Current Biology 24, 1542–1547, July 7, 2014 ª2014 Elsevier Ltd All rights reserved

http://dx.doi.org/10.1016/j.cub.2014.05.049

ReportDynamics of Neural Population Responses
in Prefrontal Cortex Indicate
Changes of Mind on Single Trials
Roozbeh Kiani,1,2,4,* Christopher J. Cueva,2,4
John B. Reppas,2 and William T. Newsome2,3
1Center for Neural Science, New York University, 4 Washington
Place, Room 809, New York, NY 10003, USA
2Department of Neurobiology, Stanford University School of
Medicine, Fairchild Building D209, Stanford, CA 94305, USA
3Howard Hughes Medical Institute, Stanford University Schoolof Medicine, Beckman Center, 279 Campus Drive, Room B202,
Stanford, CA 94305, USA

Summary
Decision making is a complex process in which different
sources of information are combined into a decision variable(DV) that guides action [1, 2]. Neurophysiological studies
have typically sought insight into the dynamics of the decision-making process and its neural mechanisms throughstatistical analysis of large numbers of trials from sequentially recorded single neurons or small groups of neurons[3–6]. However, detecting and analyzing the DV on individual
trials has been challenging [7]. Here we show that byrecording simultaneously from hundreds of units in prearcuate gyrus of macaque monkeys performing a direction
discrimination task, we can predict the monkey’s choiceswith high accuracy and decode DV dynamically as the decision unfolds on individual trials. This advance enabled us to
study changes of mind (CoMs) that occasionally happen
before the final commitment to a decision [8–10]. On individual trials, the decoded DV varied significantly over timeand occasionally changed its sign, identifying a potential
CoM. Interrogating the system by random stopping of the decision-making process during the delay period after stimulus presentation confirmed the validity of identified CoMs.
Importantly, the properties of the candidate CoMs also conformed to expectations based on prior theoretical andbehavioral studies [8]: they were more likely to go from anincorrect to a correct choice, they were more likely forweak and intermediate stimuli than for strong stimuli, andthey were more likely earlier in the trial. We suggest thatsimultaneous recording of large neural populations provides a good estimate of DV and explains idiosyncratic aspects of the decision-making process that were inaccessible
before.
Results
Psychophysical studies of the decision-making process invarious contexts suggest an underlying neural mechanism
based on integration of evidence toward a decision criterion[11–17]. Supporting evidence for this mechanism has emerged
from electrophysiological studies of the parietal cortex, frontal
cortex, basal ganglia, and superior colliculus of monkeys
performing simple perceptual decisions [3, 5, 18–22]. More

4Co-first author*Correspondence: roozbeh@nyu.edu

recently, magnetoencephalography, electroencephalography,
and functional magnetic resonance imaging studies have revealed homologous mechanisms in the human brain [23–26].
Although these studies have significantly advanced ourunderstanding of the decision-making process, they havemainly relied on statistical analyses across trials because of
the stochastic nature of spiking activity at the single-neuron
level. Yet tracking the evolution of the decision variable (DV)on single trials and relating fluctuations in the DV to internalcognitive states and overt behavior are critical for incisive testsof current models of decision making. Recent advances in
multielectrode recording promise to break this barrier throughmeasurement and analysis of the underlying neural population
responses on single trials. So far, this ability has been mainly
used in the field of neural prosthetics, where accurate, realtime decoding of neural population responses is necessary
for guidance of motor prosthetic devices (e.g., [27, 28]).
However, similar techniques can also be used to advanceour understanding of cognitive processes, especially decision
making [7, 29].
We used 96-channel multielectrode arrays to record fromneural populations in area 8Ar of the prearcuate gyrus of two
macaque monkeys while they performed a direction discrimination task [30, 31] (Figure 1A). On each trial, the monkey
viewed a patch of randomly moving dots for 800 ms. After adelay period of variable length, the monkey received the‘‘go’’ cue and reported the perceived motion direction bymaking a saccadic eye movement to one of the two available
targets (T1 and T2). The multielectrode array covered
4 mm 3 4 mm of the cortical surface (Figure 1B) and enabled
us to record simultaneously from hundreds of single- and multineuron units in a significant portion of the prearcuate gyrus.
Compatible with previous studies, many units showed differential activity for the two choices during the motion viewing
and delay periods [20, 32], in addition to the perisaccadic
period [33] (Figure 1C).
To explore the efficacy of simultaneous, high-density
recording for analyzing dynamics of the decision-making process, we trained a logistic classifier to predict the monkey’s
upcoming choice based on neural population responses at
successive times during individual trials (100 ms sliding window; see the Supplemental Experimental Procedures). The!Þ on the population
classifier finds a set of linear weights ðw!
neural responses ð r Þ that maximizes the probability ofcorrectly predicting the choice. Although it is possible toimprove the prediction accuracy by adopting more-sophisticated nonlinear models, in this report we adhere to the linear
model for its simplicity and biological plausibility. Other
models yielded qualitatively similar results. Figure 2A shows
the cross-validated accuracy (see the Supplemental Experimental Procedures) of our model, averaged across sessions.
Model prediction accuracy is near chance at the beginning of
the trial but rises quickly w200 ms after motion onset, reachingperfection just before the saccade.
Across 15 data sets, the prediction accuracy of the population responses was much higher than that of the average
single unit (Figure 2B). In the 100 ms window immediately
before the ‘‘go’’ cue, the cross-validated accuracy ofNeural Correlates of Changes of Mind
1543

A
MotionTargets on

Fixation

Delay

B

Eye movement

Go

Figure 1. Multielectrode Recording from thePrearcuate Gyrus during a Direction Discrimination Task

C
Targ Dots

Go Saccade

60
40
1 cm

as
ps

as
ps

1 mm

Firing rate (spikes/s)

200contralateral
ipsilateral

30
20
10
0
200 msMonkey T

Monkey V

the population prediction was close to 0.9 on average(mean 6 SEM: 0.86 6 0.01), whereas the average accuracyof individual units was barely above chance (mean 6 SEM:
0.557 6 0.001) and was significantly smaller than that of the
population (t test, p < 1028). More importantly, not only was
population performance better than the average single unit,
but it was consistently superior to the best unit recorded ineach session (Figure 2C; t test, p = 3 3 1025). The population
was superior to individual units in other time epochs as well(data not shown).
The increased prediction accuracy afforded by multielectrode recording enabled more accurate tracking of the decision variable over time. In essence, our logistic regression
finds the best hyperplane that separates the population
response patterns associated with the two choices. The population response pattern at each moment can be envisioned asa point in a high-dimensional space whose axes are the firing
rates of individual units. The distance of this point from the!T !
discriminant hyperplane ðwr Þ represents the strength ofmodel’s prediction: a small distance corresponds to low certainty about the monkey’s upcoming choice, and a large distance corresponds to high certainty. We call this distance‘‘model decision variable.’’ The model DV provides an estimateof the monkey’s internal DV, especially when the model prediction accuracy is high. Averaged across trials, the model DV
gradually increased from zero to large values (positive andnegative values corresponded to T1 and T2 predictions,
respectively; Figure 3A). The rate of this rise depended on
the strength of motion, especially during the motion-viewing
period (Figure 3A, inset): DV increased more rapidly for stronger stimuli, compatible with previous observations in parietal
and prefrontal neurons, where the rate of change of neural responses depends on the strength of sensory evidence [3, 6,
20, 34, 35].

(A) Behavioral task. The monkey views 800 ms of
random dot motion while maintaining its gaze ona central fixation point. The strength and directionof motion varied randomly from trial to trial. Aftera variable delay period, the monkey received the‘‘go’’ signal (fixation point disappeared) and reported the perceived motion direction with asaccadic eye movement to one of two visual targets. Correct responses were rewarded with juice
after a short hold period.
(B) Two macaque monkeys were implanted withmultichannel electrode arrays in the prearcuate
gyrus, which is marked with a blue box on thelateral surface of a typical macaque brain (top;
University of Wisconsin Brain Collection). The
exact location of each array with respect to thearcuate (as) and principal (ps) sulci is shown foreach monkey (bottom). The white squares on
the array show the locations of the ground pins.
The portions of the principal and arcuate sulcithat were visible in the craniotomy are indicatedwith black lines. Dashed segments at the end ofa sulcus indicate that the sulcus extended inthat direction beyond our window of visibility.
(C) Average responses of two example prearcuate units for correct ipsilateral and contralateralchoices. The units were recorded from the same
electrode in the same session but had different
motion and saccade selectivities. Shading indicates mean 6 SEM.

Similarly, on individual trials, the DV fluctuated aroundthe discriminant hyperplane at the beginning of the
motion-viewing period but gradually moved farther fromthe hyperplane over time. After gaining an initial distance, thepopulation-based DV typically stayed on one side of the hyperplane during the late motion-viewing period and the ensuingdelay (Figure 3B, two example trials). On a minority of trials,
however, the population response crossed from one side of
the hyperplane to the other side during the trial, signaling ashift in the predicted choice from one target to the other (Figure 3C, two example trials).
An intriguing possibility is that these changes in DV sign,calculated from the neural population response, identify
changes of mind (CoMs) that occur in human and animal
observers as they make choices on the basis of variable evidence [7–10]. Alternatively, however, changes in sign of the
DV might simply reflect noise from any number of sourcesthat are irrelevant to performance on the task.
We conducted four analyses to test whether observed variations in the DV reflect, at least in part, genuine changes ofmind. The first analysis concerns the reliability of DV fluctuations for monitoring the momentary ‘‘decision state’’ of thesystem as time passes during long-duration trials. The remaining three analyses assess whether intratrial DV sign changes
conform to change-of-mind properties that are predicted bydecision-making models and empirically observed in humans
and monkeys performing a similar decision-making task.
Prediction of Choice Is Reliable throughout Long Delay
Periods
The initial important question is whether intratrial sign changes
in the DV, like those illustrated in Figure 3C, are simply noise orwhether they accurately reflect moment-to-moment variationin the decision state of the system—the decision that would

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Figure 2. The Recorded Neural Populations
Afford High Accuracy Prediction of the Monkeys’
ChoicesA
Prediction accuracy

Dots

Saccade

Go

1.0

1.0

0.8
0.6

0.8

0.6

100 ms

Proportion

Population
Individual units
0.4
0.2
0

0.5 0.7 0.9
Prediction accuracy

C

Population accuracy

Time (ms)

B

1
0.8
0.6
0.6 0.8
1
Mean accuracyof units

be made if the trial were to end now. We addressed thisquestion by separately analyzing predictive accuracy of the
population activity for trials of different delay period duration.
During each experiment, the duration of the delay period wasvaried randomly among several preset values (see the Supplemental Experimental Procedures). We grouped the trials into
quintiles based on the length of the delay period. For eachquintile, we then calculated the hyperplane that best separated the T1 and T2 choice trials from the pattern of neural population response in the 100 ms immediately before the ‘‘go’’cue. For all quintiles, the model achieved high cross-validated
accuracies for predicting the monkey’s choice on individual
trials (Figure 4A; 0.76 6 0.02 for the shortest delays to 0.87 6
0.02 for the longest delay). The results were not criticallydependent on using a separate model for each quintile; similar
results were obtained when a single model was used for allquintiles (Figure S1 available online). Although predictive accuracy improved modestly for longer delay periods, it was
far above chance even for the shortest delays. Thus, the signof the DV during the delay period is a good predictor of choice,even for the shortest-duration trials.
Importantly, there is no distinction between long- and shortduration trials prior to the first possible ‘‘go’’ signal—the temporal structures of the trials are identical until that point. Thus,
predictive accuracy of the DV sign measured prior to the ‘‘go’’signal on shorter-duration trials provides an objective estimate
of predictive accuracy on longer-duration trials had those trials
ended at an earlier point in time. We therefore conclude that
DV sign changes on longer-duration trials (e.g., Figure 3C) provide insight into the momentary decision state of the system,
reflecting in part choices that would have been made had weterminated the trial earlier.
DV Sign Changes Reflect Expected Properties of
Behavioral Changes of Mind
After identifying candidate CoMs using DV sign changes, we
performed three analyses to determine whether candidate
CoMs exhibit properties that are associated with actual
CoMs in behavioral studies and are expected from current
models of the decision process [7, 8].

0.6 0.8
1
Max accuracyof units(A) Prediction accuracy of the recorded population for the monkey’s choice. A logistic model
was fit to 90% of the trials in each session andwas used to predict the choice in the remaining
10%, in sliding 100 ms bins. The dark trace andshading indicate mean 6 SEM across the sessions. The horizontal black bar indicates thetime window that was used in the analyses in (B)and (C).
(B) The neural population classifier is a better predictor of the monkey’s choice than the average ofthe individual units recorded in a session. The
probability densities of population and individual
unit choice prediction accuracies are highly
distinct. Prediction accuracies were calculated
for a 100 ms window immediately before the‘‘go’’ cue.
(C) Comparison of population choice prediction
accuracy with the mean (left) and best (right) individual units. Each point represents one datacollection session. Even the best individual units
are inferior to the population.

First, CoMs should happen more frequently for weak- andintermediate-strength motion stimuli than for strong motion
stimuli because counterevidence that elicits a CoM will occur
less frequently for stronger stimuli [8]. Figure 4B showsthat the predicted trend is indeed present in our data
(Equation S3 in the Supplemental Experimental Procedures,
b1 = 20.23 6 0.04, p = 1.6 3 1028).
Second, CoMs are more likely to steer the decision from anincorrect to a correct option than vice versa because they arebased on evidence that is not yet processed during the initialstages of choice formation [8, 9]. On average, incorporationof additional evidence should improve the decision maker’s
accuracy. Consistent with this prediction, we observed thatcandidate CoMs derived from our neural population data
were more likely to shift the predicted choices from the incorrect target to the correct target (Figure 4C). The difference in
CoM toward correct versus wrong choices was significantly
larger than zero (sign test, p < 1028) and grew as a functionof motion strength (Equation S4 in the Supplemental Experimental Procedures, b1 = 0.19 6 0.07, p = 0.009). Thus, CoMs
increased the monkey’s overall reward intake. We also tested
whether the monkey’s final choices after CoMs were more
likely to be correct compared to the trials in which CoMs
were not detected. Controlling for motion strength and delay
duration, we found no significant difference between the twotrial types (Equation S5 in the Supplemental Experimental Procedures, b2 = 20.004 6 0.043, p = 0.92). Since CoMs improved
the probability of a correct response, they must have occurred
selectively on trials for which the initial decision state was
likely to be incorrect, perhaps due to lapses of attention earlier
in the trial.
Third, the probability of a CoM should decrease as themonkey waits during the delay period. Due to the finite latencyof visual signals, processing the last sensory evidence necessarily occurs during the delay period, and memory processes
related to the visual stimulus may influence the final decision
as well. As the delay period proceeds, however, a final commitment to a choice is increasingly likely. Consistent withthis hypothesis, we observed a monotonic decline in theprobability of a CoM with delay period duration (Figure 4D;

Neural Correlates of Changes of Mind
1545

−8

stronger stimuli (Figure S2A; Equation S3 in the Supplemental
Experimental Procedures, b1 = 20.064 6 0.021, p = 0.003) andwere more likely to change the DV in the direction of a correct
judgment (Figure S2B; Equation S4 in the Supplemental Experimental Procedures, b1 = 0.71 6 0.18, p = 0.001). The frequency
of candidate CoMs at the beginning of the motion-viewing
period was low because the DV is initially near chance andmust first build up toward one of the choices before a CoM
can be detected reliably (see the Supplemental Experimental
Procedures). Thus, CoM frequency increased initially but
declined after 300 ms of motion viewing (Figure S2C) due toincreased likelihood of commitment to a choice, consistent
with the delay period results (Figure 4D). These results fromthe motion-viewing period are encouraging but should be interpreted cautiously because of sensitivity of some results(Figure S2C) to time window sizes (see the Supplemental
Experimental Procedures).
Overall, candidate CoMs identified from high-density recordings of prefrontal cortex conform to all three predictions
based on behavioral analysis of changes of mind.

8

8

Discussion

4

4

0

0

−4

−4

Neurophysiological studies have typically sought insight into
the dynamics of decision making and its neural mechanisms
through statistical analysis of large numbers of trials fromsequentially recorded single neurons or small groups of neurons. Measurement and analysis of the DV on individual trials
has been challenging due to technical and conceptual limitations. We sought to overcome these limitations by (1)recording simultaneously from hundreds of units in corticalareas hypothesized to contribute to the decision-making process, (2) developing simple, efficient algorithms for estimationof the covert DV from neural population responses, and (3) implementing a new analytic approach to verify the accuracy ofthe estimated DV fluctuations during the delay period.
The ability to track moment-to-moment variation of the DV
enables the study of important aspects of the decision-making
process that have been largely inaccessible thus far. As aproof of concept, we focused on changes of mind during perithreshold judgments of motion direction. Our behavioral task
created fertile conditions for CoMs due to the noisy, temporally extended nature of the visual motion stimulus. Our first
new finding is that the covert DV can be accurately tracked
during single behavioral trials using the methods introducedin this paper. Crucially, trials with short delay periods verify
the accuracy of estimates of the covert DV on longer trials; inessence, short-delay trials act as ‘‘probes’’ of ongoing DV
estimates on longer trials [34, 36, 37]. Our second new findingis that changes in the sign of the DV identify candidate CoMs
and that candidate CoMs conform to three different predictions based on prior behavioral and modeling studies.
Together, these results demonstrate the power of high-density
neural recordings for single-trial estimates of the fluctuating
DV and for detection of covert changes in decision statecommonly referred to as changes of mind.
CoMs can arise from various sources: changing sensory
evidence [8], correction of an initial confusion about stimulus-response association [9], incorporation of a new decision
policy, or retrieval of new information from memory [8]. Our
monkeys’ CoMs may stem from any of these sources or others,
such as simple lapses in attention or effort. Accumulated overtime, CoMs tend to be self-corrections, often benefitting thedecision maker by improving accuracy. By characterizing

Dots

Decision variable(log odds)

A

Go

4

L

SaccadeT1 choices
T2 choices

4

H

2

2

0

0

−2

−2

−4

−4
400

800

−200 0−200 0

200

B

8

8

Decision variable(log odds)

0

4

4

0

0

−4

−4

Decision variable(log odds)

C

−8

−8

0

0

400

400
Time (ms)

800

800

−200 0−200 0−200 0 −200 0

200

200

−8

Figure 3. The Model Decision Variable Indicates Accumulation of Evidence
over Time, and Intratrial Changes in the Sign of the DV Identify Candidate
Changes of Mind
A logistic regression (Equation S1 in the Supplemental Experimental Procedures) was used to find the best hyperplane that separates the population
response patterns corresponding to the two choices. The distance of the
population response pattern from this discriminant hyperplane represents
the model belief about the upcoming choice. We call this distance the model
decision variable, or DV.
(A) Average decision variable across the sessions. The inset shows that thebuildup of the decision variable during the motion-viewing period depends
on stimulus strength (H, motion strength R 20%; L, motion strength % 6%).
The dark traces and shading represent the mean 6 SEM.
(B) Two sample trials in which the model DV built up to a positive (solid) or
negative (dashed) value and maintained its sign throughout the trial. The
trials ended with T1 and T2 choices, respectively.
(C) Two sample trials in which the sign of the model DV flipped during thedelay period, indicating a change of predicted choice based on the model.
Arrows indicate the time of flip.

Equation S6 in the Supplemental Experimental Procedures,
b2 = 20.21 6 0.01, p < 1028).
The success of the model for the delay period encouraged
us to investigate the properties of candidate CoMs during
the motion-viewing interval as well, even though success
was less certain for two reasons. First, because we used a
constant stimulus duration in all experiments, we were unable
to validate candidate CoMs during motion viewing using shortduration trials as described above for the delay period. Second, candidate CoMs were less reliable during motion viewing
as reflected in the lower predictive power of the model during
this interval (Figure 2A). Nevertheless, the properties of candidate CoMs during the motion-viewing interval were similar to
those during the delay period. CoMs were less frequent for

A

B

0.8

0.6
1

2
3
4
Delay duration quintile5

Switch rate (quintile transition−1)

C

Figure 4. The Sign of the Model DV Reliably
Reflects the Incipient Decision throughout the
Delay Period

0.25

0.2

0.15

C1
C2
C3
Motion strengthDerror to correct
correct to error
0.12
0.1
0.08
0.06
C1
C2
C3
Motion strength

Switch rate (quintile transition−1)

Prediction accuracy

1

Switch rate (quintile transition−1)

Current Biology Vol 24 No 13
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0.35
0.3
0.25
0.2

1−2

2−3
3−4
4−5
Delay quintile transition

the neural DV and identifying CoMs on individual trials, weshow that monkeys, like humans, exhibit self-correcting
behavior.
Past studies have documented cortical and subcorticalfluctuations in neural activity that might correspond tochanges of mind [7, 29, 38]. Those studies focused on thedetection of discrete hidden states in the responses of single
neurons [38] or small numbers of simultaneously recorded
neurons [7, 29]. The discrete states are defined as specificpatterns of spiking across the recorded population. Transitions from one state to another —often formalized by a hidden
Markov model—can occasionally signal changes of mind.
Here we extend those studies by extracting a continuous
measure of the DV, characterizing its dynamics, and confirming the inferred CoMs by interrogating the monkey’s choice
at variable times.
The probabilistic characterization of the choice provides ananalog estimation of the DV, compatible with the quantitativemodels of the decision-making process [12, 17, 35, 39]. In
those models, sources of information are integrated into ananalog variable [31] that explains both the choice and reaction
time. However, it remains to be seen whether various factors,
such as priors and value information, that bear on the decisionin those models also modify our estimated DV.
Our model incorporates the responses of all neurons
recorded on the array in a given experiment. Unlike in many
classic single-neuron studies, we did not focus on merely theunits that were highly selective for the motion directions ortarget locations used in the task [20, 40, 41]. We do not knowwhether all of the recorded neurons contributed to the decision-making process. Nor do we know the exact role thatthey may play in the process. However, the recorded neurons
are informative about the monkey’s upcoming action as indicated by the model’s high prediction accuracy. We simply
exploit this information to provide a probabilistic glimpse
into the DV that supports choice and CoM. Our model is nota mechanistic account of how the DV is constructed or how
commitment to a choice is made. Addressing those questions
requires further experiments and selective recording andIntratrial changes in the sign of the DV conform to
CoM properties expected from theoretical andbehavioral studies.
(A) Cross-validated prediction accuracy of themonkey’s choice for different delay durations.
Trials were grouped into quintiles based on delay
period duration. Accurate choice prediction on
short-duration trials confirms that variation in DV
reflects the monkey’s decision state at early points
in long-duration trials. Thus, intratrial changes in
DV sign are consistent with CoM as opposed to
extraneous noise (see the Results).
(B) Probability of switching from one predictedchoice to another in consecutive delay quintiles
declines for stronger motion (C1, motion strength% 6%; C2, 6% < motion strength % 20%; C3, motion strength > 20%).
(C) Switches in the predicted choice were more
likely to rectify an erroneous choice, especially forstronger motion stimuli.
(D) Switches were more frequent early during
delay.
Error bars indicate the SEM. See also Figures S1and S2.

manipulation of neurons based on their response selectivity(e.g., [18, 34, 42–44]).
The advent of techniques for routine, simultaneousrecording of tens to hundreds of neurons offers unique opportunities for cognitive neuroscience, particularly for the detection and tracking of cognitive states and processes that occur
unpredictably in time and have no overt behavioral correlate.
Covert cognitive processes are difficult to monitor in classicalneurophysiological studies that require time-locking andacross-trial signal averaging, but they are potentially detectable in real time from neural population activity. Even when
covert neural processes are detectable, however, their interpretation will depend on creative strategies for behavioral verification. Our study of CoM offers a first step in that direction.
Supplemental Information
Supplemental Information includes Supplemental Experimental Procedures
and two figures and can be found with this article online at http://dx.doi.org/
10.1016/j.cub.2014.05.049.
Author Contributions
R.K. and W.T.N. developed the concept. J.B.R. collected the data. R.K.
designed the analyses. R.K. and C.J.C. implemented the analyses. R.K.
and W.T.N. wrote the paper.
Acknowledgments
We thank K. Shenoy, M. Kaufman, D. Kimmel, V. Mante, D. Peixoto, V.
McGinty, and M. Churchland for helpful discussions, and we thank Jamie
Sanders, Jessica Powell, Sania Fong, and Julian Brown for technical assistance throughout the project. We are particularly grateful to Stephen Ryu,
who was the primary surgeon for the array implants. This research was supported by the Howard Hughes Medical Institute, the Air Force ResearchLaboratory (agreement number FA9550-07-1-0537), a Berry Postdoctoral
Fellowship to R.K., and a Sloan Research Fellowship to R.K.
Received: April 21, 2014
Revised: May 20, 2014
Accepted: May 21, 2014
Published: June 19, 2014

Neural Correlates of Changes of Mind
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Current Biology, Volume 24
Supplemental Information

Dynamics of Neural Population Responses
in Prefrontal Cortex Indicate
Changes of Mind on Single Trials
Roozbeh Kiani, Christopher J. Cueva, John B. Reppas, and William T. Newsome

Switch rate (quintile transition−1)

B

Prediction accuracy

1

0.8

0.6
1

2
3
4
Delay duration quintile

5

D

Switch rate (quintile transition−1)

C
0.12

error to correct
correct to error

0.1

0.08
0.06
0.04

C1
C2
C3
Motion strength

Switch rate (quintile transition−1)

A

0.25
0.2
0.15
0.1

C1
C2
C3
Motion strength

0.25
0.2
0.15
0.1

1−2

2−3
3−4
4−5
Delay quintile transition

Figure S1. A single discriminant hyperplane is adequate to achieve reliable prediction of
choices and changes of mind for all delay quintiles, Related to figure 4. (A-D) Same as Fig.
4A-D but for a single logistic model trained and cross-validated for the last 87-100 ms of thedelay period of all trials. See Experimental Procedures for details.

A

B
Switch rate (trial−1)

Switch rate (trial−1)

0.24
0.2
0.16
0.12
C1
C2
C3
Motion strengthC−1

Switch rate (m s )

3

0.15

0.1

0.05
C1
C2
C3
Motion strength

−3

x 10

2.5
2
1.5
1
0.5

0

200

400
600
Time (ms)800

Figure S2. Changes of model DV during motion viewing conform to expected behavioral
properties of changes of mind, Related to figure 4. (A-C) Same as Fig. 4B-D but for the
motion-viewing period. See Experimental Procedures and Results for details.

Supplemental Experimental Procedures
We recorded from populations of neurons in the prearcuate gyrus of two macaque monkeys
while they performed a direction discrimination task. All training, surgery, and recording
procedures conformed to the National Institutes of Health Guides for the Care and Use ofLaboratory Animals and were approved by the Stanford University Animal Care and Use
Committee. Due to the similarity of results across the monkeys we pooled the data for all
analyses to increase statistical power.
Behavioral task. Figure 1A illustrates the sequence of events on each trial. Each trial beganwith the appearance of a central fixation point (FP; 0.3° diameter) at the center of the display
monitor. The monkey was required to maintain gaze within ±1.5° of FP as long as it was
visible on the screen. Eye position was measured with a scleral search coil (CNC Engineering,
Seattle, WA), and inappropriate fixation breaks resulted in termination of the trial.
After the monkey fixated on the central fixation point, two targets appeared on the screen (T1and T2). After a 250 ms delay, a random dot motion stimulus was presented for 800 ms andwas followed by a delay period of variable duration. At the end of the delay period the FP
disappeared (Go cue), instructing the monkey to report the perceived motion direction bymaking a saccadic eye movement to one of the targets. For a valid response the monkey’s
saccade was required to land within 2-4° of the target (depending on target eccentricity). In 10
of 15 sessions the two targets were positioned on opposite sides of the screen (T1 contralateral,
T2 ipsilateral). On the remaining 5 sessions both targets were positioned contralateral to therecorded hemisphere (T1 and T2 were randomly assigned). On each trial, motion direction waseither toward T1 or T2. We controlled the difficulty of the trials by varying the percentage ofdots moving coherently in the same direction (motion strength or coherence) as described
previously [S1, S2]. The set of motion strengths for each monkey were chosen to afford a wide
range of accuracies, from chance to perfection. For monkey 1, the set included 0%, 2.5%, 5%,10%, 20%, and 40% coherence. For monkey 2, the set included 0%, 1.2%, 2.4%, 4.8%, 9.6%,
19.2%, and 38.4% coherence in most sessions. For two sessions we tested slightly different
sets: 0%, 6%, 12%, 24%, and 48% coherence in one session, and 0%, 1%, 2%, 4%, 8%, 16%,and 32% coherence in the other. The motion direction and strength varied randomly from trial
to trial, but were fixed within each trial. The monkey received a liquid reward for choosing thetarget that corresponded to the motion direction. For 0% motion strength the monkey was
rewarded randomly on half of the completed trials irrespective of the direction of the choice.
The variability of the delay period duration plays a crucial role in our analyses because it
provides an objective means to test the accuracy of our neuronal model predictions about the
subject’s impending choice. Different delay durations were used in various sessions, permitting
useful tests of the robustness of our results. In seven sessions the delay duration of each trial
was drawn randomly from these five values: 323 ms, 510 ms, 698 ms, 885 ms, and 1073 ms. In
six sessions the delay durations were 673 ms, 760 ms, 848 ms, 935 ms, and 1023 ms. In one
session they were 473 ms, 560 ms, 648 ms, 735 ms, and 823 ms; and in the last session they
were drawn randomly from several discrete values in the range 300-1500 ms. None of ourresults strongly depend on the exact delay durations used in each session. We therefore present
aggregated results across sessions.

The 15 sessions used in this study were chosen based only on the reliability of recordings,
number of trials (>1000), and number of recorded units (>150). The dataset consists of 20938
trials and 3257 units.
Neural recording. The monkeys were implanted with 96-channel microelectrode arrays(electrode length=1.5 mm; spacing=0.4 mm; Blackrock Microsystems, Salt Lake City, UT) in
the prearcuate gyrus (Fig. 1B). Neural spike waveforms were saved online (sampling rate, 30
kHz) and sorted offline (Plexon Inc., Dallas, TX). To improve the quality of sorting we usedcustomized algorithms to remove recording artifacts that were registered by a large number ofelectrodes. Also, we merged redundant spike waveform clusters based on waveform shapes,
firing rates and inter-spike intervals. We identified 100-250 single- and multi-units in eachsession (median=219). Throughout the paper we use the term ‘units’ to refer to both isolated
single neurons and multi-units. All units were retained in our analyses irrespective of theirselectivity.
Data analysis. We quantified the time-varying firing rate of each unit on each trial by counting
the number of spikes in a sliding 100 ms window (step size=20 ms). We used an L1regularized logistic regression [S3] to predict the monkey’s choice based on neural responses
on each trial:nLogit ⎡⎣ Pt (T1 ) ⎤⎦ = β 0 ( t ) + ∑ βi ( t ) ri ( t )(Equation S1)

i=1

where ri ( t ) is the firing rate of unit i at time t , n is the number of recorded units and the βcoefficients are model parameters. L1-regularization imposes a constraint on the L1-norm of
the coefficients to avoid overfitting. The model was cross-validated by using 90% of trials ineach session as ‘training set’ for fitting the parameters and the remaining 10% as ‘test set’ tomeasure the model’s prediction accuracy. The best regularization parameter of the model was
found by a 10-fold cross-validation within the training set. At any moment in time the model
predicts a T1 choice if Logit ⎡⎣ P (T1 ) ⎤⎦ > 0 and a T2 choice if Logit ⎡⎣ P (T1 ) ⎤⎦ < 0. The model
prediction is correct if it matches the monkey’s actual choice at the end of the trial. Fig. 2Ashows the model prediction accuracy averaged across sessions. We used a similar logistic
regression to gauge the prediction accuracy of individual units:

Logit ⎡⎣ Pt ,i (T1 ) ⎤⎦ = β 0 ( t ) + β1 ( t ) ri ( t )(Equation S2)

To compare individual units with the population (Fig. 2B-C), we analyzed data from the 100
ms window immediately before the Go cue.
The logistic regression of Equation S1 essentially finds the hyperplane that best separates the
population response patterns corresponding to the two choices. The population response
pattern at each moment can be envisioned as a point in a high-dimensional space whose axes
are the firing rates of individual units. The distance of this point from the discriminant
hyperplane (the right-hand side of Equation S1) represents the model belief about theupcoming choice ( Logit ⎡⎣ Pt (T1 ) ⎤⎦ , the left-hand side of Equation S1). A small distancecorresponds to a weak belief and a large distance corresponds to a strong belief. We call thisdistance the ‘model decision variable’ (DV) and use the changes in the sign of the DV to
identify candidate ‘changes of mind’ (CoM) for the monkey (Fig. 3C). This approximation isvalid especially where the model predicts the monkey’s choice accurately.
Our criterion for detecting possible CoM—a simply sign change in the DV—is lenient. It
ensures that actual CoM’s are not missed, but it can include spurious CoM’s due to neuralnoise or the imperfection of the logistic classifier. We have explored more stringent andcomplex criteria. For example, a change of mind can be defined as a swing from high certainty
for one choice (e.g. large positive DV) to another (e.g. large negative DV). These more
stringent criteria have additional degrees of freedom (e.g., criterion on the magnitude of DV)
and can be fine tuned to reduce the number of detected CoM’s. We explored this space, but theresults reported in this paper are not critically dependent on the choice of criteria. For all
analyses in this paper, therefore, we employed the simple sign change criterion to avoid
additional degrees of freedom and fine-tuning of results.
To determine whether putative neural CoM’s conformed to properties expected from priorstudies of behavioral changes of mind [S4, S5], we analyzed neural CoM statistics during thedelay period (after the dots and before the Go cue) when the model prediction accuracy wasabove 75% (Figs. 2A and 4A). We first divided the trials of each session into quintiles basedon the length of the delay period. As explained above, in 14 of the 15 sessions the delay period
was chosen randomly from five distinct values. Therefore the trials in each quintile of a session
had identical delays and our grouping did not create spurious boundaries or mix trials withvariable delay durations. In contrast to the “sliding window” analysis described above (e.g.
Fig. 3), here we calculated the predicted decision (sign of the DV) independently for eachdelay period quintile. We retrained the logistic model (Equation S1) separately for the trials ineach quintile using the last 100 ms of their delay period. For the sessions where the timedifference between consecutive quintiles was less than 100 ms, we slightly reduced the size of
the window for the calculation of firing rates (87 ms) to ensure no overlap between the quintile
models. We then calculated the number of neural CoM’s observed on each trial. For trials withthe shortest delay periods (first quintile) it was impossible (by definition) to detect a CoM
since only a single DV was calculated. For trials of the second quintile, a single opportunity
for a CoM occurred, two opportunities for trials of the third quintile, and so forth. Importantly,
the high overall prediction accuracy of the model (>75% correct) for trials of the shortest
duration (first quintile) creates confidence that the DV calculated within each quintile of longer
trials accurately estimates the choice the animal would have made had we stopped those trials
earlier. It is thus reasonable to consider neural CoM’s detected on long trials to be realchanges in the decision state of the animal even though we have no direct behavioral readout of
the hidden decision state on these trials. Quantitative analyses in Figure 4 (see equations
below) measured CoM statistics for those longer-duration trials (second and higher quintiles).
The results presented in this paper were not critically dependent on training separate models
for different delay periods. The discriminant hyperplanes calculated for different delay
quintiles were closely related to each other. Consequently, training and cross-validating asingle model based on the last 87-100 ms of the delay period of all trials replicated all key
results (Fig. S1).

To identify candidate CoM’s during the motion-viewing period (Fig. S2) we used the changes
in the sign of the decision variable, calculated from the models trained on all trials of a session(Fig. 3). In contrast to the delay period, we could not independently verify the choicepredictive accuracy of CoM’s during the motion-viewing period because the motion duration
was the same for all trials. A priori, candidate CoM’s based on only a DV sign change will beless reliable during the motion-viewing interval due to the lower overall accuracy of the model
predictions early in the trial (Fig. 2A). To compensate for this reduced accuracy we used amore stringent criterion. To quantify the frequency and direction of CoM for different motion
strengths (Fig. S2A-B), we required the sign of DV to persist for 150 ms before and after a signchange (‘persistence window’) to qualify as a CoM. To quantify the time course of CoM (Fig.
S2C), we reduced this requirement to 75 ms to increase the number of independent estimates ofthe decision state during motion viewing. The trends in Fig. S2A-B are robust to variations of
the persistence window. The trend in Fig. S2C, however, is sensitive to the duration of thepersistence window and should be interpreted cautiously; larger windows reduce and even
abolish the decline of CoM frequency in the late motion-viewing period. This occurs because
long persistence windows impose a sterner criterion for measuring decision states anddetecting CoM’s, which inevitably delays CoM’s to later stages of the motion viewing interval
and makes the decision state less likely to change once established. We have observed similarsensitivity to window size in simulations (data not shown).
To test whether the frequency of CoM’s during the delay period varied with the stimulus
strength we used a linear regression model:η = β 0 + β1C + β 2 q(Equation S3)

where η is the number of CoM detected by the model in each trial, C is the motion strength,q is the quintile that the trial delay duration belonged to (2 to 5), and βi are the regression
coefficients. Only trials of the second and higher quintiles contributed to the analysis; as
described above, the first quintile could not have a CoM in the delay period. q was included in
the regression to control for the increased probability of CoM detection due to increased
number of quintile transitions for longer delay periods.
We used a related linear regression to test whether CoM’s were more likely to change themonkey’s response from an incorrect to a correct choice for stronger stimuli:

Δs = β 0 + β1C + β 2 q(Equation S4)

where Δs is the difference between the number of CoM’s that move the choice prediction
from incorrect to correct and vice versa ( Δs > 0 implies more incorrect to correct). This
analysis focused on trials with C > 0 in which at least one CoM was detected. Trials with
C = 0 were excluded because of ambiguity in the definition of a correct response. The null
hypothesis is that Δs does not change with motion strength ( H 0 : β1 = 0 ). After rejecting thenull hypothesis via the linear regression analysis, we used a sign rank test to show that themedian of Δs was larger than zero across all trials used in the regression analysis (significant
prevalence of incorrect to correct changes).
To test whether the overall probability of being correct was larger on trials in which CoM’s
were detected we used the following logistic regression:
Logit ⎡⎣ P ( cor ) ⎤⎦ = β 0 + β1C + β 2 I + β 3q

(Equation S5)

where I is an indicator variable (0 for trials with no CoM and 1 for trials with CoM). C andq are the motion strength and delay duration quintile, respectively (same as in Equation S3).
β 2 > 0 indicates that the subject was correct more frequently on trials in which CoM’s weredetected.
We tested the dependence of the probability of changes of mind on time using a logistic
regression:
Logit ⎡⎣ P ( switch ) ⎤⎦ = β 0 + β1C + β 2 q′

(Equation S6)

where q′ is the delay quintile in which a CoM could be detected minus one. Only trials in thesecond or higher quintiles contributed to this analysis because at least two delay bins wererequired to detect a CoM, as described above. Each trial contributed as many data points aspermitted by the length of its delay period (maximum=4). The null hypothesis is that theprobability of observing a switch does not depend on time ( H 0 : β 2 = 0 ).
All completed trials (correct and incorrect) were included in the calculation of discriminant
hyperplane and subsequent analyses. The grouping of motion strengths to C1 (C≤6%), C2(6%<C≤20%), and C3 (C>20%) in Fig. 4, S1, and S2 is for illustrative purposes only. All
statistical analyses that are mentioned above were performed using the actual motion strengthsof the trials.

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