “certain” ratings corresponding to greater CPP amplitude before the initial choice but lower ampli- tudes before the final choice. Previous observations led us to suspect that this trend arose from certainty-dependent variations in the duration of the post-choice evidence accumulation. Specifically, in previous studies in which participants withheld perceptual reports until the provision of a delayed response cue, the CPP has been shown to peak and decay long before response cue onset on easy trials (Rogge et al., 2022; Twomey et al., 2016). Under a standard decision model, this would occur because the boundary is reached, after which the deci- sion variable stops accumulating and presumably decays back to baseline. As stronger evidence drives earlier decision termination, trial-averaged CPP ampli- tude measured late in the post-stimulus window will scale inversely with evidence strength (Rogge et al., 2022; Tagliabue et al., 2019; Twomey et al., 2016). We reasoned, therefore, that in the present data, post- choice accumulation may also be terminated as soon as a criterion level of certainty in one of the choice alterna- tives has been reached. A post-hoc exploratory analysis found that the post-choice CPP did peak significantly earlier on trials with higher final certainty, and the peak was followed by a return to baseline consistent with the process being terminated (Fig. 5a-b). Aside from the CPP data, several other results are consistent with earlier termination of the decision pro- cess on trials with higher final certainty. First, final- response RTs were significantly faster on trials with high final certainty (Fig. 5c), consistent with actions being selected long in advance of the response cue. Second, effector-selective motor lateralisation signals exhibited earlier and greater lateralisation in favour of the ultimately chosen effector on trials with higher final certainty (Fig. 6b & f). The question remains why participants opt to stop accumulating while evidence remains available. Plausible explanations include a reduction in effort or energetic costs (Sharot et al., 2023) and/or reducing time-on-task by allowing final responses to be prepared before the cue appears. These observations have important implications for mathematical models of choice confidence which have tended to disagree with the stopping rules applied to post-choice accumulation. In particular, our results appear to be at odds with models that assume a purely time-based rule and others assuming that accumulation continues until confidence reports are probed (Pleskac & Busemeyer, 2010; Yu et al., 2015). The use of free- response confidence ratings during EEG recordings in future work will allow the relationship between post- choice accumulation dynamics, confidence, and elapsed time for the more finely probed. While we have referred to this pattern as “certainty- dependent” stopping, our data do not allow us to pin- point the precise nature of the stopping rule that is being applied and several alternative proposals exist in the lit- erature. According to the “optional stopping model” pro- posed by Pleskac and Busemeyer (2010), the decision variable is translated into confidence (relative to the ini- tial-choice) based on its proximity to “confidence thresh- olds” that are tied to the distinct confidence levels that can be reported, and evidence accumulation is immedi- ately terminated when the decision variable reaches the extreme confidence thresholds (corresponding to “cer- tain CoM” and “certain no-CoM” in our task). This model can account for a range of behavioural effects (Moran et al., 2015), and a version of this model was recently shown to produce superior behavioural fits to a time- based stopping rule (Desender, Donner, et al., 2021). Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 17 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 Figure 8 illustrates that the observed CPP trends can be reproduced by such a decision process with fixed certainty-thresholds, and there are two key features of the CPP that account for this. First, the CPP is positive- going irrespective of the alternative that is favoured by the cumulative evidence (O’Connell & Kelly, 2021), thus the signal is expected to rise on average even when the evidence favours the alternative that was not initially endorsed. Second, the CPP decays back to baseline fol- lowing a choice commitment which ends the trial and accumulation (Fig. 2e). Assuming the same occurs with a latent certainty-threshold crossing that terminates accu- mulation, this would predict lower average amplitudes later in the delay period on trials which reached the threshold earlier (e.g., Twomey et al., 2016). Thus, the more trials which terminate early in the delay period, the more the signal decay will dominate the average sig- nal, while the signal will build positively on average in trial types with later and/or fewer threshold crossings. Importantly, this account does not require that evidence accumulation signals evolve in the same way regardless of changes-of-mind (e.g., “certain CoM” vs “certain no-CoM”); these trials can differ in the time taken to reach their respective confidence thresholds and still have decreasing average accumulation signals as long as the decaying signal from trials which have stopped accumulating outweigh the increasing signals from trials still accumulating. Detailed modelling, not feasible given the relatively low trial numbers and fixed evidence strength in the cur- rent dataset, will be required to clarify exactly how such a stopping rule is implemented in our task. For example, in the model of Pleskac and Busemeyer (2010), while accu- mulation immediately terminates upon reaching the extreme confidence bounds, a lower probability of stop- ping is also assigned when passing intermediate thresh- olds that correspond to the intermediate confidence levels that can be reported. Alternatively, rather than ter- minating accumulation probabilistically upon reaching an intermediate confidence threshold, the confidence level required to terminate post-choice accumulation may decrease as a function of time (Moran et al., 2015), similar to a collapsing bound or dynamic urgency effect (Hanks et al., 2014; Yau et al., 2021). Finally, it is possible that certainty-dependent stopping could occur at the time of the initial choice, so that trials where participants were already highly confident in their initial response would have no additional accumulation at all, a possibility that would require measuring confidence at the initial choice time to investigate. A certainty-dependent stopping rule can also account for key observations in the literature on the Error Positiv- Illustration of how halting accumulation upon early certainty-boundary crossing can give a decreasing signal. Fig. 8. Trials (thin solid lines) which cross the certainty-threshold (and are thus classed as “certain” for that option; dark red+blue) exhibit a decay afterwards, giving a decreasing trial-average signal (thick dashed lines). However, trials which do not reach this certainty-threshold by the end of the delay period (and thus are classed as “maybe” in this simplified illustration; cyan+yellow) do not decay, thus giving a shallow positive-going trial-average signal. The CPP is represented here by the absolute decision variable, meaning that CoM and no-CoM trials both have a similar signal, although differences in the slopes (and therefore crossing-times) can still exist. Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 18 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 ity (Pe), a signal that shares many functional similarities with the CPP, including its polarity and topography (Murphy et al., 2015). The Pe is typically examined in the context of tasks in which errors primarily occur due to a strong prepotency being established for one of the choice alternatives, either through differences in choice outcome probability, as in Go/No-Go tasks (e.g., Endrass et al., 2012; Niessen et al., 2017; Shalgi et al., 2009), or due to response-biases such as the antisaccade task (Falkenstein, 1990; Nieuwenhuis et al., 2001) or flanker task (Overhoff et al., 2021; Selimbeyoglu et al., 2012). It has been well established using these kinds of tasks that the Pe is elicited by erroneous choices that are explicitly detected by participants and is greatly diminished or absent following correct choices and undetected errors (Endrass et al., 2012; Nieuwenhuis et al., 2001; O’Connell et al., 2007; Steinhauser & Yeung, 2010). These observa- tions have fuelled the theory that the Pe reflects the oper- ation of a process that is designed specifically to detect action errors (Desender, Ridderinkhof, et al., 2021). That is, rather than being referenced to the original choice alternatives, post-choice evidence is accumulated in a new reference frame representing the probability that the preceding choice was incorrect. However, our results highlight another plausible functional account in which the Pe can be understood as a continuation of the same process indexed by the CPP, i.e., an evidence accumula- tion process mapped to the choice alternatives that is subject to a certainty-dependent stopping rule. Taking the example of the Go/No-Go task, Go trials have much greater probability than No-Go trials and therefore the decision bounds would be expected to be much higher for the latter than the former. Consequently, for a partici- pant to change their mind with high certainty following an error of commission on a No-Go trial, post-choice evi- dence would need to accumulate to the higher No-Go bound, leading to a larger signal following errors com- pared to correct Go responses. However, our data do not exclude the possibility that the post-choice CPP reflects a metacognitive operation that is distinct from the evidence accumulation process that it traces prior to the initial choice. While we have pre- sented the stopping-rule as a continuation of the initial decision process, it can be equally applied to a metacog- nitive accumulation process that evaluates the initial choice accuracy (e.g., Desender, Donner, et al., 2021; Fleming & Daw, 2017), yet stops earlier when highly certain that the response was either correct or erroneous. These two possibilities give very similar predictions for the neural and behavioural data, especially in the current paradigm and dataset, so we are not able to distinguish between them. Future experiments measuring confidence at initial and final choices, and manipulating post-choice evidence, will aim to directly compare these two theories. Two previous studies have examined the post-choice CPP on tasks in which a delay was imposed between initial choice and confidence reporting, but with no intervening evidence (Boldt & Yeung, 2015; Feuerriegel et al., 2022). In the case of Boldt and Yeung (2015), the post-choice parietal ERP was found to scale negatively and monotonically with confidence-in-initial-choice, contrary to the present results. However, in that study, signals were baseline-corrected to an interval immedi- ately prior to the initial choice, which potentially con- founds pre- and post-choice variations in cumulative evidence. Interestingly, their confidence effects remain when using a pre-stimulus baseline, although they appear to manifest only in the trials rated as errors (cor- responding to CoM trials in the present study). Compar- ison with our results is difficult, as waveforms with pre-stimulus baselines are not presented to allow exam- ination of effects before or after their amplitude mea- surement window (250-350 ms). When Feuerriegel et al. (2022) applied a pre-stimulus baseline correction, these post-commitment confidence effects on amplitude were substantially diminished and observed only following erroneous choices. We found a similar pattern here, with the application of a pre-response baseline period pro- ducing significantly greater post-choice CPP ampli- tudes for low confidence-in-initial-choice ratings, which were not observed with a pre-stimulus baseline (see Supplementary Fig. 3). We also found that the encoding of the sensory evi- dence (differential contrast) in early visual areas, as indexed by the differential SSVEP, was highly sensitive to confidence (Fig. 7). Unlike the CPP and motor lateral- isation signals, the differential SSVEP scaled most strongly with the participant’s confidence relative to their initial choice, with stronger responses on initially correct trials that were rated as likely to be correct and weaker responses on trials rated as likely to be incorrect (and vice-versa following an initial-error). Previous stud- ies have found sensory ERPs are stronger on higher confidence trials (Squires et al., 1973; Zakrzewski et al., 2019), but to our knowledge this is the first finding of the SSVEP showing a similar scaling. The differential SSVEP signals remained at a relatively constant level through- out the post-choice delay period even on trials with high final certainty, suggesting that early termination of the decision process did not result in a disengagement of Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 19 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 visual processing resources from the stimulus. It was not possible in the present study to establish whether these signal modulations by confidence manifest before or after commitment to the final confidence report. Again, the use of speeded confidence reports would be useful in this regard. While the focus of this study was on probing post- choice evidence accumulation, Experiment 1 found that pre-choice CPP amplitudes increased with simultaneously rated confidence, consistent with previous analyses of stimulus-locked CPP amplitudes (Davidson et al., 2022; Gherman & Philiastides, 2015, 2018; Herding et al., 2019; Tagliabue et al., 2019). This shows that neural signatures of confidence are available at the time of the initial choice whether confidence is rated simultaneously or 1 second later without post-choice evidence continuing. Possible mechanisms to explain why a neural signature of cumula- tive evidence measured prior to the choice report would scale with confidence include that the initial choice is sub- ject to a collapsing boundary (e.g., Kelly et al., 2021; Steinemann et al., 2018) and/or starting-point variability. Future investigations can explore whether including these in post-choice confidence models can account for the pat- terns we report here, such as confidence-effects being present before initial-responses occur, or even before response-cues appear, as in Experiment 1. In our task, delayed confidence reports did not cor- relate with pre-choice CPP amplitudes if post-choice evi- dence was presented. The weakening of this relationship can be explained by the fact that the neural and behavioural data indicate that a greater amount of post- choice evidence accumulation occurred in this condition and, thus, the amplitude of the CPP at the time of the initial choice would be less predictive of the participant’s final confidence level. A previous study in which stimuli were extinguished during a delay period between initial choice and confidence reports found no link between pre-choice CPP and post-choice confidence (Feuerriegel et al., 2022). One possible explanation for this discrep- ancy with our own results is that Feuerriegel et al. (2022) presented participants with brief static stimuli and shorter response deadlines which may have promoted a greater degree of post-choice evidence accumulation from iconic memory. As was the case in our continued evidence condition, this further accumulation may have degraded the relationship between pre-choice CPP amplitude and final confidence. The stimulus variables that determine whether evidence accumulation will continue in the absence of a physical stimulus is an interesting question for future research. We found that “certain” responses were substantially more common than “maybe,” and CoM responses were relatively rare, especially when the initial response was correct. We used a quadratic scoring rule in combination with trial-by-trial accuracy feedback, which incentivises maximising initial-accuracy and the accuracy of the con- fidence responses, and should push people to accurately rate their confidences (Staël von Holstein, 1970). While monetary incentives have been shown to improve meta- cognitive performance (Lebreton et al., 2018), they have also been reported to induce overconfidence (Lebreton et al., 2018), and quadratic scoring rules can cause con- fidence responses to cluster at the edges of confidence scales (certain correct and certain error; Hollard et al., 2016). A different way of incentivising accurate confi- dence reports may have given a more even spread of responses, and thus lower variances for those rarer responses, facilitating more detailed investigation of the more extended accumulation dynamics on those trials. Our analyses used the CSD-transformed data, as this minimises volume conductance between separate com- ponents (Kayser & Tenke, 2006), and reduces the influence of frontocentral preparation signals on CPP amplitudes (Kelly & O’Connell, 2013). A previous study found the CSD transformation was necessary in order to distinguish con- fidence effects on frontocentral components and the CPP (Feuerriegel et al., 2022). Here too, we found that the CSD transform influenced the extent to which CPP-confidence effects were observed. A look at the non-CSD data for Experiment 1 (Supplementary Fig. 6a) shows that the scal- ing of the pre-choice CPP with confidence was relatively unchanged. However, in Experiment 2, the relationship between pre-choice CPP and confidence no longer dif- fered between Extinguished and Continued condition, with both showing confidence-effects. In addition, the removal of the CSD transform eliminated both the effects of post- choice evidence on post-choice CPP amplitude and its relationship with confidence-in-initial-choice. This sug- gests the CSD transform is needed to uncover post-choice evidence and confidence effects on the CPP. In conclusion, our data suggest that evidence accumu- lation persists following initial choice commitment when physical evidence remains available and is terminated in a certainty-dependent manner. Whether post-choice evi- dence accumulation is mapped to the choice alternatives or is reframed to evaluate the accuracy of the initial choice remains an open question. In general, our study highlights some important methodological considerations when measuring post-commitment CPP activity; trial-averaged amplitudes can vary as a function of the duration of the Downloaded from http://direct.mit.edu/imag/article-pdf/doi/10.1162/imag_a_00005/2154736/imag_a_00005.pdf by guest on 09 September 2023 20 J.P. Grogan, W. Rys, S.P. Kelly et al. Imaging Neuroscience, Volume 1, 2023 accumulation process as well as the bounds associated with each of the choice alternatives. Using paradigms in which participants make speeded, rather than delayed, post-choice confidence reports may facilitate the acquisi- tion of CPP measurements that are more reflective of the state of the decision process at the time the participant commits to their final confidence report. DATA AND CODE AVAILABILITY Task scripts and anonymous data are available at https:// osf . io / 4dqkz/ and MATLAB code for analysing this data is available at https://doi . org / 10 . 5281 / zenodo . 7550910. AUTHOR CONTRIBUTIONS John P. Grogan: Data curation, Formal analysis, Investiga- tion, Visualization, Writing—original draft, and Writing— review & editing. Wouter Rys: Conceptualization, Data curation, Investigation, Methodology, Project administra- tion, and Writing—review & editing. Simon P. Kelly: Con- ceptualization, Writing—review & editing. Redmond G. O’Connell: Conceptualization, Funding acquisition, Super- vision, and Writing—review & editing. DECLARATION OF COMPLETING INTEREST The authors declare no competing financial interests. ACKNOWLEDGEMENTS J.R.G. and R.G.O. were supported by Horizon 2020 Euro- pean Research Council Consolidator Grant IndDecision 865474. S.P.K. was supported by Science Foundation (15/CDA/3591) and The Wellcome Trust Ireland (219572/Z/19/Z). The funders had no involvement in the study. SUPPLEMENTARY MATERIALS Supplementary material for this article is available with the online version here: https://doi . org / 10 . 1162 / imag _ a _ 00005. REFERENCES Bang, D., & Fleming, S. M. (2018). Distinct encoding of decision confidence in human medial prefrontal cortex. Proceedings of the National Academy of Sciences of the United States of America, 115(23), 6082–6087. https:// doi . org / 10 . 1073 / pnas . 1800795115 Boldt, A., & Yeung, N. (2015). 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